CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Authors: Thibaud Southiratn
Bonil Koo
Yijingxiu Lu
Sun Kim
Venue: ICML 2025 poster (2025)
Keywords: Dual-target Molecule Generation
Fragment-based Drug Discovery
Monte-Carlo Tree Search
Pareto Optimization
Search Space Reduction
Primary area: applications->health_medicine
TL;DR: CombiMOTS is a framework that designs dual-target compounds using industrial building blocks and Pareto MCTS for favorable multi-objective trade-offs and improved synthesizability.

Abstract: Dual-target molecule generation, which focuses on discovering compounds capable of interacting with two target proteins, has garnered significant attention due to its potential for improving therapeutic efficiency, safety and resistance mitigation.
Existing approaches face two critical challenges.
First, by simplifying the complex dual-target optimization problem to scalarized combinations of individual objectives, they fail to capture important trade-offs between target engagement and molecular properties. 
Second, they typically do not integrate synthetic planning into the generative process.
This highlights a need for more appropriate objective function design and synthesis-aware methodologies tailored to the dual-target molecule generation task.
In this work, we propose CombiMOTS, a Pareto Monte Carlo Tree Search (PMCTS) framework that generates dual-target molecules.
CombiMOTS is designed to explore a synthesizable fragment space while employing vectorized optimization constraints to encapsulate target affinity and physicochemical properties.
Extensive experiments on real-world databases demonstrate that CombiMOTS produces novel dual-target molecules with high docking scores, enhanced diversity, and balanced pharmacological characteristics, showcasing its potential as a powerful tool for dual-target drug discovery.
The code and data is accessible through \url{https://github.com/Tibogoss/CombiMOTS}.

CombiMOTS:
Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Thibaud Southiratn
Bonil Koo 23 Yijingxiu Lu
Sun Kim 1234
Abstract
1. Introduction
Complex diseases and disorders such as cancers are gener- ally caused by intricate interacting pathways. To treat them, traditional therapies focused on the single-target paradigm by developing drugs selective towards a unique mechanism, therefore "blind to other processes" yet equally involved in biological systems Miedina-Francee et al., 2013). Single- target drugs are prone to resistance and can risk the activa- tion of unwanted compensatory signaling pathways (Yang et al., 2024b). To overcome this limitation, rising field of study aims develop treatments which exhibit better efficacy by interacting with multiple related targets. An intuitive approach known as combination therapy (Kum- mar et al., 2010; Foucquier & Guedj, 2015) consists in ad- ministering various synergetic single-target medications to address distinet but related pathogenic mechanisms. How- ever, these approaches often risk adverse effects or poor treatment adherence (Ye et al., 2023). As promising alter- natives, dual-target drugs are increasingly drawing atten- tion, demonstrated by a trend in FDA-approved drugs (Li et al., 2016; Lin et al., 2017: Layman et al., 2024). They involve one agent simultaneously interacting with two tar- gets with better pharmacokinetics and safety profiles, thus avoiding undesirable drug-drug interactions (Hopkins et al., 2006). This inevitably imposes challenges: (1) The Structure-Activity Relationship (SAR) profile of consid- ered compounds must consider different biological targets (Morphy & Harris, 2012; Raghavendra et al., 2018). (2) The identified compounds have to be synthesizable through known experimental protocols.
Dual-target molecule generation, which focuses on discovering compounds capable of interact- ing with two target proteins, has garnered sig- nificant attention due to its potential for improv- ing therapeutic efficiency, safety and resistance mitigation. Existing approaches face two criti- cal challenges. First, by simplifying the com- plex dual-target optimization problem to sealar- ized combinations of individual objectives, they fail capture important trade-off's between tar- get engagement and molecular properties. Sec- ond, they typically do not integrate synthetic planning into the generative process. This high- lights need for more appropriate objective func- tion design and synthesis-award aware methodologics tailored the dual-target molecule generation task. In this work, propose CombiMOTS, Pareto Monte Carlo Tree Search (PMCTS) framework that generates dual-target molecules. CombiMOTS is designed to explore synthe- sizable fragment space while employing vec- torized optimization constraints to encapsulate target affinity and physicochemical properties. Extensive experiments on real-world databases demonstrate that CombiMOTS produces novel dual-target molecules with high docking scores, enhanced diversity, and balanced pharmacolog- ical characteristics, showcasing its potential as a powerful tool for dual-target drug discovery. The code and data accessible through ht https: / //github.... www www.e///itooossssoooooooooeeeeee iMOTT.
In the past few years, deep generative models (Zeng et al., 2022) and geometric deep learning (Powers et al., 2023) tackled SAR for single-target drug design, but the data scarcity and expensive computational cost limit their ap- plication on the dual-target setting. Recently, machine learning models allowed to bridge the gap between predic- tive and intuitive dual-target drug design (Feldmann et al., 2021). Notably, great efforts were made Fragment- -aased Drug Discovery (FBDD) by leveraging property predictors and oracles to extract, combine and autoregressively com- plete molecular substructures. supposedly responsible for the bioactivity of known compounds on both given targets
'Department of Computer Science and Engineering, Scoul National University, Scoul, Republic of Korea 'iteeriisciplinayy Program in Bioinformatics. Seoul National University, Seoul, Re- public of Korea AIGENNDRUG Co., Ltd., Seoul, Republic of Korea 'Interdisciplinary Program in Artificial Intelligence, Seoul National University. Scoul, Republic of Korca. Correspondence to: Sun Kim <sunkim. bioinfo@ smr.
Proceedings of the nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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CombIMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
(Jin al., 2020; Lee al., 2023; Chen et al., 2024). Nev- ertheless, the key limitation of such methods is the trans- lation from multi-objective problem to a single-objective formulation. Despite integrating various constraints, their reward function aggregates weighted objectives into a scalar
We propose Combinatorial Multi-Objective Tree Search (CombiMOTS), extending MCTS to Pareto optimization and fragment-based drug discovery to narrow down a large molecule fragment space into a synthesizable one, specific to any target pair.
value without considering potential conflicts, leading to overall high-scoring generations with imbalanced properties (Fromer & Coley, 2023; Luukkonen et al., 2023). More specificallyy, by assuming convex search space, distinguish- ing between competing characteristics becomes intractable and resulting molecules can exhibit idealistic properties while being nearly impossible to synthesize (Gao & Coley, 2020; Stanley & Segler, 2023). Furthermore, solely relying on desirability metries during the generative process cannot guarantee true synthesizability (Vinkers al., 2003; Erll & Schuffenhauer, 2009). Consequently, new frameworks also need to condition their processes on synthetic routes (Segler& & Waller, 2017; Segler et al., 2018). Swanson et al. (2024) applied Monte-Carlo Tree Search (MCTS) to assem- ble make-on-demmane molecules with associated synthetic procedures yielding an average success rate over 80%, but fall again into the single-objective limitation.
Through the task of dual inhibitor generation, we demon- strate and analyze CombiMOTS' ability to find optimal candidates across conflicting objectives complex multi- objective multi-target settings.
In particular, we evaluate our model on the GSK3,-INK33 pair and curate data for two new target pairs, EGFR-MPR and PIK3CA-mTOR to illustrate the utility of Combi- MOTS in dual-target drug design.
On all experiments. CombiMOTS consistently generates molecules that yield better diversity and trade-off between docking score, drug-li,,ness, and synthetic accessibility.
2. Related Work
Multi- Mujti-Objective Molecule Generation The success of prior generative models for sign does not trivially apply to multi-objective parameter- ization (Angelo et al., 2023). These methods commonly optimize embeddings of molecular sequences or graphs, relying on bayesian inference or reinforcement learning. Multi-objective molecule generation approaches can be categorized into three categories. The first category uses encoder-decoder architectures (Jin et al., 2018; 2020) or autoregressive frameworks (Gong et al., 2024; Yang et al., 2024a) to attempt learning continuous latent representations of target compounds to generate candidates with encour- aging predicted properties. However, they highly depend on the quality of the learnt latent space, which is burden- some in multi-objective tasks where data is scarce. The second category being reinforcement learning, operates in the explicit chemical space to allow more robust training, but are hard to train due to reward sparsity when combin- ing multiple objectives (Guimaraes et al., 2017: Olivecrona et al., 2017; Popova et al., 2018). More specific to dual- target drug design, Li et al. (2018); Jin et al. (2020); Xie et al. (2021) utilize a machine learning property predictor to guide the generation of bio-active compounds, but still require high-quality labeled data to properly work. As the third category, Structure- -ased Drug Design (SBDD) meth- ods integrate binding affinity indicators moderate data scarcity while enhancing SAR with target proteins (Chen et al., 2024; Zhou et al., 2024). Compared to these methods, we utilize both property predictors and binding score oracles to cooperatively account for pharmacological characteristics and dual-target affinity.
drug de-
Other fields such as robotics and the computational game domain employ Pareto optimization to explore attainable solutions presenting optimal tradeoffs regardless of compet- ing objectives and property imbalance (Luc, 2008). This flexibility enables to adjust priorities and selection crite- ria as new information becomes available, without needing to restart the optimization process with different weight- ings. Few recent works apply Pareto optimality to MCTS in the fields of multi-constrained retrosynthesis planning (Lai et al., 2025) and atom-by-atom molecule SMILES gen- eration ( (Yang et al., 2024a). However, its application to dual-target molecule generation remains underexplored as the choice of objectives, state space or action space is chal- lenging.
In this paper, draw inspiration from Pareto MCTS (PMCTS) to propose novel approach to combinatorial multi-objective drug design. We propose fragment- based molecule generation approach that optimizes multi- constrained properties of dual-targets within a synthesizable space. To achieve this: (1) We perform search space reduc- tion by extracting target-aware fragments from known target inhibitors and mapping them
building blocks. (2) We extend PMCTS to a combinatorial frame- work alongside vectorized objectives tailored for dual-target molecule generation, ultimately generating interpretable compounds exhibiting better tradeoffs in all objectives com- pared to competing methods. We experimentally validate the effectiveness of our method through the case of dual inhibitor generation as a real world scenario. We summarize our contributions as follows:
Fragment-Basee Molecule Generation Fragment- approaches have emerged as a promising direction in drug discovery. The intuition to derive multi multi-property candi-
2

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
dates from initial single-property molecular substructures as building blocks. Recent research in this area be broadly categorized into fragment extraction and assembly methods for generation. For fragment extraction, early ap- proaches relied on rule-based bond breaking selection ( (Yang et al., 2021) or motif frequency-based selection (Kong et al., 2022). The drawback of these heuristic methods generally to not consider target molecular properties. This moti- vated succeeding works to try identifying property-aware substructures. Jin et al. (2020); Chen et al. (2024) extract and assemble core fragments from full molecules rather than true fragments, leading to limited novelty and diversity in generation. For generation methods, MCMC sampling strat- egy can be applied for its flexibility adding and deleting fragments (Xie et al., 2021), while reinforcement learning (Tan al., 2022; Du et al., 2023), and VAE-based mod- els for fragment assembly (Maziarz et al., 2021) remain widely used. Interestingly, Swanson et al. (2024) proposed method that does not require to extract fragments as building blocks. They use the industry-ready Enamine REadily Ac- cessibLe (REAL) Space database (Grygorenko et al., 2020), with building blocks and reaction templates as inputs to MCTS, with single property predictor guiding the space navigation modeled as chemical reactions. This presents the advantage of keeping high chance to synthesize iden- tified leads in real world laboratory settings. We propose to extend their work to the dual-target molecule generation task by leveraging property-aware available building blocks, subsequently assembled using a vectorized multi-objective parametrization guided by oracles tailored the target pro- teins.
element of Py:
Ad E (1,,,..,,), Px,a Py,
(I)
ii) At least one coordinate of Px is larger than the corre- sponding element in Py:
EE {1. ................................ D} s.t. Px, Py,
(2)
If only the first condition is satisfied, X is said to weakly- dominate Y, denoted by X 2 Y or Y 3 X. When neither
X = Y nor Y f X holds, X and Y are said incomparable (X
Remark 3.2. i) and ii) can be summarized as: > X "never worse" and "at least better than Y in one objective". Definition 3.3 (Pareto Fronts). Given an non-empty set of vectors S C RD obtained from candidate solutions found in the objective space, the first Pareto front (or Pareto optimal set) consists of all non-dominated solutions:
S = (Px E S: Py E Stt. Y X3.
(3)
Subsequent Pareto fronts S₁ are defined recursively by ex- cluding all solutions belonging to the preceding {S.)/=1
k-1 S₁ = PPx Py E E U Y x3. (4)
i=1
Remark 3.4. All solutions from the same Pareto front considered equivalent, they are either identical or incom- parable:
3. Preliminary Pareto Optimization
VS$ C,X((XY)) E Se (X]I).
(5)
Multi-objective problems involve optimizing several objec- tives, often competing. A common approach is to aggregate them into one scalarized reward, naturally inducing over- simplification of the problem's complexity by depending on importance weighting and its a priori knowledge. Pareto optimization (El-Sharkawi, 2005) alleviates this issue by maintaining& a vectorized problem formulation, thus defining sets of solutions whose components are all considered equal, allowing proper optimization in the attainable solution space. Without loss of generality, we assume a maximization prob- lem over D objectives, where each solution is charac- terized by D-dimensional property vector.
4. Proposed Approach: CombiMOTS
We propose CombiMOTS, PMCTS method designed to navigate a dual-target specific synthesizable space by lever- aging the strengths of both FBDD and Pareto optimization. We first outline in Sec.4. 1 how to reduce a large chemical space to available tagl-ttaggt--peecffe building blocks. We then describe our reaction- based PMCTS implementation in Sec.4.2. We provide additional implementation details in Appendix D.3.
4.1. Synthesizable Search Space Reduction
Definition 3.1 (Pareto Dominance). Let X and Y be two distinct objects, each associated with their respective objec-
The estimated size if the drug-like chemical space exceeds 1033 molecules, making exhaustive search for compounds with desirable chemical and structural properties computa- tionally infeasible (Polishchuk et al., 2013).
tive vectors P Py E DR where Px,a and Pr, denote the values of X and Y on the d-th objective, respectively. We define Pareto dominance as follows: X dominates Y, denoted by X > Y (or equivalently Y < X), if and only if:
To address this challenge, we narrow the search space using curated subsets of Enamine REAL Space (Grygorenko et al.,
No coordinate of Px smaller than the corresponding
3

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CombiMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
2020), refined by Swanson al. (2024). This ensures that our method remains computationally tractable while main- taining its practical relevance. Given target pair, we reduce the search space by (1) identifying target-aware fragments from known active inhibitors, and (2) aligning them with the REAL Space building blocks and reactions (Figure 1).
Search Space Reduction To ensure interpretable and real- istic generations, the core implementation of CombiMOTS relies on predefined building blocks from the Enamine REAL Space, After obtaining we curate the final set of building blocks by mapping learnt fragments to existing Enamine building blocks with a Tan- imoto similarity above a fixed threshold (Figure 1). We empirically find in Section 5.7.2 that using ECFP4 Morgan fingerprints and a threshold value of 0.4 generally leads to an appropriate search space size (~14k blocks and ~25 possible reaction products).
fragments,
GaK38
Cual-targef-wwire frugmants
Enariin REAL Spaci
Informed Building Blocks
4.2. Pareto Monte-Carlo Tree Search
0.5
4.2.1. MONTE-CARLO TREE SEARCH
JNK
0448
Fragment Groph Information Bottlenekk
Birilarit
MCTS is decision Docision-making algorithm that systematically explores a search space by balancing exploration and ex- ploitation through four distinct phases.
Figure 1. Search Space Reduction. Property- aware fragments are extracted for each target using Fragment- wise Graph Information Bottleneck (Lee et al., 2023). By applying Tanimoto similarity threshold to a synthesizable search space, we curate a final set of informed celustty-ready building blocks.
(i) The selection phase aims at traversing a search tree from the root node to a leaf node, using the Upper Confidence Bound (UCB) formula to greedily select the most promising actions based both their estimated UCB value and the uncertainty of those estimates. Given synthesis tree T to search, node with parent p, we denote C positive exploration constant, R(n) the cumulative reward of n and (nn) the number of times n was visited:
Fragment Extraction To extract chemically meaningful fragments from active molecules, we employ Fragment- wise Graph Information Bottleneck (FGIB) (Lee et al., 2023). FGIB provides sophisticated approach to extracting sub- structures using BRICS decomposition (Degen et al., 2008) from known active compounds, highly contributing to their target property. Its theoretical foundation lies in the Graph Information Bottleneck (GIB) principle (Wu et al., 2020), where the objective function balances between preserving property-predee predictive information and compressing an original molecular graph representation. This is achieved through dual optimization process, where the goal is to simultane- ously maximize information between extracted fragments and target properties, while minimizing the mutual infor- mation between fragments and the original graph. Given a molecule graph G and its target property Y, GIB identifies an informative set of fragments G by optimizing:
R(n) N(n)
(n(N N(n)
UCB(n)=
+C
exploitation
exploration
The 'exploitation" term favors selecting high-property nodes, while the 'exploration' term encourages selecting less ex- plored nodes, jointly guiding the traversal of both promis- ing and uninvestigated outcomes. (ii) In the expansion phase, reaching a leaf node triggers the creation of child nodes, each representing a new potential state or action in the search space. (iii) The simulation (rollout) phase iter- atively applies steps (i) and (ii) from the newly expanded node until reaching terminal state predefined depth. (iv) In the backpropagation phase, the statistics of all nodes along the traversed path are updated, propagating simula- tion outcomes upward to refine value estimates and visit counts. This iterative process continues until computational constraints or convergence criterion are met, progressively constructing a search tree that balances exploration and ex- ploitation while ensuring sufficient search space coverage.
min I(G Y)+ + BI(Grub G) Gud
where T(-l-) denotes mutual information and / is a positive hyperparameter balancing informativeness and compres- sion.
FGIB utilizes Message Passing Neural Networks (MPNN) to compute graph embeddings and introduces a novel noise injection mechanism that modulates information flow based on fragment importance. This mechanism enhances our model's 's ability to identify chemically meaningful substruc- tures by selectively preserving informative signals, while reducing redundancy.
4.2.2. PARETO MCTS FOR DUAL-TARGES MOLECULES
We propose an extended version of MCTS that incorporates Pareto optimization through vectorized properties, integrat- ing property predictors and docking oracles based on com- binatorial chemistry principles (Liu et al., 2017) to identify
4

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CombIMOTS: Combinatorial Multi-Obeective Tree Search for Dual-Target Molecule Generation
synthetically accessible compounds that jointly target proteins.
of each building block and creating one node per addition. The rollout iteratively repeats these steps until reaction product is reached (terminal node). When a terminal node is reached, the backpropagation step updates the reward vectors of all nodes along the traversal path, before initiating the next rollout. The algorithm ends once the specified number of rollouts is completed, returning all encountered reaction products.
Algorithm 1 High-Levee CombiMOTS Algorithm
1: Input: Reactions R, rollouts Nyollout
Require: Multi-objective Oracles
2: Initialize MCTS tree T with empty root node
3: for i= == to Ryollout do
4: e t Rollout(T.rrott)
5: end for
5. Experiments
6: return Pareto optimal molecules from visited nodes
5.1. Datasets
7:
8: function Rollout(node)
As our work focuses on dual-target molecule generation, we demonstrate the practical utility of CombiMOTS in real- world scenarios by evaluating it on three disease-related protein target-pairs. Notably, we curate and release new datasets for the EGFR-MET and PIK3CA-mTOR pairs. De- tailed data statisties and curation methods provided in Appendices D. and M.
9: if node is a product then
10: return (nodles(mode) > Backpropagation
11: end if
12: children +- (erChildNNodesnnode)) > Expansion
selected + ParetoSelcciinncchlleeee)
14:
V Rollout(sclectee
15:
if selected is product then
16:
Flem-wise-max(g selected. Backprop.
17: endie if'
GSK3 These are two kinases related to Alzeih- mer's Disease (AD) (McCubrey al., 2014; Koch al., 2015). Designing dual-inhibitors for these targets open pos- sibilities towards more efficient AD therapies. We utilize the data curated by Li et al. (2018) as commonly used benchmark for dual-target generation (Jin et al., 2020; Xie et al., 2021; Chen et al., 2024).
18: Update statistics of selected
19: return
end function
The major modification from the single-objective version MCTS described in Section 4.2.1 is the design of multi- dimensional property vectors, enabling element-wise opti- mization. This formulation allows the application of Pareto principles (Section 3) by optimizing vector coordinates across the full objective space, but it also requires modi- fications of the MCTS core steps. In this setting, tree traver- sal can no longer greedily select the highest-scoring node. Given the property vector (ra(n) obtained from Oracles and D the number of objectives, Equation (7) becomes the Pareto UCB formula (PUCB):
In non-small cell lung cancer (NSCLC), re- sistance to EGFR inhibitors often involves compensatory activation of MET, leading to tumor progression (Fang et al., 2024). Therefore, a dual-target molecule that simultane- ously inhibits EGFR and MET could overcome drug resis- tance and improve therapeutic outcomes (Ren et al., 2024). This strategy is supported by multiple studies showing the potential benefits of combined EGFR and MET inhibition in patients with EGFR mutations and MET amplification or overexpression (Fang et al., 2024; Ren et al., 2024).
EGFR-MET
((n) PUCB(n) +CxOratml In(DD + In(1 N(p))
Rl(m)
1+ (())
PIK3CA-MTOR Mutations in PI3K, particularly PIK3CA, and dysregulation of mTOR contribute to cancer cell growth, proliferation, and survival (Fruman & Rommel, 2014). Dual inhibitors targeting both PI3K and mTOR provide more comprehensive blockade of this pathway, addressing potential resistance mechanisms, as demonstrated by the PI3K/mTOR dual inhibitor VS-5584 (Hart et al., 2013). Simultaneous inhibition of both targets is expected to more effectively suppress P13K-mTOR sig- naling compared to isoform-seleetive inhibitors, potentially overcoming feedback activation that limits single-target therapies (Rodrik- (Rodrik-Qutmezguing Outmezguine et al., 2016).
The Figure 2 and Algorithm illustrate a complete rollout of CombiMOTS, while Algorithm provides a detailed description of the algorithm. During the selection step, after computing the PUCB vector of all child nodes, the non- dominated nodes form a local Pareto front, from which the next selected node is randomly sampled. In our problem, each node represents a tuple of multiple building blocks. Upon reaching a leaf node, the expansion step generates new child nodes in two ways: (a) by applying all possible reactions to the building blocks in the node and creating one node per product, or (b) incorporating all matching reactants
5

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Selection
Expansion
Rollout
Backpropagation
+
[0.7 [0.7|0.3]
[0.3|0.8]
[0.4|0.5] I
00
[ra
+
Local Pareto Nodes
Selection
+
D
Building Blocks
Property Predictor
Backpropagation
Reaction Templates
Figure 2. One full iteration of the CombiMOTS Algorithm. (i) Selection from local Pareto fronts occurs until a leaf node to expand is found. (ii) During expansion, two types of nodes created by consulting the reaction templates: those representing products from current building blocks and those incorporating compatible reactants. Upon creation, oracles predict properties for all child nodes to establish their local Pareto front. We illustrate property vectors with two objectives. (iii) Selection and Expansion steps iteratively occur until a reaction product is found. (iv) The property vector of the reaction product is backpropagated up the path.
5.2. Baselines
The proportion of molecules adhering to all chemical rules. Uniqueness (%): The proportion of distinct molecules within the generated set, where a low value suggests repet- itive generation. Novelty (%): As defined by Olivecrona et al. (2017), the proportion of generated molecules whose nearest training set dual-active neighbor has a Tanimoto similarity score below 0.4, reflecting the model's capacity to generate sufficiently different, yet desirable compounds. Diversity (%); The proportion of generated molecules with a pairwise Tanimoto similarity below 0.4 across all genera- tions, indicating the model's 's ability to explore broad regions of the chemical space rather than narrow subset. Activity Success Rate ( (%): The proportion of generated molecules predicted to be active towards both target proteins, indicat- ing the model's is ability to identify potential dual-inhibitors. We denote such molecules as "dual-actives".
RationaleRL (Jin et al., 2020) identifies important struc- tural components from active compounds through MCTS. then systematically merges these components while main- taining their shared structural elements, followed by targeted fine-tuning of a generative model to append appropriate side chains. REINVENT (v3.2) (Blaschke et al., 2020) adopts sequence-based approach, utilizing recurrent neural net- work architecture to generate molecular SMILES strings. The framework incorporates reinforcement learning tech- niques to optimize multiple molecular properties simulta- neously, enabling the design of compounds with activity across multiple objectives. MARS (Xie et al., 2021) se- lects the top 1,000 fragments from the ChEMBL dataset based on their size and frequency. The obtained fragments have less than 10 heavy atoms with frequent occurrence in the dataset. It employs graph neural networks (GNNs) and Markov Chain Monte Carlo (MCMC) sampling to re- fine molecules with enhanced properties, from addition or deletion of these fragments.
Quality We interpret property distributions by visualiz- ing density plots of dual-active compounds. We analyze: Docking Score (DS) as an approximation of binding affin- ity between target proteins and molecule ligands. A lower docking score indicates better molecular interactions. Quan- titative Estimate of Drug-likeness (QED) quantifies the potential of compound presenting desirable drug capabil- ities based on properties such as topological polar surface area and the number of hydrogen donors/acceptors. Rang- ing from O to 1, higher score is preferable. Synthetic Accessibility score (SA) measures how difficult given compound is to synthesize, based on fragment contribution and complexity penalty. Ranging from 1 to 10, compounds with a low SA score are easier to obtain.
5.3. Evaluation Metrics
For each model, we generate N= = 10,000 molecules for all target pairs, then compare the performance of models to assess their ability to generate original and biochemically potent compounds. We evaluate generations with metrics fitting two categories:
We gauge the models' ability to generate orig- inal compounds using the following metries. Validity (%)
Originality
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CombIMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
Details on used oracles and molecular docking settings are given in Appendix D.3.
5.6. Results
As shown in Figures and 7, CombiMOTS consistently identifies optimal tradeoffs across all three target pairs un- der each metric. In contrast, competing methods exhibit inconsistent performance across target pairs, often gener- ating compounds with suboptimal properties or excelling in a single objective while underperforming in others. No- tably, displayed density distributions are normalized, high- lighting the rarity of high-quality candidates produced by alternative methods. Furthermore, Table suggests that REINVENT and RationaleRL can generate invalid SMILES, and all models struggle to generate unique, novel and di- verse compounds on all tasks. In every setting, Combi- MOTS outperforms other methods in generating novel and diverse molecules with well-balanced physicochemical and structural properties, as visualized in Figure 4. Finally, we compute the respective first Pareto front of all models and report in Table 2 their average R2-distance to the utopia point, well as the size of their optimal set (details in Ap- pendix D.3): our approach steadily finds more Pareto opti- mal solutions. This evidence demonstrates the effectiveness of our approach navigating the complex multi-objective landscape of dual-target drug design.
5.4. Objectives
RationaleRL and MARS are reproduced in their best re- ported settings. Following Li et al. (2018), they random forest (RF) classifiers for each target, alongside QED and SA scores to condition their generation. REINVENT is reproduced with the same property predictors with QED score only as SA score is not supported.
The objectives of CombiMOTS integrate both biological ac- tivity and structural constraints. Following Li et al. (2018); 8);
Jin et al. (2020); Xie et al. (2021); Swanson et al. (2024), we use activity towards both targets as an empirical esti- mator of inhibition, derived from real experimental assays used to train machine learning predictors. For instance, the GSK3,-JNK3 training data originates from PubChem and ChEMBL (Gaulton et al., 2012; Kim et al., 2016), fil- tered based on bioactivity data, particularly IC50 values. We employ Chemprop (D-MPNN) classifier for multi-task prediction of dual-target activity. Unlike baselines, we pri- oritize molecular docking scores for both targets over QED and SA. Specifically for dual-inhibitor design, we argue that to accurately consider SAR during generation, "We Should at Least Be Able to Design Molecules That Dock Well" (Cieplinski et al., 2020): CombiMOTS successfully cap- tures ligand- binding affinity, as showcased in Section 6.1. Details and justification on objective design are given in Appendices D.3, 1.2 and 1.3.
Ratarasi HERWENT
Rraseii RERWENT
Donay
02
De
22
-14
.00
-12
cor3a Dedking Scure
JV3 Docding Score
We conduct additional experiments in Appendix E. They include comparative analysis of: (i) A scalarized version of CombiMOTS to emphasize the utility of Pareto MCTS. (ii) A variant prioritizing QED/SA over docking scores and six objective version which also incorporates QED and SA scores. (iii) Implementations of MARS and REINVENT aligned with our objectives by replacing QED and SA with docking score. (iv) A comparison against AlxFuse (Chen et al., 2024), a model using collaborative reinforcement learning and active learning, on the DHODH-ROR-y pair to investigate how our model handles data scareity.
MATIS
Aufues
03-
04
DCD
Figure 3. Normalized distributions of the generated molecules across dual-docking scores, QED and SA scores on the GSK3B- JNK3 target pair.
5.5. Experimental Settings
For RationaleRI,, REINVENT and MARS, we generate N 10,000 molecules across all three target pairs. As CombiMOTS is fundamentally search method, it does not 'generate' fixed number of outputs but instead returns all reaction products within computational budget. We fix Nroliout = 50,000 for all tasks (GSK3 EGER-MET, TIK3CA-mTOR) and randomly sample 10,000 found dual- active molecules. Therefore, we do not need to compute activity success rate for CombiMOTS.
Figure 4. Radar charts summarizing performance on the GSK38- JNK3 (left), EGFR-MEN MET (middle) and PIK3CA-MTOR (right) tasks. We report average values of originality metries and median values of quality metrics, normalized to the best score each axis.
5.7. Ablation Studies
To demonstrate the effectiveness of the Search Space Reduc- tion step, we conduct experiments to emphasize the role of FGIB in fragment extraction (Section 5.7.1) and the impact
7

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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Table 1. Performance comparison across different target pairs and molecular generation models based on 10,000 sampled molecules from three runs. (*8; p < 0.001; :: p 0.01)
Table 3. Search space size and dual-actives candidates over all generations using FGIB, Naive BRICS and MiCaM. + refers to blocks not used in the specified method.
Targut Pairs
Madele
Valid. (8)
Uni..
Novel
Metrics
Div. (%)
Act, SK (16)
Method
Aitulddnng Blocks
#Poesile Products
#Uual-Acctves
BRICS MrCaM
-1.7M 12:274 (8 428 FGIR)
4,430 (147 + FGBB)
1881/12.559 (14.45%)
RationaleRL
99.50ucci
50.46uzs
100
70.52
266
1,44/13,223 (10.90%)
GNK3
CumbiMOTS
REINVENT
MARS
99,56ars
109,00
100.00
26.02.304
100
98.96
70.64.2
88.67
99.36ur
PGIB (Base)
(106883 BRICS.
10,530 y MICaM)
14,366
25M
3,662/15,433 (23.74%)
Rationllell.
21
100 1
EGFR MET
RLINVENT
MARS
99 19.15
108
96.80 14 14
80 10
99.82 10.8
91.59"
$9.59 59
69 114e
70 aT
CorhiMOTS
100
100.000
99.81,122
90.75
moto metric being fingerprint-basse changing a small motif is relatively impactful. (ii) For higher thresholds, the search space is too small to allow good exploration. There is a significant drop in number of dual-actives, and other metrics (Appendix B) suggest that thresholds above 0.6 yield drop in diversity (88.67-78.73345 and consistency across molec- ular properties. (iii) For lower thresholds, CombiMOTS has "more room to explore" but finds worse tradeoff's across QED and less dual-actives. As more reactions are possible, Pareto fronts are larger and convergence to optimal solutions is slower (Appendix L). Optimal thresholds are specific to the target properties, but our experiments suggest that a search space of magnitude 10M yields better convergence within reasonable budget (~10k rollouts).
Rational:RL
99.9 99,99
48 34
27. 27.04
66. 55
99 u
REINVENT
50.4
96 99
67.91
97 Alle
MARS
15.00..
73.82
CorchiMU1S
100
1m0
90.88.
Table 2. Average R2- Ri-distance the utopia point normalized in range to (lower is better) and size of Pareto optimal sets.
Model/Task
GSK3/3-JKK3
EGFR-MET
PIK3CA-mTOR
CombiMOTS
0.8075 (174)
0.8419 (268)
0.8143 (210)
MARS
0.7830 (102)
0.8845 (142)
0.8144 (89)
RationaleRL
0.8307 (137)
0,9388 (148)
0.8852 (113)
REINVENT
0.8223 (93)
0,8518 (177)
0,8035 (174)
of Tanimoto similarity thresholds on the search space size (Section 5.7.2).
5.7.1.
FRAGMENT EXTRACTION
Table 4. Search space size and dual-actives candidates over all generations using different similarity threshold values.
FGIB extends BRICS by breaking molecules into retrosyn- thetically interesting fragments, which is preferred over mule/frequency-bassee based methods when combined with Enam- ine REAL Space. Some works adapt BRICS to needs with fixed goal c.g. PBRICS (Vangala et al., 2023) for AD- MET explanability, thus not suited for the dual-inhibition task where target proteins are user-defined. Our goal is to capture high-property fragments for any target property. To further justify our choice, we report results from 10k roll- outs on the GSK33-JNK3 task when replacing FGIB with naive BRICS and MiCaM (Geng et al., 2023), a connection- aware motif-mining approach to decompose known active compounds. Table 3 shows that FGIB successfully iden- tified goal-specific fragments, resulting in a significantly higher rate of dual-active compounds. For other metrics (Ap- pendix B). all methods exhibit similar performance, which is sound as FGIB only impacts the search space through the selection of initial blocks: MCTS objectives and conver- gence are "as good" but the attainable space contains more compounds likely exhibiting dual-activity potential.
Threshold
#Building Blocks
# Possible Products
Dual-Actives
(Full Space)
139,493
>31B
(Not Performed)
0.3
54,811
4478M
2,833/13,558 (20.90%)
0.4 (Base)
14.366
-255
3,662/15,423 (23.74%)
0.5
3,737
~..I
1,380/1 1.631 (11 86%)
0.6
858
4.3
317/9,433 (3.36%)
6. Case Studies
6.1. Visualization of potential dual-inhibitors for GSK3,-JNKK3
CSK3 (SYES)
JNKX CONNEEE
Compound
GED- 0.000
Compound
5.7.2. SENSITIVITY OF THE SEARCH SPACE SIZE
SA-2
Dock kigiingggg Soor--rt -T Ocoliino
Decking Ston 1155 (calined
We investigate the use of various thresholds and report re- sults from 10k rollouts on the GSK3 task for lower and higher values of 0.3, 0.5 & 0.6. Table 4 shows that (i) the threshold greatly affects the search space size due to the small nature of FGIB fragments and Enamine blocks. Tani-
Figure 5. Examples of molecules generated by CombiMOTS on the GSK3,6INK33 target pair. They both yield high drug-likeness likeness and synthesizability metries, and different (colored) parts of the compounds are positioned into each protein pocket.
We show in Figure 5 two example dual--taget molecules
8

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
(Compound I and Compound 2) generated by CombiMOTS
1.0
Moan
inhibit both GSK3/3 and JNK3. Through in silico docking, each compound was predicted to occupy the ATP binding pocket of both targets, reproducing key interaction patterns highlighted in previous structural and biochemical studies (Lu et al., 2018; Cheng et al., 2022). Notably, hydrogen- bond interactions the hinge region (e.g.. VAL135 in GSK33: MET149 in JNK3) and the engagement of hy- drophobic pockets (VAL70, LEU132 in GSK33; ILE70, VAL78 in JNK3) were consistently observed, indicating strong binding complementarity.
0.8
Predicted toxicity
0.6
0.4
0.2
0.0
Non-toxic
Selected tour
Generated
Toxic
Compound exhibited strong predicted affinity, with dock- ing scores of - kcal/mol for GSK3, and -11.9 kcal/mol for JNK3. Hydrophobic interactions with residues such as VAL70 (GSK33) and ILE70 (JNK3) stabilized its position- ing in catalytic clefts. Hydrogen bonds with residues such as ASN64 (GSK3,8) and LYS93 (JNK3) further reinforced dual-target binding, aligning with known hinge-directed in- hibitor interactions (Quesada-Romero et al., 2014; Cheng et al., 2022).
Figure 6. Toxicity predictions for generated molecules on the GSK3 target pair. 'Generated' refers to all 10,000 gener- ated samples. 'Selected four' refers to the compounds discussed 6.2.
remains below that of the 112 truly toxic compounds, with some generations predicted as potentially non-toxic. (ii) Four randomly selected samples with predicted toxicity be- low 0.2 exhibit high scores across all properties (Figure 19). Despite toxicity not being optimized, these four samples appear the first two Pareto fronts, suggesting that Pareto- optimal solutions may hold promise for lead identification. We perform additional experiment toxicity optimiza- tion in Appendix 1.2.
Similarly, Compound 2 achieved favorable docking scores (-11.4 kcal/mol for GSK33, -11.5 kcal/mol for JNK3). Key hydrogen bonds with ASP133 (GSK33) and MET149 (JNK3), along with hydrophobic contacts involving ILE62 (GSK35) and ILE70 (JNK3), support its effective active-site engagement QQuesda-Romeen et al., 2014; Lu et al., 2018; Cheng et al., 2022). These interactions indicate robust dual- target binding for both compounds. The full list of identified interactions found in Appendix G.
7. Conclusion
Beyond binding predictions, both compounds display QED values around 0.56 and SA scores under 3, suggesting rea- sonable balance of like properties and ease of synthe- sis. These findings highlight the promise of CombiMOTS- driven design in generating dual-target molecules that not only recapitulate essential interaction motifs but also meet fundamental criteria for drug discovery.
We proposed CombiMOTS, a novel approach to combinato- rial multi-objective drug design by integrating PMCTS with fragment-basel molecule generation. By leveraging dual- target-aware fragments available in industry and extending PMCTS to a combinatorial framework, our method effec- tively navigates the complex design space of dual-target drug discovery while ensuring synthesizability. Through comprehensive evaluations on multiple dual-target inhibitor tasks, we demonstrate that CombiMOTS consistently out- performs existing methods by generating diverse and inter- pretable molecules that achieve favorable trade-off' across key objectives. Our results highlight the potential of Combi- MOTS as valuable tool in rational drug design, paving the way for further advancements in multi-objective optimiza- tion for molecular generation.
6.2. Toxicity Prediction
To further demonstrate the applicability of our method in drug discovery, we estimate the toxicity profile of molecules generated by CombiMOTS. Following Swanson et al. (2024), we train an ensemble of ten Chemprop models on the ClinTox dataset (Wu et al., 2018) using clinical toxi- city binary labels. The dataset comprises 1,478 molecules, with 1,366 experimentally validated as non-toxic (0) and 112 identified as toxic (I).
Future directions could extend our framework to larger chemical libraries e.g., Freedom Space (Protopopov et al., 2024) broader multi-objective applications. While Appendix offers preliminary investigations of selective molecule generation, toxicity optimization and protein- protein interaction modulation, we envision future works to explore various strategies to expand the applicability of CombiMOTS in real-world scenarios.
Figure 6 compares the predicted toxicities of 10,000 CombiMOTS--eneeree molecules for the GSK3,3JNK33 task against ground truth compounds from ClinTox. While some generations tend to be toxic, we make two key observa- tions: (i) The average predicted toxicity of 10,000 samples

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CombiMOTS:
Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Acknowledgements
aware dual-target drug design through collaborative learn- ing of pharmacophore combination and molecular simu- lation. Chemical Science, (5(27):10366-10333 2024.
This study was supported by the Bio & Medical Technology Development Program of the National Research Foundation (NRF), funded by the Ministry of Science and ICT, Repub- lic of Korea ASS-202--NR06793)) the NRF grant funded by the Korea government (MSIT, RS-2023-00257479,, the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare. Republic of Korea (RS- 2024-00403375), and Institute of Information commu- nications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT, RS-2021-II2) 1343, Artificial Intelligence Graduate School Program (Scoul Na- tional University). This study is also funded by AIGEN- DRUG Co., Ltd. and ICT at Seoul National University provided research facilities.
Chen, W. and Liu, L. Pareto monte carlo tree search for multi-objective informative planning. arXiv preprint urXiv:2111.0822 2021.
Cheng, C., Liu, M., Gao, X., Wu, D., Pu, M., Ma, J., Quinn, R. J., Xiao, Z., and Liu, Z. Identifying new ligands for jnk3 by fluorescence thermal shift assays and native mass spectrometry. Acs Omega,
2022.
Chenthamarakshan, V., Das, P., Hoffman, S., Strobelt, H., Padhi, I., Lim, K. W., Hoover, B., Manica, M., Born, J.. Laino, T., et al. Cogmol: Target-specific and selective drug design for covid- 19 using deep generative models. Advances in Neural Information Processing Systems, 33: 4320-4332, 2020.
Impact Statement
Cieplinski, T., Danel, T., Podlewska, S., and Jastrzebski, We should least be able design molecules that dock well. arXiv preprint arXiv:2006. 16955, 2020.
We release CombiMOTS to be effective in real-world drug discovery tasks and useful to practitioners. Common risks involve using this tool to design harmful compounds or having complete faith in machine-learned predicted prop- erties with no post-hoc validation. For instance, metrics as validity, uniqueness, novelty and diversity can easily be di- verted through small modifications on an original SMILES string (Renz al., 2019). Though such challenges remain common in other domains such as language and image, we encourage users to work closely with Inliicatioo-driverr experts such as medicinal chemists or health institutes.
Constantin, T. A., Varela-Carver, A., Greenland, K. K., de Almeida, G. S., Olden, E., Penfold, L., Ang. S., Orm- rod, A., Leach, D. A., Lai, C.-F., et al. The cdk7 inhibitor ct7001 (samuraciclib) targets proliferation pathways to in- hibit advanced prostate cancer. British Journal of Cancer, (28(1))2326-2337, 2023.
Degen, J., BeesshhiddGGerlchh C., Zaliani, A., and Rarey, M. On the art of compiling and using' 'rug- chemical fragment spaces. ChemMedChem, 3(10):1503, 2008
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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
A. Property Distributions for EGFR-MET and PIK3CA-MTOR
A
B
16-
Ralion
Rall MARO
079
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MET Druking Scare (1)
PVO Oodkngg (coee
matoi Secvt
Takona
Puti skrl
0.75
0.60
Com214375
Combaro01
03
0.1
1.0
053 (7)
24 (1)
085 (1)
Figure 7. Normalized distributions of the generated molecules across dual-docking scores, QED and SA scores on the (A) EGFR-MER
(B) PIK3AA-mTOR target-pairs.
B. Tables and Property Distributions Ablation Studies
Table 5. Performance comparison of fragmentation methods on the GSK3,-JNK3 task for 10,000 sampled molecules on three independent runs.
Metries
Method
Valid. (%)
Uniq. (%)
Novel. (%)
Div. (%)
BRICS
100.0.00
100
.8.54.009
88.31
MiCaM
100.0.00
100
98. 08
87.99.1.34
FGIB (base)
100
100.0.00
99.96.0.0
88.67.0.52
FGIB
0.4
0.4
BRICS
BRICS
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MiCaM
Density
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SA
Figure 8. Distributions plots comparing fragmentation methods on the GSK3,-JJK3 task.
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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Table Performance comparison across different threshold values based on 10,000 sampled molecules on the GSK3 task for three independent runs. Note the drop in Diversity for threshold value of 0.6, reflecting redundancy related to limited search space.
Metrics
Threshold
Valid. (%)
Uniq. (%)
Novel. (%)
(%)
0.3
100
10000:00
98.80
88,38
0.5
100,000
100
99,93
86,28.o35
0.6
100
100
99.95
78.73
0.4 (hase)
100,0.0
100
99.962001
88.67
0.3
0.4
0.3
0.4
0.4
Density
Densiyy
0.3
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JNK3 Docking Score (4)
0.3
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Densily
0.6
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QED (f)
SA (J)
Figure Distributions plots comparing Tanimoto similarity thresholds the GSK3 task. value of 0.3 converges slower in QED. Values of 0.4 and 0.5 perform similarly but 0.4 presents more dual-actives. From 0.6, the search space is too small to find better tradcoffs.
C. t-SNE Visualizations
We provide t-SNE visualizations of the baseline models for all three tasks using ECFP4 fingerprints (2048 bits), perplexity of 30, 1,000 iterations and the seed number 42. We plot Figures 10 to 12 using the same generation runs than for Figures and 7.
Key observations follows:
RationaleRL generations are clustered on all tasks. Its workflow revolves around (i) extracting and merging "rationales" from high-property compounds, then (ii) training & finetuning a graph completion module to obtain novel molccules from merged rationales. Generation occurs by auto-regressively complete the same structural cores, thus leading to poor diversity and similar fingerprints.
REINVENT and MARS are not consistently generating sparse point clouds. For example REINVENT is performing poorly on the GSK3,-JNKS3 task, and MARS on the EGFR-MET task where small clusters are forming.
CombiMOTS generates sparse and wide point clouds across all tasks, indicating its consistency in generating novel and structurally diverse compounds.
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CombIMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
Figure 10. t-SNE distributions on the GSK3,-JNK3 task.
Figure 11. t-SNE distributions on the EGFR-MET task.
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CombiMOTS: Combinatorial Multi-Objectin Tree Search for Dual-Target Molecule Generation
Figure I-SNE distributions on the PIK3CA-mTOR task.
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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
D. Data Preparation
D.I. Curation of EGFR-MET and PIK3CA-MTOR
We downloaded the EXCAPE-DB (Sun et al., 2017) from the following zenodo record and retained only entries with a Tax_ ID of 9606 (Homo sapiens). Using RDKit, we then converted all molecular structures to canonical SMILES. Finally, filtered out molecules that did meet the following criteria-baving fewer than 50 heavy atoms and containing only the elements H, B, C. N, O, F, P. S, CI, Br, and Lad retained only those that satisfied these requirements (Li et al., 2018).
D.2. Curation of CDK7 and Off-targets
We downloaded the PubChem database (as of 2024, November 25th) (Kim et al., 2016) to curate bioactivity data. We filtered out molecules having conflicting labels or which did not meet the following criteria-having a molecular weight (MW) below 1.000g//mol, having more than 12 heavy atoms, not containing metal atoms or ions and whose activity was measured in at least two proteins- and retained only those that satisfied these requirements (Sun et al., 2017). The final curated data comprises a total of 18,478 molecules which statistics are specified in Table 7.
Table 7. Distribution of molecules based on their activity against CDK targets.
CDKI
CDK2
CDK5
CDK7
CDK9
CDK12
CDKI3
Active
1,358
2,249
988
923
1,065
434
149
Inactive
733
15,592
15,805
530
533
239
334
Total
2,091
17,841
16,793
1,453
1,598
673
483
D.3. Implementation Details
All experiments were done using an Intel Xeon Gold 6526Y and a single NVIDIA RIX A6000 GPU.
CombiMOTS Activity Predictors: Following Swanson et al. (2024)
Chemprop (D-MPNN).
Baseline Random Forest Classifiers:
For RationaleRL, REINVENT, MARS and MolSearch, we follow Li al. (2018)
to train random forest classifiers for each different target pair. The data splitting follows a random 80:20 (Train:Test) ratio, implemented with scikit-learn (Pedregosa et al., 201 1) with number of estimators of 100. RDKit is used to calculate the ECFP6
Molecular Docking: We use QuickViin-GPU-22 (Tang et al., 2024) as our oracle. Target structures and binding centers coordinates are curated through Protein Data Bank (PDB) and ligand preparation is made with OpenBabel (O' O''oyle et al., 2011). We list the used PDB IDs for each target: GSK33 (6Y9S), JNK3 (4WHZ), EGER (1M17), MET (4MXC), PIK3CA (8V8D, mTOR (3FAP), DHODH (6QU7), ROR (5NTP).
For the CDK7 selective generation task (Appendix I.1), we used: CDK1 (4Y72), CDK2 (3PXF), CDK5 (7VDP), CDK7 (8PL2), CDK9 (3TN8), CDK12 (7NXK), CDK13 (5EFQ).
Objective Scaling: Contrary to the baselines, the implementation of vectorized properties implics (i) the non-necessity to scale the objectives, (ii) and the possibility to simultaneously maximize some objectives while minimizing others. For better readability in our code implementation, we still conform them the standard [0. I] range to be maximized. Following Lee et al. (2023), we apply the following transformations docking scores and synthetic accessibility scores:
DDS and SA +- SA
DS + 20
(Transf.)
9
Normalized R2-distance to the utopia point: Following Kusanda et al. (2022), consider objectives to be maximized. More specifically, our main setting uses four objectives to be maximized in range 0 to I (after Transf.), leading to a final range of 0 to 2. The metric is defined as:
70
max(0, Uuto.i y1)
D(y, Vuto)
Σ
Vuto,
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CombiMOTS: Combinatorial Multi-Obeective Tree Search for Dual-Target Molecule Generation
E. Additional Experiments
E.1. Objective Settings of CombiMOTS
To investigate the performance of our objective design, we compare the base settings CombiMOTS against two modified settings: a linearized version not using Pareto optimality (E.1.1) and six-objective version additionally considering QED and SA scores 1E.).2). We also dwell into the prioritization of docking score over QED and SA in E.1.3.
E. SCALARIZATION
We empirically showcase how Pareto principles (Luc, 2008) help finding optimal tradeoffss in a given search space. We implement scalarized version of CombiMOTS using the same four objectives (predicted dual-activities and dual-docking scores) with equal weights set to 0.25 (no priori assumption), and run Nrollout= 10,000 iterations on the GSK3 task, using the exact same search space as our base setting. Figure 13 compares the normalized distribution the generated molecules.
first observation that after 10,000 iterations completed, the scalarized MCTS only found 1,488 dual actives, compared to 3,662 using Pareto optimization.
A second observation is that the scalarized version finds molecules with better QED score, but worse in all other metrics. As expected, this evidence supports the fact even with aligned objectives and identical search space, the naive aggregation of multiple objectives cannot effectively find compounds with balanced propertics, making these approaches unsuitable for complex multi-objeccivv settings.
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Figure 13. Normalized distributions of CombiMOTS against its scalarized version on the GSK33-JNK3.
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CombIMOTS:
Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
1.1 SCALABILITY NUMBER OF OBJECTIVES
We investigate the impact of considering more constraints in our framework. The theoretical analysis in Appendix discusses convergence bounds and regret of the PUCB formula, well the effects of dimensionality (number of objectives). Intuitively, Theorem L.4 suggests that using ponder-to-distinguiss local Pareto fronts. We aim to approach optimal solutions within a reasonable time scale, hence the need to properly select objectives, efficient oracles and search space size.
objectives leads slower convergence due to larger, thus
implement version CombiMOTS using the same four objectives (predicted dual-activities and dual-docking scores) as our base setting, adding QED and SA scores as two additional objectives. We run N 20,000 iterations on the GSK3,3JJK33 task, using the exact same search space base setting. Figure 14 compares the normalized distribution of the generated molecules.
A first observation is that after 20,000 iterations are completed, the six-objective CombiMOTS implementation found 5, 7,748 dual actives, compared to 8,606 using only four objectives. Compared to the scalarized approached discussed in Appendix E.1, , the number of predicted dual-actives is relatively closer to our setting, hinting at the better exploration of Pareto MCTS given multiple objectives.
second observation that the six objective version finds molecules with similar QED and SA score distribution as our base setting, but worse in docking scores. This behavior corroborates that adding objectives leads more 'directions' to explore and induces slower convergence toward Pareto optimal solutions. Table supports this claim.
We also note an additional computational overhead (from an average Is/rollout to 25s/rollout), mainly due to the QED and SA oracles, slowing individual rollouts. Appendix F.2 further analyzes the complexity our tree traversal.
0.8
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Figure 14. Normalized distributions of CombiMOTS against version prioritizing QED/SA docking score, and its six objectives version on the GSK3,-JIN33 task.
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CombiMOTS: Combinatorial Multi-Obeective Tree Search for Dual-Target Molecule Generation
1.3. SCALABILITY IMPORTANCE DOCKING SCORE
The previous section (E.1.2) interrogates on the need prioritize some objectives over others. Our base setting utilizes four objectives being predicted biological activity and docking score for both targets. We first emphasize how the structural and mechanistic relevance of docking lead to unveiling better candidate compounds, before empirically supporting this claim.
Docking score is critical in drug design as directly evaluates ligand-target binding affinity, which is essential for therapeutic efficacy. Unlike QED/SA, which focus on general drug-likeness or synthetic feasibility, docking scores are structurally and energetically tied to the biological activity the molccule. Studies have shown that incorporating docking scores during molecular generation leads higher binding affinity and improved hit identification (Chenthamarakshan et al., 2020), whereas QED/SA cannot ensure target specificity (Agu al., 2023; Xu al., 2024). Therefore, docking score should be prioritized in early drug discovery stages, with QED and SA used later for optimization (Xue al., 2025).
Table 8 and Figure 14 show how prioritizing QED/SA over docking scores compares to our base setting. We observe that not optimizing docking scores leads to a significant decrease of overall quality. Though QED is marginally improved, SA remains almost unaffected while binding affinity gets considerably worse: our base setting still leads to acceptable scores even without explicitly optimizing QEDISA.
On the GSK3 task, we show Table 9 the size of the first six Pareto fronts from 10k randomly sampled products, as well as the number of Pareto fronts in three different objective settings: prioritizing docking score over QED/SA, prioritizing QED/SA over docking score and using all six objectives. We observe that expected, using six objectives leads to fewer Pareto fronts which are individually more populated. Also, using docking docking score interestingly enables better differentiation between Pareto fronts, more numerous and individually less populated.
Though these results are empirical, they perfectly align with necessity to consider both target affinity and molecular properties within the limitations of dimensionality scaling for Pareto MCTS.
Table Performance of base settings compared using QED, SA as objectives the GSK38-JNK3 task for three independent runs.
Metries
Setting
Valid. (%)
Uniq. (%)
Novel. (%)
Div. (%)
QED, SA
10000.00
100 #0.00
99.92.n.m
90.32
Docking Scores (base)
20.00
10.00000
99.96.0.01
88.67
Table 9.
Number molecules across Pareto fronts for different objective settings on GSK33-JNK3 task.
Pareto Rank
Activity + Docking
Activity + QED SA
Six Objectives
Rank
60
69
729
Rank
135
204
1,416
Rank
180
257
1,809
Rank
233
370
1,771
Rank
263
456
1,456
Rank
316
502
1,153
Number of fronts
40
29
12
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CombIMOTS:
Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
E.2. Aligned Baselines
We investigate the performance of MARS and REINVENT when using dual docking scores objectives instead of QED and SA, with equal weights set to 0.25. For REINVENT, we generate 10,000 molecules using the integrated DockStream tool. For MARS, we implement Quick VincGGU-UP
online oracle. However, as MARS generates N samples at every step of run, the computational cost of molecular docking does not allow to generate 10,000 compounds. We therefore only run MARS to generate 500 molecules and analyze the samples from the converged step. Figure 15 compares the normalized distribution of the returned molecules.
We observe once again the property imbalance of both MARS and REINVENT, supposedly due to their scalarized objective design. MARS generates compounds exhibiting better docking score, but lower QED score, while REINVENT contrarily generates compounds with worse docking score for both targets but high QED scores. On the other hand, CombiMOTS is the only model consistently identifying compounds with high property tradeoffs.
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Figure Normalized distributions of CombiMOTS against aligned versions of MARS and REINVENT on the GSK3,-JJK33 task.
E.3. Impact of Data Availability
We investigate the performance of CombiMOTS against AlxFuse (Chen al., 2024). AlxFuse is method extracting pharmacophores using docking pose protein-ligand analysis, before collaboratively use RL and Active Learning (AL) for fragment assembly. It progressively learns how to fuse and dock the extracted fragments better. We run the notebooks following the original GitHub guidelines and generate 10,000 molecules with 4 iterations. Figure compares performance on the GSK3,-JNK3 task, while Figure 16 compares performance on the DHODH-ROR+ task proposed by the authors. Specifically, the DHODH-ROR target pair was not curated by only using ground-trutt experimental assay results. Due to data scarcity, Chen et al. (2024) make assumptions on the ChEMBL dataset to curate additional data.
On the GSK3,-JJNK3 task (Figure 3), AlxFuse's performance is reasonably fair due the high quality of the data. However, this does not hold true for the DHODH-ROR~ target pair. In particular, docking scores of the generated molecules are particularly low. We note that in both tasks. AlxFuse exhibits a lower QED score than all baselines. This behavior could also be explained by the linear design of AlxFuse's 's objective function failing to find tradeoffs. In contrast, CombiMOTS still manages to find satisfying candidates, exhibiting once again the efficacy of our pareto-based approach and complementary choice of objectives.
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CombiMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
AlxFuse CombiMOTS
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Figure 16. Normalized distributions of the generated molecules across dual-docking scores, QED and SA scores the DHODH-ROR=;t
target pair.
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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
E.4. Comparison against Pareto MCTS baselines
We investigate the performance of CombiMOTS against other Pareto MCTS methods: Mothra (Suzuki al., 2024) and MolSearch (Sun al., 2022).
Mothra is multiobjective molecular generation system that integrates recurrent neural networks (RNN) with Pareto MCTS to simultaneously optimize multiple properties like target protein affinity, drug-likeness, and toxicity. Compared to CombiMOTS, Mothra is natively limited to single-target RNN decoding. We adapt Mothra to support dual-target settings by running molecular docking for both proteins, and using the returned scores during generation.
MolSearch is Pareto MCTS--ased framework that starts with existing molecules and uses two-stage search strategy with transformation rules derived from compound libraries to gradually modify them for multi-objective optimization. Compared to CombiMOTS, MolSearch is natively focused dual-target optimization using RF classifiers, rather than de novo generation. We adapt MolSearch to the EGFR-MER and PIK3CA-MTOR tasks by training RF classifiers as detailed in Appendix D.3.
For both methods, we perform three independent runs following the original GitHub guidelines show in Table 10 and Figure metrics for generated molecules.
Mothra returns extremely few valid molecules, among which less dual actives: for the displayed in Figure 17, 1,125/131,688 molecules valid and 6 are dual actives. MolSearch returns sound candidates in terms of molecular properties but is has high computational cost: the run of Figure 17 was interrupted after 57 hours and generated 493 molecules. For both methods, generated compounds exhibit weak binding affinity towards GSK388 and JNK3, with Mothra performing poorly in SA score. Appendix F discusses how these compare terms of computational cost.
0.8
CombiMOTS
CombiMOTS
MolSearch
0.6
MolSearch
Density
Mothra
Density
Mothra
0.4
0.4
0.2
0.2
0.0
0.0
-10
-10
GSK3$ Docking Score (+)
JNK3 Docking Score (4)
1.5
CombiMOTS
CombiMOTS
MolSearch Mothra
MolSearch
Densily
Density
Mothra
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
QED (f)
SA (4)
Figure 17. Normalized distributions of CombiMOTS against Mothra and MolSearch on the GSK38-INK task.
25

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Table 10. Performance against additional Pareto MCTS baselines across target pairs.
Results are obtained from three independent runs.
Metrics
Target Pairs
Models
Valid. (%)
Uniq. (%)
Novel. (%)
Div. (%)
Act. SR (%)
MolSearch
100.0.00
72. 14...4
74.57
=5.99
98.34,1.20
GSK3
Mothra
g.68
99.82
10000.00
95.04.0.25
0.52.0.18
CombiMOTS
100 $0.00
100,0.00
99,96+0.01
88.67
MolSearch
10.00
81.64.n.46
75.83
82.48
92.56.3.84
EGFR-MET
Mothra
0.92
99.70
99.9920.02
94.7420.58
52.92
CombiMOTS
100 20:00
100
99.81 11.62
90.7520.40
MolSearch
100 20.00
80.6222.76
100
83.76_2.16
89.22 20.87
PIK3CA-mTOR
Mothra
0.69 20.34
99.7220.01
100
95.35 21.06
85.32
CombiMOTS
100g0:00
100
99.994a.01
90.88
CombiMOTS MolSearch
QED
Mothra
Diversity
0.4
0.2
Validity
Dock JNK3
Uniqueness
Dock GSK3B
Novelty
Figure 18. Radar chart the GSK33-JNK3 task against Mothra and MolSearch. We report average values of originality metries and median values of quality metrics, normalized to the best score on each axis.
26

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CombiMOTS: Combinatorial Multi-Ojeective Tree Search for Dual-Target Molecule Generation
F. Runtime and Complexity Analysis
In this section, we first report how the empirical runtime all baseline methods compare against CombiMOTS F.I, then provide in F.2 a complexity analysis of the Pareto MCTS algorithm implemented in CombiMOTS.
E.. Runtime Comparison
Note that RationaleRL finetuning step takes over 2 hours per epoch the number of rationales is large. Among PMCTS methods (in gray), CombiMOTS is significantly more efficient, and just requires to train oracles if needed (below 10 minutes). Notably for Mothra, the original work performs 14-days experiments using two Intel Xeon E5-2680 V4 processors and four NVIDIA Tesla P100 GPUs, which represents far more resource than what CombiMOTS requires. For MolSearch, the original work reports average of 0.4-1.0 hours per molecule in both HIT-MCTS and LEAD-MCTS stages using TITAN RTX GPUs (24GB), which is intractable when exploring large chemical spaces.
Table 11. Approximate runtimes on the GSK38-INK3 task.
Model
Pretraining
Finetuning
Sampling/Searching Time
Total Search Time
Total Generations
(per iteration/rollont)
RationaleRL.
Yes
Yes
~10s/200 samples
-mmin
10k
MARS
Yes
No
~8min/step of 10,000 samples
66rss
10k
REINVENT
Yes
Yes
below Is/sample
~1mmin
10k
Mothra
Yes
Yes
~ 17min/iteratiin
330rs (interrupted)
131k, below 1% valid
MolSearch
Yes
No
23min/teraation
57hrs (interrupted)
493
CombiMOTS
(Oracles)
No
9s/iteration
4days, 6hrs
79k
F.2. Complexity Analysis
As Appendix F.1 presents approximate runtimes, further investigate the algorithmic complexity of CombiMOTS during the tree search. We consider our problem setting, which details explicitely described in Appendix L.I.
We remind the following notations: Nchildren the number of children from parent node node, B the set of building blocks, R the set of reactions, Oracles()) the ensemble of property predictors.
The initialization step runs in (1). Then, during a single rollout:
If the selected node is product (O(1)):
Returning the product property vector runs in @(Orackes(producl)) as it is never precomputed.
Else:
The expansion node creates Rehhldren in Omndee.moleccles Card(B)) * Card(
We compute node properties upon creation:
If the scores are precomputed (using lookup hash table), assign them to child_node in 0(1);
Else, compute them in
(child node));
The Pareto selection step computes the ParetoUCB vector of all children nodes, running in Nehildrens
The backpropagation step runs in (1) the maximum depth of the synthesis in bounded by the maximum allowed synthetic steps in R (using Enamine REAL Space, one to two steps).
Therefore, single tree traversal is bounded by the slowest operation between (pacles(product) and Rehaldren Oracle((child_nnds Moreover, if scores of building blocks are precomputed, this bound is further reduced to the slowest operation between Oracles(product) and (Tohhatdren)
27

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
G. Identified Interactions of Case Study 6.1
Compound Hydrophobic interactions with VAL70, ALA83, LEU132, GLN185 (GSK33) and ILE70, LEU144, LEU148, MET149 (INK3). Hydrogen bonds with ASN64, VAL135 (GSK33) and LYS93, GLNI55, LEU206 (JNK3)
Compound Hydrogen bonds with ASP/33, VAL/35, ASNI86 (GSK33) and MET149, GLN/55 (JNK3). Hydrophobic contacts involving ILE62, VAL70, TYRI34 (GSK33) and ILE70, VAL78 (JNK3).
H. Selected compounds of Case Study 6.2
Compound A
Compound B
Compound C
Compound
[0.63, 0.60, -11.7, -11.3]
[0.90, 0.76, -10.3, -11.4] [0.85, 0.76, -11.0, -10.7]
[0.99, 0.99, -11.0, -10.6]
QED: 0.189
QED: 0.385
QED: 0.415
QED: 0.335
SA: 2.62
SA: 2.25
SA: 2.29
SA: 2.26
Toxicity: 0.108
Toxicity: 0.072
Toxicity: 0.194
Toxicity: 0.054
Pareto Rank: 1/124
Pareto Rank: 2/124
Pareto Rank: 2/124
Pareto Rank: 2/124
Figure 19. The four selected compounds for toxicity prediction. The vector values account for GSK33-JN33 predicted activities, and GSK33-JNK3 predieted docking scores, respectively.
I. Generalizability Broader Applications
discuss in this section how CombiMOTS could adapted to other multiobjective tasks. A key advantage of using Pareto-based tree structure and nodes to flexibly design property vectors to be either maximized or minimized. To exemplify this applicability, Appendix I.1, ablation study of toxicity optimization (extending the observations made in Section 6.2) in Appendix I.2 and briefly debate protein-proteli interaction modulator generation in Appendix I.3.
conduct preliminary case study for Cyclin-dependent kinase 7 (CDK7) selectivity in
I.1. Selective Molecular Generation
Selective molecular generation aims to identify compounds that active only towards given target. The intricacy of this task lies in avoiding off-targets often related to the main target protein, limiting the effectiveness of drugs even risking adverse effects.
Prior works (Fisher, 2005: Sava et al., 2020) established CDK7 as a regulator of both cell cycle and global transcription, supporting its inhibition as potential way to target deregulated cell proliferation. This motivated further research to identify off-targets, ultimately attempting to find selective inhibitors more relevant polypharmacology for complex discases (Olson al., 2019; Constantin al., 2023). We follow these studies identify candidates selectively inhibit CDK7 while being inactive to six off-target kinases: CDKI, CDK2, CDK5, CDK9, CDK12, CDK13. Appendix D.2 contains details on the data curation.
In parallel, efforts were also made in targeted transcription regulation cancer. Notably, Kwiatkowski et al. (2014) successfully discovered and characterized a covalent CDK7 inhibitor which achieved greater selectivity through its ability to target cysteine residue outside of the canonical kinase domain.
28

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Thanks to these findings, adapt CombiMOTS through initiatives:
During the tree traversal, selectivity can be translated as maximization objective towards CDK7 activity while minimizing all off-targets' activity. We train random forest predictors for each kinase using the curated data in a 8:1:1 training/validatiionnest ratio.
The search space reduction step can be applied to preliminarily select building blocks susceptible to react into cystein- targeting products. Inspired by Huang al. (2022), we identify four substructures from known inhibitors leading 81 similar initial building blocks corresponding to over 2.3M possible products.
We propose the following pipeline:
1. From the four initial substructures, identify similar building blocks;
2. Run 200k rollout tree search, only guided by CDK7 (maximize), CDK2 and CDK9 (minimize) bioactivity predictors. Note that we only select three objectives to converge faster towards Pareto optimal solutions;
3. We (re)-perform post-hoc bioactivity predictions for all kinases, and only retain molecules with predicted values above 0.5 for CDK7 and below 0.5 for off-targets;
4. Optionally perform post-hoc docking simulation for added practical information:
5. Apply industrial and medicinal filters to obtain a final list of candidates. We retain molecules with the following criteria: -0.4 < LogP= < 5.6 (Ghose et al., 1999), 250 < MW < 500, less than 5 Hydrogen Bond Donors (HBD), less than 10 Hydrogen Bond Acceptors (HBA) (Lipinski's Rule of Five), less than 10 rotatable bonds, 50 < TPSA S 140A (Veber's rule) and does not contain imine group (Kalgutkar, 2019) chiral center or stereocenter.
Table 12 summarizes the key described steps and Figure 20 shows examples of final candidates.
Table 12. Schematic workflow of case study CDK7 specific inhibitor search.
Step
Statistic
Initialization
(2 known inhibitor scaffolds, 2 warheads)
Search Space Reduction
81 building blocks, 2.3M possible products 348k generations
Tree Search (200k rollouts)
Filter - Selective Activity
3,491 candidates
Post-hoc docking simulation
Filter (from medicinal chemistry)
1,554 final candidates
IN
10.7, 0.49, 0.48, 0.24, 0.42, 0.36, 0.16]
[0.68, 0.49, 0.36, 0.18, 0.42, 0.37, 0.20]
[0666. 0.42, 0.47, 0.24, 0.44, 0.20, 0.11]
Figure 20. Example of found molecules active to CDK7 and inactive to off-targets. Vectors are predicted activities towards CDK7, CDK1, CDK2, CDK5, CDK9, CDK12, CDK13 respectively.
29

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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
1.2. Toxicity Optimization
We run 50k rollouts on the GSK3 task with an added objective being the predicted toxicity (to be minimized), We use the same Chemprop predictor trained in Section 6.2 during the tree search. As expected, observe in Figure 21 that overall generations are less toxic and present notable increase in density of molecules with very low toxicity (below 0.2).
Meen
0.8
Predicted toxicity
0.6
0.4
02
0.0
Non-toxic
Generated (base setting)
(toxioily (ettmerd)
Tostc
Figure 21. Chemprop predictions of molecules generated while aiming to minimize toxicity.
L.3. Protein-Protein Interaction Modulator Generation
In this paper, we mainly tackle the task of identifying dual inhibitors by targeting two proteins related to the same disease. An other field of application differing from traditional protein-ligand binding, would be the of protein-protein interaction. Though both interactions rely similar physical forces, PPIs exhibit distinct physicochemical properties, such generally larger interface areas or more complex geometry. In particular, developing small molecules tailored to PPI interfaces remains a challenge. Few recent works (Wang et al., 2024; Sun et al., 2024) implement interface-aware generative frameworks by considering hot-spot residues or known PPI complexes, enriching the landscape of SBDD.
We could envision CombiMOTS to be adapted to this task by either setting appropriate biological targets, or by aiming to mimic pharmacophoric features of hot-spot residues through the use of structure-oriented scorers during the tree traversal. We leave such investigations to future works.
J. Retrosynthesis Study
We quantitatively assess the utility of using industrial databases like Enamine REAL as the initial search space of Combi- MOTS by discussing the pitfalls of synthesizability metries in drug design. As generative models construct or optimize molecular structures, the general purpose of such metrics to quantify the feasability of experimentally synthesizing the proposed candidates. Synthesizability metries can roughly be distributed into three categories:
Rule-based metrics (c.g., SAscore) make predictions out of deterministic features (motifs, molecular mass, etc.). Though they are intuitive and computationally efficient methods, they often fail to capture real-world constraints.
Retrosynthetic-based approaches are more interpretable as they recursively break down a target compound into industry-availant precursors. However, they often lead consequent computational overheads and are limited to pre-defined reference stocks. For example, Aizynthfinder (Genheden et al., 2020) is limited to the ZINC database, Our approach is based upon the opposite idea: from a set of known precursors, we attempt to find Pareto optimal reaction products. This enables us to flexibly explore any chemical space at disposal, instead of iteratively testing known synthetic routes for a given target.
Learning-based methods (c.g., RAscore (Thakkar et al., 2021), BR-SAscore (Chen & Jung, 2024)) have the advantage of being adntext-adaptable but become inherently dependent on the quality, format and availability of the training data.
30

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CombiMOTS: Combinatorial Multi-Obeective Tree Search for Dual-Target Molecule Generation
We first propose highlight the inconsistencies across these metrics by evaluating the generations from CombiMOTS, RationaleRI, MARS and REINVENT, well Enamine building blocks and COMPAS-3 (Wahab & Gershoni-Poranne, 2024) representatives of easy-to-synthesize and hard-to-synthesize molecules, respectively. Notably, the COMPAS-3 dataset exclusively contains (poly) compounds. We plot and report the molecular distributions in Figure 22.
As expected, we observe several inconsistencies: COMPAS-3 deemed synthesizable by SA and RAscore but not by BR- SAscore. Enamine excels on RAscore but performs similarly or worse on other metrics. MARS unrealistically outperforms CombiMOTS outperforms baselines on RAscore but aligns with/worsens on others.
Enamine on
Additionally, attempt to find Aizynthfinder routes for the final candidates found in the preliminary selective inhibitors (Appendix 1.1). Because CombiMOTS leverages Enamine through their in-house validated synthetic procedures, we would normally expect all candidates to find be solvable, i.e. find route for each compound. However, among 1,544 molecules, 162 (10.42%) are not solved by Aizynthfinder-dus to its ZINC dependency. Figures 23 and 24 show examples of failure cases, as well as the route proposed by CombiMOTS.
study for CDK7
These inconsistencies motivate the use of Enamine REAL Space over mere metric evaluation: though its true synthesizability still cannot be perfectly predicted, its empirical high synthesis success rate is more aligned with real-world feasability.
RasornilLL REIMENT
RasionateRL.
REINENNT
Dersty
1.0
ContRMMTSS
CombiMOTS
Enaniin datasot
10
Enaamine dataset
COMPAS dataset
COMPAS dataset
RAscore
BBT (0l-SAccee (4)
Figure 22. Plot distributions across synthesizability metrics. For generative models, we evaluate candidates from the GSK3,-JNK3 task.
x
A
0-H
B
Reactant 1
Reactant
Product
Figure 23. A) Unsolved routed of Aizynthfinder and B) Enamine building blocks found by CombiMOTS leading to the product. (Case 1)
31

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Targe Molecule Generation
Doyto
D
Reactant
Reactant
Product
Figure 24. C) Unsolved routed of Aizynthfinder and Enamine building blocks found by CombiMOTS leading the product. (Case
32

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CombiMOTS: Combinatorial Multi-Ojeectiv Tree Search for Dual-Target Molecule Generation
K. Detailed Implementation of Pareto MCTS in CombiMOTS
Algorithm Complete Pareto MCTS for CombiMOTS
Input: Synthesis tree T', Number of rollouts Arollout
Data: Property predictors Oracles, building blocks B, reactions R. exploration weight C
// Main Monte Carlo Tree Search Function
Function ParetoMCTSS(T Initialize the tree Trroot for 4 1 to Rrollout do Rollout (T.rool)
return All visited nodes in T that are reaction products
// Rollout Function Function Rollout(node):
node is reaction product then
return (rucles(node) // Terminal node
Backpropagation starts
chidd Expansion(node) // Expand leaf node
parent.visits E (visits of all children)
12
mexl_mode + PuretoSelection o parenl_ // Select from the local Pareto front T + Rollout nert node)/ Recursive unroll Simulation
13
14
neat_node is a reaction product then
e seement-wise-matee Oracles(neat.nodee)
15
16
Update next node statistics (exploit score, visit count)
return Reward vector Backpropagation
18
// Expansion Function Function Expansion(node):
19
20
Initialize E 0
foreach reaction R do
22
if nodeemolecules compatible with reaction then Add one node per reaction product to E foreach building block E B do
25
if 3 reaction R compatible with b then Add node to E with (node.moleecuees b) // @: tuple concatenation
26
return E
Pareto Selection Function
28
Function PuretoSelectionn(cill) nodes, nodes,parent parent visils):
29
foreach node E child_nodes do
30
Compute ParetoUCC = N Local ParctoFront +- non-dominated child nodes
W
+ C x Oracles(node) x
I+N
31
32
return uniformly sampled node from Local PrretoFront
33

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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
L. Theoretical Analysis
this section, we remind, adapt to our implementation and provide further analysis the previous claims and demonstrations from Kocsis & Szepesvári (2006); Kollat al. (2008); Chen & Liu (2021).
L.1. Problem Definition Node Selection
In a Pareto synthesis tree, consider a D objective optimization problem. A node has a D-dimensional property vector Ora(v) obtained from Oracles. Suppose parent node Up with K child nodes (vx) all selected at least once (initialization). After n E N+ rollouts, the 6dhh child has been selected n& E [1..m] times (such as = >R= R==l and a D-dimensional random reward vector Nx, is backpropagated along the selection path. For all (k, n) E [1..K] x N we note 1= the reward vectors of child node uk upon consecutive selections, all drawn from an unknown distribution with an expectation vector pk-
At any step, the selection problem consists in choosing which child node Us to select based on an user-defined policy.
The goal of such policy is to minimize the number of selection of any sub-optimal node: we demonstrate that the following policy complies to this goal.
Policy (Pareto Selection):
1. Compute the PUCB formula for each child node up:
PUCB(K n) Xx,n, +C + In(D) x In(1 + n)
where C E RR* is an exploration constant. (10)
1 + 7k
2. Randomly select a child node among the Pareto front built upon the PUCB formula.
Definition L.1. (Most Dominant Optimal Node)
Following Chen & Liu (2021), the demonstration uses the concept of e-dominance of multi-objective optimization (Kollat al., 2008). Suppose a node vs dominated by a set of nodes such Veg V, Uje > fg.
The dominance hypothesis implies that for any dominating node Usr V, uw is better than ea across at least one dimension. Therefore, there trivially exists unique minimum positive constant Eg/ defined by:
E = min 3d E [1..D), + > MK,a)
The most dominant optimal node of ug. denoted ug- is the node from V where:
k- arg maz
k²
Conceptually, the most optimal node is the "farthest away" from ug in the sense that its minimum distance with es across any dimension is maximized.
From now we index such node with a star (*).
Assumption L.2. (Convergence of Expected Average Rewards).
The tree search problem allows possible drift over time of the expected reward of nodes. For any child node uy, the expectation of its average rewards E.N converges pointwise a limit pt:
A lim E[X
(11)
Given sub-optimal node and its most dominant optimal node ey- from the Pareto optimal set P we define 4 = 1= 1 as the difference of their rewards" limits.
Assumption L.3. (Adapted Process and Convergence of Residual Drift).
Let (ks d) E [1..K] x [1..D] and {Fr,t,) be a filtration such that (Xu.eaee is Fr.e,a and X a is conditionally independent of FR.441,4 FR.42,d.... given FiA--1d-
34

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CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
In other terms, the resulting "non-anticipative" stochastic process accounts for information only available at given time. For notation simplification, we define pk,nz [[ k. and the residual drift ŌR.n Mk,ma
p.g.
By Assumption L.2, lim Ōk. O.
Thus, by definition of limit, VV 0, (N)(E) such that Vnu 2 No(E). Aa (1,2..... D3, mo S SE
L.2. Theorems and Proofs
The following theorems and lemmas support the design of the used Pareto UCB formula in our search algorithm.
In particular, each proof is followed by analytic interpretation the theorems' significance to CombiMOTS. notably in terms of scalability.
Theorem L.4. (Logarithmic Bound of Sub-optimal Node Selection)
Consider Assumption L.2 and Assumption L.3 satisfied in our problem setting. Let ug be sub-optimal node (i.e. Uk $ P*)
selected To (T) times during the first n steps.
Then [|na] is logartthmically bounded:
16 x In(n) +4x +4xln(D) No(E) 0(1). (12)
vg 0, (E) IN, IN",such that (n No(E)) [[T((n]] S CC
(1 (1-E)* E)² x (min Ax,)
k.d
Proof. (To Theorem L.4)
Let variable I, be the index of the selected child node at decision step and 1 be an indicator function.
We first demonstrate the theorem with the bias term of Chen & Liu (2021) using Cr, v In(D))+xlu(()
Remark L.S. Without loss of generality, our bias term in Eq. (10) is Ct,a C Ora(vu) the theoretical guarantees. In fact, the additional exploration term in our work controls the convergence speed, thus its name.
In(D) (xln((+) and preserves
Its
For any sub-optimal node up and any / E E+* we can bound (n) (the number of times node is selected):
(n) Σ 1
Σ
11 <I+
Σ 11 - Tr
(13)
1=K+1
t=
By the Pareto selection policy, node selected at time only if its PUCB value is not dominated by any other node on the Pareto front. Particularly, it must be dominated by the most dominant optimal node ug-. Therefore:
Tk(n) 1
Σ t=++1
1(x + +Q & XET((I + -- Ta(t- 1) 2 l..
(14)
PUCB most dominant node
We reindex the with (t and 8% Te(t to get:
[T(n) 11+
ΣΣΣ 1x + Ct,s * Xk + ) ==
(15)
The condition X + cr. + Xx.0z + Cr,yy implies that at least one of the following must hold:
X + 11 Ct.s
(A)
35

---

CombIMOTS: Combinatorial Multi-Obeective Tree Search for Dual-Target Molecule Generation
X X k,ez A Pk,st Ct
(B)
Pgg A pk,s + 201,5k
(C)
We prove this by contradiction. Let's assume (A) and (C) both false, i.c.:
X = u - Ct, and pig > pk.s + 201
(16)
Both can be combined:
X y pk,s 20t,.
Ct, pk,s Ca
(17)
4,01
Then if (B) is also false, i.c. Xk, 3 pk,sk
Ct,e R3 Nk,0z - C we would have:
X₂ > Mk,s Ct,ok
Xh, + 20t,8k
X Cta > Xx. + 20, + Ct.e
X + a,s > Xk,s + Ct,sn"
(18)
This would contradict our original condition select node k. Therefore, at least one of (A), (B), or (C) must hold true.
We bound the probabilities of events (A) and (B) using Chernoff-Hoeffding Bound and Union Bound:
P(X, z 14 cr,0) = P((X",, < 1G,1 ct,o) V... V (X..D < <oDD c,,))
$
P(X s, < 1edd a.,))
(Union Bound)
D
1
P(X, z 14 - cc,0) <
(Chernoff-Hoeffding Bound)
(19)
D
d=1
Similarly, P(X k. A Mk.sh 04,s) 5 5t-
Now, let define:
Shnt + 21m D
max
Nu(E)
(20)
(1 - E ming, a A? k,d
With this choice of we ensure that for 8ı condition (C) becomes false. This is because:
1. For 8y 2 No(E), we have sl < { ا for all d E (1, D}.
1l the confidence term Ct.s, becomes sufficiently small: 2. For 8k (I- mins.a A
4nt + In
Ct.sk
2sk
4nd + In
8ln Aint-2nn
(1-E)² mins, a Ai
(1 V) mink,d A
4 Alt + In D
V2
8ln/ 2ln
(1 à) mingd Avdd
Cr.sk 5
(21)
36

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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Therefore, for any dimension d:
Hedd Hk,s,d 1d Pk,d + 37,d
Ōk,
2 Abdd - %x,d| |0x,ez
A k.d
A kdd
2 Ard -
2
= (1 5)
Ped Pkadd 2 201,0x
(22)
This implies 14 > Pk,s + 2z, making condition (C) false. Therefore, injecting above results into the bound of Equation (15) and taking expectations of both sides, we get:
1xx; + Ct. + Xbse + aco
E [[T S1+
SI+E
86
21+
P(X; 4 13 -t,,) + P(XKi A ph.n ct,s)
1-1 t-1
11+ ΣΣ Σ 24
1=1 6=1 m6-L
8 In 21m D
No(E) + 1+ π
E (T))n v
(23)
(1 k) mina A
from trpple sum
from
In fact, the triple sum can be shown converge to 1 + 3 using Euler's approach to the Basel problem. Thus, obtain:
8lnn 2
No(E) +1+ x²
E [na]
(24)
(1 {) mina A
Since our PUCB formula in Eq. (10) uses an exploration constant C and denominator (1 + n)) instead of (2n) like Chen & Liu (2021), the bound becomes:
1aln++4h + No(E) O(1. (1 - 2 ming 22,a
D n4
C
(25)
which completes the proof.
Interpretation From the obtained Bound, we make three key observations:
1. Bound In(n): This logarithmic factor implies that selecting sub-optimal nodes becomes less and less frequent over time.
2. Bound x (D): Increasing the number of objectives also increases regret by a logarithmic factor.
3. Bound & mina At,, The regret becomes lower when sub-optimal nodes are more distinguishable from the optimal Pareto front. Intuitively, the harder it to distinguish optimal and sub-optimal nodes, the slower convergence speed becomes. Directly impacting the second point, sound settings should carefully select search objectives to enable Pareto convergence within reasonable time.
37

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CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
Lemma L.6. (Existence of a Lower Bound Node Selection Count)
There exists strictly positive constant p R s.t. V(n k) E [L...K]]]. N T2(n) 2 [plog(n)]
Lemma L.7. (Tail Inequality)
After enough selections of given node, its average reward will concentrate around its expectation.
For all > O, let a = 9V 2
Then, (N) e N s.t. Vn 2 (1) Ad E (1.2, D):
P(X 2 E[x, n.al + 0) S ? P(X B(x n.d
(Upper bound of range)
(26)
σ) S n. (Lower bound of range)
(27)
The correctness of Lemmas 1.6 and 1.7 is demonstrated by Kollat et al. (2008).
Theorem L.8. (Convergence of Failure Probability)
Consider the settings and policy described previously in L.1. Let It be selected child node whose parent is the root and " be the Pareto optimal node set. Then,
mlmg Pual
P(4 $ Pt) S Ct-
where C is positive constant.
(28)
Notably, P(I & PP") S O, Le. over time, the number of sub-optimal node selections becomes negligible. Moreover, converges to zero al polynomial rate.
Proof. (To Theorem L.8)
Let be the index of sub-optimal node. We begin by decomposing the probability of selecting non-optimal node:
P(L $ PT) E P(XA.T))) A X)-()))
(29)
This decomposition is valid because Ie き P implies that we selected some sub-optimal node Ug. which occurs only if its empirical mean reward Xx.1v(1) not dominated by the empirical mean reward of least one optimal node Xi- Equation (29) implies least one of the following must hold:
A
XL.T.00 A +
(30)
2
or
AB
X * 4² +
(31)
2
We prove this by contradiction. Suppose both Equations (30) and (31) are false. Then:
N..TA(0 x 3/4 +
A
= 14
+
11a
14k
N4 + 1
(32)
2
2
2
AB
Xi-(0) > 4¹ +
(33)
2
Since 1²= M4 (by definition of optimal vs. sub-optimal nodes), and Xx.7((0) uh + 4r, would have Xi
M4 + A 2 > Xx.r,(t)- But this contradicts our original assumption that Xa,T(()) A Xi--(9)
Therefore, at least one of must hold true.
This allows us to bound the probability by injecting (30) and (31) into (29):
38

---

CombIMOTS: Combinatorial Multi-Objeetive Tree Search for Dual-Target Molecule Generation
Ak +(X (8) * p )
Ak
P(X&,T.)) * x7-(1)) S P(X * ph
(34)
2
first term
second term
For simplicity, we only show how to bound the first term in detail:
AB P(X.TAOO p4 A Σ P(A.T.())))) > Me, Akd)
(Union Bound)
(35)
Here, for (t) A Pk 2 to hold, there must be at least one dimension d where (t). Madd +
Avd 2
By definition of the drift term de,T)( PR,Ti Hk.d, which represents the difference between current expected value and limiting value:
A 2
Akd converges to 0
P(Xe,1,0 A Ams +
S
Σ d=1
P( P(X P.TT(0)) 16 (t)
(36)
Aed (1) converges to as increases. Eventually, for sufficiently large we have 16 1 S
which gives:
4
A
Σ P(X.ma)) 2 (a.a Akd
P(XE.T()) * pk +
(37)
Now we apply Lemma L.7, which provides critical tail inequality for bounding the probability of large deviations between empirical means and their expectations. Recall that Lemma L.7 states:
For arbitrary 17 and 21/2nn/) there exists Ni such that Vn (n)),, Ad E (1....,D} Vn
P(Xn, 2 E E(xp,d n.d + +o) 51
(38)
P(Xn,d < E X - σ) Sn
(39)
We set = (7) mink a Axa 36
where comes from Lemma L.6. This gives us 9/ 2ln(2r 8
ming g. Ag
56
VTa(()
By Lemma I.6, we know that (t) 2 p log(t) for all nodes. Therefore:
== 21222(2) +2 2.2 " mini. Ae. 2n
36
(T)(()
9 2ln + p miny a And In(()
36
S
Vplog(t)
21n(2)
mins a Ar,d
a 5591 /6 plog(t)
36 log(t)/ In())
(40)
39

---

CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
For sufficiently large I, the first term becomes negligible, and after appropriate simplification:
ming, Ax.d
(41)
This is precisely what we need to bound our probability term. Applying Lemma L.7 with our chosen 7/:
minn Ap.
Akdd
(1)
P(NA.Tutn 2 PR +
S
4
Summing across all dimensions provides the bound:
5
ming, skid )2
1
36
P(XA..))) A + 2
constant x
(Lemma L.7)
(42)
The second term P(X; (1) A n² + + can be bounded through an analogous process. Combining these bounds and summing over all sub-optimal nodes yields:
miing And
P(,, P*) Σ
constant
UL
P(I P*) SCxt ming.
(43)
where C is a positive constant. This demonstrates that the failure probability converges zero polynomial rate, with the convergence speed determined by:
p: how quickly samples accumulate for each node
ming,a Ag. the minimum gap between sub-optimal and optimal nodes
By trivial limit convergence of positive functions, lim P(4 & P*) 0, which completes the proof.
The theorem implies the guaranteed convergence of node selection towards Pareto optimality at polyno- mial rate. In our work, this property is relevant nodes are single building block (to be combined), leading to product: one traversal of the synthesis tree only comprises single reaction step.
Interpretation
This design therefore allows a relatively fast convergence towards Pareto optimal products, contrarily to other Pareto MCTS methods. Appendices E.4 and F compare CombiMOTS to example Pareto MCTS methods (Molsearch and Mothra) in both generation quality and efficiency. For these methods, the slow Pareto convergence mainly due to their tree structure: node is represented as an intermediate molecule (single token addition for Mothra, augmentation rules for MolSearch). Therefore, suboptimal nodes are translated enormous amounts of possible molecules.
40

---

CombIMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation
M. Data Statistics
In tables below, / indicates that the molecule is active for the target, indicates inactivity, and NaN signifies that activity was measured for the target. The table presents the number molecules in each activity category combination.
Table 13. Distribution of molecules based on their activity against GSK33 and JNK3 targets.
GSK33
JNK3
# of molecules
190
X
70
V
NaN
3,013
X
9
NaN
707
X
X
7638
X
NaN
41,786
NaN
X
41,746
Table 14, Distribution of molecules based on their activity against EGFR and MET targets.
EGFR
MET
# of molecules
651
X
NaN
3,600
110
NaN
V
1,958
X
13
NaN
720
NaN
X
116
Table 15. Distribution molecules based on their activity against PIK3CA and mTOR targets.
PIК3СА
mTOR
# of molecules
766
X
32
NaN
1,368
21
NaN
2,012
7
NaN
170
NaN
43,048

---

CombiMOTS: Combinatorial Multi-Objectivy Tree Search for Dual-Target Molecule Generation
Table 16. Distribution of molecules based on their activity against DHODH and RORytt targets.
DHODH
RORet
# of molecules
NaN
1,168
NaN
5,868
42


Reviews:
[{"review_id": "p0937GgJG0", "reviewer": "Reviewer_6Myy", "summary": "This paper introduces CombiMOTS, a novel method for dual-target molecule generation.  It addresses the limitations of existing approaches, which often simplify the multi-objective nature of the problem into a linear combination of objectives and may not consider synthesizability.  CombiMOTS leverages Pareto Monte Carlo Tree Search (PMCTS) within a fragment-based drug discovery framework.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer **6Myy**, we appreciate your insights which helped improve our work! Particularly, ablation studies allowed us to strengthen our claims. We address your concerns below and through https://anonymous.4open.science/r/CombiMOTS-0FEB.\n\n---\nConcern\n-\n> A) \"SA score doesn't guarantee perfect synthesizability\".\n\nSee reply `4` to **KAF5**.\n\n---\nAsked Questions\n-\n> 1. **Computational Cost and Scalability** - *#Objectives*, *Runtime* & *Solution Convergence*.\n> 2. **Objective Function Design** - Docking Score over QED/SA.\n\n&rarr; See reply `I` to **pmFQ** and `2` to **KAF5**.\n> Have you experimented with different weightings[...]?\n\nTo clarify the use of weights, CombiMOTS uses property vectors to compute Pareto fronts and sample nodes: weights don't affect the relative difference between nodes.\n\n> 4. **Fragment Extraction** - FGIB & 6. **Ablation Study**\n\nFGIB extends the widely used BRICS [1] method by breaking molecules into retrosynthetically interesting fragments, which is preferred over rule/frequency-based methods when combined with Enamine REAL Space.\nSome works adapt BRICS to needs with a fixed goal (e.g. connectivity-awareness [MiCaM [2]], ADMET explanability [pBRICS [3]]), thus not suited for the dual-inhibition task where target proteins are user-defined.\nOur goal is to capture high-property fragments for any **target property**.\nTo further justify our choice, we report results from 10,000 rollouts on the GSK3B-JNK3 task when replacing FGIB with naive BRICS and MiCaM, a connection-aware motif-mining approach to decompose known active compounds.\n|Method|#BuildingBlocks|#PossibleProducts|#Dual-Actives|\n|-|-|-|-|\n|BRICS|4,430 (747 not found by FGIB)|~1.7M|1,815/12,559 (**14.45%**)|\n|MiCaM|12,274 (8,428 not found by FGIB)|~26M|1,445/13,263 (**10.90%**)|\n|FGIB (base)|14,366 (10,683 unique vs. BRICS, 10,520 vs. MiCaM)|~25M|3,662/15,423 (**23.74%**)|\n\nFGIB successfully identified goal-specific fragments, resulting in a **significantly higher rate** of \"dual-active\" compounds predicted to interact with both proteins. \n\nWe report metrics/distribution plots in the `rebuttal` folder of the anonymous github.\nAll methods exhibit similar performance, which is sound as FGIB only impacts the search space through the selection of **initial blocks**: MCTS objectives and convergence speed are \"as good\", but the attainable space contains less dual actives.\n> B) Potential limitations of FGIB.\n\nFGIB uses MLP-based modules to learn data features: its performance depends on data quality. However, our ablation study (`Appendix C.3`) demonstrates that combined with Pareto MCTS, data scarcity is alleviated to some extent.\n\n> 5. **Search Space Reduction** - Thresholds & 6. **Ablation Study** - Search Space Reduction\n\nWe investigate the use of various thresholds and report results from 10k rollouts on the GSK3B-JNK3 task for lower and higher values of 0.3, 0.5 & 0.6.\n|Threshold|# Blocks|# Possible Products|# Dual-Actives|\n|-|-|-|-|\n|0 (Full Space)|139,493|>31B|(not done)|\n|0.3|54,811|~478M|2,833/13,556 **(20.90%)**|\n|0.4 (base)|14,366|~25M|3,662/15,423 **(23.74%)**|\n|0.5|3,737|~1.1M|1,380/11,632 **(11.86%)**|\n|0.6|858|~43K|317/9433 **(3.36%)**|\n\nYou may refer to metrics and figures added to the repository.\nWe make three observations:\n\n- The threshold greatly affects the search space size due to the small nature of FGIB fragments and Enamine blocks. Tanimoto metric being fingerprint-based, changing a small motif is relatively impactful.\n- For higher thresholds, the search space is too small to allow good exploration. There is a significant drop in #dual-actives, and metrics also show that using thresholds above 0.6 yield a drop in diversity (88.67→78.73%) and consistency across molecular properties.\n- For lower thresholds, CombiMOTS has \"more room to explore\" but finds worse tradeoffs across QED and #dual-actives. As more reactions are possible, Pareto fronts are larger and convergence to optimal solutions is slower (see `H) Theroretical Analysis` to reviewer **pmFQ**).\n\nOptimal thresholds are specific to the target properties, but our experiments suggest that a search space of magnitude 10M yields better convergence within a reasonable budget (~10k rollouts).\n\n> 3. Generalizability\n\nWhile dual-target inhibition is our main task, we design CombiMOTS can be adapted by customizing property oracles as objectives, or by targeting specific biological systems, narrowing the search space on fragments of interest.\n\nAmong applications, reviewer **KAF5** and yourself mentioned:\n- Protein-Protein Interaction (PPI) modulator discovery, where search can aim to uncover molecules tailored to PPI interface [Hot2Mol [4], GENiPPI [5]].\n- Toxicity Optimization (see reply `6` to **KAF5**).\n- Molecular Selectivity (see discussion `B` with **KAF5**).\n\n---\nReference\n-\n[1] Degen et al., *ChemMedChem*, 2008\n\n[2] Geng et al., *arXiv*, 2023\n\n[3] Vangala et al., *JCIM*, 2023\n\n[4] Sun et al., *bioRxiv*, 2024\n\n[5] Wang et al., *J. Cheminform.*, 2024", "claims_and_evidence": "The claims made in the submission are generally well-supported by the evidence provided. \n\n*   **Claim:** CombiMOTS outperforms existing methods in generating dual-target molecules with better trade-offs between target engagement and molecular properties.\n    *   **Evidence:**  Table 1 and Figures 3, 6, and the supplementary figures provide strong quantitative evidence.  CombiMOTS consistently achieves higher novelty and diversity scores, while maintaining competitive or superior docking scores compared to the baselines. The density plots visually demonstrate the superior trade-offs.\n    *   **Concerns:** None major.\n\n*   **Claim:** The use of Pareto optimization is crucial for achieving these improved trade-offs.\n    *   **Evidence:**  The comparison with the scalarized version of CombiMOTS (Figure 7 and Appendix C.1.1) provides compelling evidence.  The scalarized version performs worse in terms of finding balanced properties, highlighting the importance of the Pareto approach.\n    *   **Concerns:** None major.\n\n*   **Claim:** The fragment-based approach and use of the Enamine REAL Space ensure synthesizability.\n    *   **Evidence:**  The methodology section clearly describes the process of mapping fragments to REAL Space building blocks and using reaction templates. The reported SA scores are generally low, indicating good synthesizability. The comparison with Swanson et al. (2024), who focused on the REAL space.\n    *   **Concerns:** While SA score is a good proxy, it's not a perfect guarantee of synthesizability. Experimental validation would *strengthen* this claim, but is beyond the scope of a typical ML paper.\n\n* **Claim:** CombiMOTS has practical utility, analysis of Case Studies\n    * **Evidence:** Analysis of case studies for compounds generated for GSK3B-JNK3.\n    * **Concerns:** None.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are generally appropriate for the problem.\n\n*   **Methods:** The use of PMCTS is a well-established technique for search and optimization.  Adapting it to a combinatorial, multi-objective, and fragment-based setting for drug discovery is novel and well-motivated.  The use of the Enamine REAL Space is a good choice for ensuring synthesizability.\n*   **Evaluation Criteria:**  The chosen metrics (validity, uniqueness, novelty, diversity, docking score, QED, SA) are standard and relevant for evaluating generative models in drug discovery.  Using multiple target pairs (including newly curated datasets) strengthens the evaluation.  Comparing against relevant baselines (RationaleRL, REINVENT, MARS) is also appropriate.\n*    **Concerns** The justification for choosing to prioritize the molecular docking score, other than the other metrics, is not solid.", "theoretical_claims": "The paper does not present significant theoretical claims in the form of theorems and proofs.  The theoretical underpinning is the application of Pareto optimality and MCTS, which are well-established concepts. The description of Pareto dominance and Pareto fronts is correct.", "experimental_designs_or_analyses": "The experimental designs are generally sound.\n\n*   **Datasets:**  Using established datasets (GSK3β-JNK3) and curating new ones (EGFR-MET, PIK3CA-mTOR) according to established protocols is good practice.  The data curation process is described in detail in the appendices.\n*   **Baselines:**  The chosen baselines are relevant and represent different approaches to molecule generation.  The authors made efforts to reproduce the baselines in their best reported settings and even adapted them to use docking scores as objectives for a fairer comparison.\n*   **Metrics:**  The use of multiple metrics to evaluate different aspects of the generated molecules is comprehensive.\n*   **Ablation Studies:**  The comparisons with the scalarized version of CombiMOTS and the six-objective version (in the appendix) are valuable ablation studies that demonstrate the importance of the Pareto approach and provide insights into the impact of adding more objectives.\n*    **Concerns:** Ablation study of the Fragment Extraction and Search Space Reduction is missing.", "relation_to_broader_scientific_literature": "The paper is well-situated within the broader scientific literature on drug discovery, generative models, and multi-objective optimization. It builds upon:\n\n*   **Fragment-Based Drug Discovery (FBDD):**  The paper clearly positions itself within the FBDD paradigm and cites relevant work.\n*   **Generative Models for Molecules:**  It cites and compares against relevant generative models, including VAE-based, RL-based, and MCMC-based approaches.\n*   **Multi-Objective Optimization:**  It correctly references Pareto optimization and its application in other fields.\n*   **Monte Carlo Tree Search (MCTS):**  It builds upon existing work on MCTS and PMCTS, citing relevant papers.", "essential_references_not_discussed": "Essential related works have been discussed.", "other_strengths_and_weaknesses": "**Strengths:**\n\n*   **Novelty:** The combination of PMCTS with a combinatorial, fragment-based approach for dual-target molecule generation is novel and well-motivated.\n*   **Effectiveness:** The experimental results demonstrate that CombiMOTS outperforms existing methods on the chosen tasks.\n*   **Synthesizability:** The focus on synthesizability through the use of the Enamine REAL Space is a significant strength.\n*   **Comprehensive Evaluation:**  The use of multiple metrics and target pairs, along with ablation studies, provides a thorough evaluation.\n\n**Weaknesses:**\n\n*   **Computational Cost:** The paper acknowledges the computational cost of PMCTS, particularly with more objectives.  While the authors provide runtimes, a more detailed discussion of scalability and potential optimizations could be helpful.\n* **Justification of Docking score:** The paper needs more justification, why molecular docking score is the main objective.\n*   **Limited Scope:** The evaluation is limited to three dual-target pairs and a specific set of objectives.  While this is understandable, it would be interesting to see how CombiMOTS performs on a wider range of tasks and with different objective functions.\n* **Missing Ablation study**: The ablation study is missing for Fragment Extraction and Search Space reduction steps.", "other_comments_or_suggestions": "Reference to the **Weaknesses** part.", "questions_for_authors": "1.  **Computational Cost and Scalability:** Can you elaborate on the scalability of CombiMOTS, particularly as the number of objectives or the size of the search space increases?  Are there any specific optimizations you have considered or plan to explore to improve efficiency? How does the computational cost compare to the baselines (even if approximate)?\n2.  **Objective Function Design:** You prioritize docking scores over QED and SA.  Could you elaborate on the rationale behind this choice?  What are the potential limitations of this prioritization, and how might it affect the generated molecules? Have you experimented with different weightings or combinations of objectives, and if so, what were the results?\n3.  **Generalizability:** How do you envision CombiMOTS being applied to other drug discovery tasks beyond dual-target inhibitor design?  Could it be adapted to handle different types of targets (e.g., protein-protein interactions) or different objective functions?\n4.  **Fragment Extraction:** Could you elaborate on the choice of FGIB for fragment extraction? Were other fragment extraction methods considered, and if so, why was FGIB chosen? What are the potential limitations of the chosen fragment extraction method?\n5. **Search Space Reduction.** How sensitive is the performance of CombiMOTS to the Tanimoto similarity threshold used for search space reduction? Did you perform any experiments to optimize this threshold?\n6. **Ablation Study**: The ablation study of the Fragment Extraction and Search Space Reduction steps, are important to show the efficiency of the whole pipeline.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sgiuZne2z7", "reviewer": "Reviewer_h6f3", "summary": "The paper introduces CombiMOTS, a Pareto Monte Carlo Tree Search (PMCTS) framework for generating dual-target molecules, which are molecules that can interact with two target proteins simultaneously. The authors argue that existing methods often simplify the dual-target optimization problem by linearly combining objectives and neglecting synthetic planning. CombiMOTS addresses these challenges by exploring a synthesizable fragment space and using vectorized optimization constraints to encapsulate target affinity and physicochemical properties. The authors claim that experiments on real-world datasets demonstrate that CombiMOTS generates novel dual-target molecules with high docking scores, enhanced diversity, and balanced pharmacological characteristics. The core idea combines PMCTS with a fragment-based approach and a focus on synthesizability using the Enamine REAL Space.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer **h6f3**, thank you for your constructive review which improved our perspective! Particularly, your comments provided more clarity regarding the Pareto superiority against baselines. We address your concerns below and through https://anonymous.4open.science/r/CombiMOTS-0FEB.\n\n---\nConcerns & Replies\n-\n>A) On \"linear combination of individual objectives\" and other scalarizing methods.\n\nWe acknowledge the misuse of “linear combination” as the sole example of scalarization method. We revise our statement by generalizing the advantage of vectorized pareto optimization over scalarized methods – including those mentioned by the reviewer - for the reasons below:\n- Hypervolume assesses the quality of a solution set relative to a reference set: in the dual-target paradigm, baseline sets are either scarce or non-existing, making it hard to use in our task. `Appendix C.3` hints at the capability of CombiMOTS to still effectively find solutions in case of data scarcity.\n- Following your suggestion, we assess each model's ability to discover Pareto optimal molecules by computing their respective first Pareto front and reporting their average R2-distance to utopian point (normalized in range [0 to 2] - lower is better), as well as the size of the Pareto optimal set in parenthesis.\n\n|Model/Task|GSK3B-JNK3|EGFR-MET|PIK3CA-mTOR|\n|-|-|-|-|\n|**CombiMOTS**|0.8075 **(174)**|**0.8419 (268)**|0.8143 **(210)**|\n|**MARS**|**0.7830** (102)|0.8845 (142)|0.8144 (89)|\n|**RationaleRL**|0.8307 (137)|0.9388 (148)|0.8852 (113)|\n|**REINVENT**|0.8223 (93)|0.8518 (177)|**0.8035** (174)|\n\nThe main takeaway is that even though all methods present a good overall score, CombiMOTS consistently finds **more Pareto optimal solutions** than others.\nHowever, this scalarized score doesn't allow identifying inconsistencies among baselines. To clarify this point, we plot radar charts across all metrics used in the manuscript and publish them in the `rebuttal` folder of the anonymous github. \n\n>B) \"Selected metrics don't seem useful in Table 1.\"\n\nLike other visualizations, the role of Table 1 is to highlight inconsistencies of the baselines across metrics (including distribution plots): in all tasks, all baselines perform poorly in at least one metric. Only CombiMOTS performs equally or better than baselines regardless of the task/metric.\n\nAbout validity: even if only few generations are invalid, it demonstrates a critical flaw in the model not respecting fundamental chemical rules. CombiMOTS use SMARTS-based chemical templates, conformed to real reactions.\n\nAs requested by reviewers **pmFQ/KAF5**, we revise Table 1 to be statistically more robust and meaningful. See reply `5` to **KAF5** for details.\n>C) \"Selected metrics may be problematic[...]\"\n\nWe sincerely thank the reviewer for raising the concern about the limitations of using such metrics. In the mentioned paper, we acknowledge that \"even the best in silico scores remain fruitless if the suggested compounds cannot be synthesized.\" Ideally, synthesizing molecules and performing assay experiments would provide the most reliable validation; however, we also agree with reviewer **6Myy** as this typically exceeds the scope of machine learning papers. Thus, like many existing works in this field, we rely on widely-used computational metrics primarily to fairly compare methodologies.\n\n>D) \"It looks like RationaleRL is quite successful as well.\"\n\nWe list the weaknesses of RationaleRL in our experiments:\n- GSK3B-JNK3: Low uniqueness and lowest diversity;\n- EGFR-MET: Low diversity, weak binding affinity with MET (Fig.6A) and high SA score;\n- PIK3CA-mTOR: Low uniqueness, novelty, diversity and fairly low QED score (Fig.6B).\n\nWe discuss the low diversity of RationaleRL. Its workflow revolves around (i) extracting and merging \"rationales\" from high-property compounds, (ii) training & finetuning a graph completion module to obtain novel molecules from the merged rationales. Generation occurs by autoregressively complete the same structural cores, thus leading to poor diversity.\nWe plot and add (to the repository) t-SNE figures of generated compounds from all models: RationaleRL generations are clustered. In drug design, RationaleRL is better suited for Lead Optimization rather than Hit Discovery.\n\n>E) Suggested References\n\nWe thank the reviewer for suggesting related material. We will integrate similar topics to our related work. In the meanwhile, we comment on how our work differs:\n\nMultiobjective JANUS focuses on molecular optimization, not de novo design. [1]\n\nSynNet [2] and MEEA* [3] tackle synthesis planning, which answers: \"How can we synthesize this molecule given available stock?\"\nThis is the inverse of our approach, which asks: \"Given available stock, what optimal products can be created?\" See reply `4` to **KAF5** for more about our motives.\n\n---\nReference\n-\n[1] Kusanda et al., *NeurIPS'22*, 2022\n\n[2] Gao et al., *arXiv*, 2021\n\n[3] Zhao et al., *Commun. Chem.*, 2024", "claims_and_evidence": "CombiMOTS is able to perform dual-target optimization. The authors claim that there are intricacies in dual-target optimization that cannot be captured due to simplification by \"linear combination of individual objectives\", but there are other scalarizing methods (by hypervolume, or distance to utopia point). \n\nThe results in Table 1 seem to indicate the metrics used there are not particularly useful, with almost all models achieving scores of >99%. Evaluating generative model quality by validity, uniqueness, novelty, and diversity have been noted as problematic (https://www.sciencedirect.com/science/article/pii/S1740674920300159).", "methods_and_evaluation_criteria": "It would strengthen the claims of the pareto MCTS being superior if the optimal tradeoffs were quantified, rather than in distribution plots of Figure 3 and 6. A score that quantifies the optimality of the pareto-optimal point? From the plots, it looks like RationaleRL is quite successful as well in the multi-objective task.", "theoretical_claims": "There are no theoretical claims made.", "experimental_designs_or_analyses": "The design is logical and sound, however, may be limited in novelty. The authors used a fragment-based tree search to generate synthesizable molecules, and added multi-objective Pareto optimal score, with no significant advancements in either methods. However, I appreciate the non-triviality of implementing this workflow. Additionally, tt is also not clear that CombiMOTs are better than the models presented.", "relation_to_broader_scientific_literature": "The work builds upon tree search generation methods for objective oriented molecular generation.", "essential_references_not_discussed": "- Multiobjective benchmarking for generative models\n  - PMO (https://arxiv.org/abs/2206.12411)\n- Pareto-optimal generation (https://openreview.net/pdf?id=sWRZxIcR8qK)\n\nTree-search methods based on fragments and rules based generation have been explored before. \n- https://arxiv.org/pdf/2110.06389\n- https://proceedings.neurips.cc/paper_files/paper/2020/file/4cc05b35c2f937c5bd9e7d41d3686fff-Paper.pdf\n- https://www.nature.com/articles/s42004-024-01133-2", "other_strengths_and_weaknesses": "Strengths:\n- Clear problem definition and motivation.\n- Focus on synthesizability is key for molecular generation\n- Easy to read and follow\n\nWeakness:\n- It is not clear that the claims of CombiMOTs producing dual-target molecules is better than other methods. For example, is it possible to perform a similar case study with a candidate generated by RationaleRL?  A metric to distinguish the pareto-optimal solution being better from CombiMOTS would be beneficial.\n- The idea of using synthesizability routes and fragments to give realistic molecules is not new, particular the combination of tree-search methods with retrosynthetic routes (see early response). \n- Limited novelty\n- Other scalarizing methods that consider pareto-optimization are not considered.", "other_comments_or_suggestions": "The discussion on pareto optimization can be shortened. The comparison to scalarized results CombiMCTS are important to demonstrate the effect of PUCB optimization, and should be in the main text.", "questions_for_authors": "Please see comments above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "1rkyrV641w", "reviewer": "Reviewer_pmFQ", "summary": "The paper proposes CombiMOTS, a combinatorial multi-objective tree search framework for dual-target molecule generation. It integrates Pareto Monte Carlo Tree Search (PMCTS) with fragment-based synthesis-aware generation. Key contributions include: (1) A reduced synthesizable fragment space via target-aware building blocks; (2) A Pareto-optimized MCTS algorithm for balancing conflicting objectives (target affinity, QED, SA); (3) Empirical validation showing superior performance in generating diverse, synthesizable molecules with balanced properties compared to baselines.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer **pmFQ**, thanks for providing valuable feedback to our work! The requested theoretical analysis on PUCB significantly clarifies convergence speed and solution optimality. We address your concerns and questions below and through https://anonymous.4open.science/r/CombiMOTS-0FEB.\n\n---\nConcerns\n-\n>A) \"Table 1 lacks statistical significance.\"\n\nFollowing you and **KAF5**, we update Table 1 to improve robustness and relevance. See reply `5` to **KAF5**.\n\n>B) Overfitting concerns - Toxicity prediction\n\nWe thank the reviewer for highlighting the small size of ClinTox; we agree models trained on limited data lack real-world accuracy. Our use of ClinTox is intended primarily as a case study due to its clinical relevance (toxicity assays on FDA-approved drugs), despite toxicity data being generally scarce. Nevertheless, ClinTox remains a critical resource for evaluating machine learning models in drug toxicity prediction [1]. We will explicitly underline this limitation in future revisions.\n\n>C) Unfair objective settings across models.\n\n`Appendix C.2` reimplements REINVENT and MARS with our settings (docking score and bioactivity prediction) to investigate alignment of objectives. \nIf needed, we will release our implementations of adapted baselines.\n>D) Compared computational cost to baselines.\n\nSee reply `2` to **KAF5**.\n\n>E) Broader literature: \"Recent Pareto MCTS variants (e.g., Yang et al., 2024a) are not discussed.\"\n\nThank you for highlighting this. Our manuscript briefly cites Yang et al. (2024a) (lines 81-82); we further discuss its broader relevance (see reply `1` to **KAF5**).\n\n>F) Page 2: \"Fromer & Coley, 2023; Luukkonen & Maagdenberg, 2023\" lack full references.\n\nThanks! We will complete references.\n\n>G) Algorithm 1: Line 16 uses \"max(v, selected.P)\"—unclear if \"max\" applies to vectors.\n\nAlgorithm 1 omits details for readability. Algorithm 2 (line 17) specifies \"max\" as element-wise, common in vectorized Pareto MCTS [2].\n\n---\nAsked Questions\n-\n\n>H) **Theoretical Analysis**: Computational Cost & Pareto-optimal Convergence.\n\nOur manuscript had typos in `Equation 8` and `Algorithm 2` (l.36) on the PUCB formula, omitting a constant of 4. We correct it to: \n$\\vec{PUCB(n)} \\gets \\frac{\\vec{R(n)}}{N(n)}+C*\\vec{Oracles}\\sqrt{\\frac{ln(D)+\\textbf{4}*ln(1+N(p))}{1+N(n)}}$.\nWe provide theoretical grounding by adapting theorems from [ParetoMCTS]. Due to space limits, we summarize key statements below:\nUnder assumptions satisfied by our D-dimensional problem setting,\n- **Theorem 1**: Consider a node with a child node $v_k$ visited $T_k(n)$ times in $n$ steps. \nIf $v_k$ is a sub-optimal node, $\\mathbb{E}(T_k(n))$ is logarithmically bounded.\n$\\forall \\xi>0, \\exists N_0(\\xi) \\in \\mathbb{N^*}, \\text{such that}  \\ (n \\geq N_0(\\xi)) \\implies \\mathbb{E}[T_k(n)] \\leq \\frac{8ln(n) + 4ln(D)}{(1-\\xi)^2 * (\\underset{k,d}{min}\\Delta_{k,d})^2} + N_0(\\xi) + O(1),$ where $(\\underset{k,d}{min}\\Delta_{k,d})$ is the minimum reward gap (across D dimensions) between $v_k$ and its most dominant node in the Pareto front (i.e. the \"farthest away\").\nThis bound implies: (i) the logarithmic regret $\\alpha ln(n)$ implies that sub-optimal node selections decrease over time. (ii) The denominator depends on the minimum reward gap, implying lower regret when sub-optimal nodes are more distinguishable from the Pareto front. (iii) Increasing the number of objectives D also increases regret by a logarithmic factor $\\beta ln(D)$, but makes it harder to distinguish sub-optimal and Pareto nodes, directly impacting (ii).\nThus, (ii) and (iii) motivate us to wisely select our objectives.\n\n- **Theorem 2**: With $I_t$ the selected child node at step $t$ and $(C,\\rho$) constants, $\\mathbb{P}(I_t$ is sub-optimal$)\\leq Ct^{-\\frac{\\rho}{2}\\left(\\frac{ \\min_{k,d}\\Delta_{k,d} }{36}\\right)^2} \\xrightarrow{t\\infty}0.$\nThis implies the guaranteed convergence towards optimal nodes at a polynomial rate. In our work, we aim to approach optimal solutions in a reasonable time, thus the need to properly select objectives, efficient oracles and search space size (ablations asked by **6Myy**).\n>I) Why prioritize Docking Scores over QED/SA?\n\nWe list our motives below:\n- Fingerprint-based predictions lack structural interpretability (e.g. RationaleRL, MARS, [MolSearch suggested by **KAF5**]) compared to *in-silico* docking simulation.\n- Experiment `C.1.2` suggests that using all objectives leads to worse tradeoffs due to the larger Pareto fronts (now supported by question `H`). An additional experiment (50k rollouts optimizing QED/SA over docking scores) is reported in the repository. We observe that QED slightly increased at the cost of much worse docking scores but the inverse is not true: not considering QED/SA during search still converges towards good scores.\n- As we use Enamine REAL Space, we discuss the non-necessity of SA score (see reply `4` to **KAF5**).\n---\nReference\n-\n[1] Tran et al., *JCIM*, 2023\n\n[2] Yang et al., *Commun. Biol.*, 2024", "claims_and_evidence": "Claims about \"superior diversity\" (Table 1) lack statistical significance tests (e.g., p-values).\n\nToxicity prediction (Section 6.2) uses an ensemble of Chemprop models trained on a small dataset (1,478 molecules), risking overfitting.", "methods_and_evaluation_criteria": "Use of industry-ready Enamine REAL Space ensures practical synthesizability. Pareto optimization aligns with multi-objective drug design.\nHowever, docking scores are prioritized over QED/SA without justification. This may bias results toward unrealistic molecules.", "theoretical_claims": "The Pareto UCB formula (Equation 8) combines scalar exploration terms with vectorized rewards. This lacks theoretical grounding—how does it guarantee Pareto optimality?", "experimental_designs_or_analyses": "Concern: Baseline implementations (e.g., REINVENT) use different objectives (QED-only vs. docking scores), making comparisons unfair.\n\nIssue: Computational cost of CombiMOTS (25s/rollout for 6 objectives) is not compared to baselines.", "relation_to_broader_scientific_literature": "The work builds on Swanson et al. (2024) but extends MCTS to multi-objective settings. However, recent Pareto MCTS variants (e.g., Yang et al., 2024a) are not discussed.", "essential_references_not_discussed": "Pareto optimization in drug design: Medina-Franco et al. (2013) proposed multi-target optimization frameworks.\n\nMulti-objective RL: Yang et al. (2024a) applied Pareto MCTS to molecule generation but is uncited.", "other_strengths_and_weaknesses": "Weaknesses: Methods are well-described, but theoretical justification for Pareto UCB is unclear.", "other_comments_or_suggestions": "Page 2: \"Fromer & Coley, 2023; Luukkonen & Maagdenberg, 2023\" lack full references.\n\nAlgorithm 1: Line 16 uses \"max(v, selected.P)\"—unclear if \"max\" applies to vectors.", "questions_for_authors": "How does the Pareto UCB formula ensure convergence to Pareto-optimal solutions? A theoretical analysis is needed.\n\nWhy prioritize docking scores over QED/SA in objectives? Would including all metrics (as in Appendix C.1.2) improve practicality?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "IQKuN8JBGy", "reviewer": "Reviewer_KAF5", "summary": "The paper introduces CombiMOTS - a Pareto Monte Carlo Tree Search based approach that is designed to efficiently handle complex multi-objective optimization problems. In particular, the authors tackle the dual-targeting molecule generation problem and evaluate the framework using three protein pairs. For this, they narrow down a large molecule fragment space into a synthesizable one and generate molecules with optimization of docking scores against two proteins.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear reviewer **KAF5**, thank you for your constructive suggestions. We address your concerns below and through https://anonymous.4open.science/r/CombiMOTS-0FEB.\n\nConcerns\n-\n\n### 4. Synthesizability Metrics and Retrosynthetic Evaluation\n\nWe assess CombiMOTS's synthesizability against baselines to justify using Enamine rather than post-hoc evaluation.\n\nSynthesizability metrics can be:\n- **Rule-based** (e.g., SAscore): Efficient but fail to capture real-world constraints.\n- **Retrosynthetic-based**: Recursively breaking down a target into industry-available precursors. However, it is expensive and limited to reference stocks (e.g.,Aizynthfinder [1] on the ZINC database). We use the opposite workflow (from precursors, find optimal solutions within bounded iterations - see reply `H` to **pmFQ**)\n- **Learning-based** (e.g., RAscore, BR-SAscore): Context-adaptable but data-dependent.\n> Note: Enamine’s 80% synthesis success rate and SyntheMol’s experimental validations [2] motivate practical synthesis over mere metric evaluation.\n\n#### Comparative Analysis\n- **Density Distributions:**\n  Density distributions (in repo) include:\n  - Generated molecules (all models)\n  - Enamine building blocks (expects high synthesizability)\n  - COMPAS-3 dataset [3] (contains hard-to-synthesize polycyclic compounds)\n- **Observations:**\n  - COMPAS-3 is deemed synthesizable by SA & RAscore but not by BR-SAscore.\n  - Enamine excels on RAscore but performs similarly or worse on other metrics.\n  - MARS unrealistically outperforms Enamine on SA/BR-SAscore.\n  - CombiMOTS outperforms baselines on RAscore but aligns with/worsens on others.\n#### Aizynthfinder [1] Retrosynthetic Study\nAmong 1544 CombiMOTS molecules, 162 (10.42%) are not solved by Aizynthfinder—due to its ZINC dependency (example in repo).\nThese inconsistencies among metrics underscore why leveraging available precursor data is relevant to our motives.\n\n>B) Selective molecule generation\n\nWe explore a workflow for CDK7 inhibitors as a case study. Off-targets (CDK1, 2, 9, 12, 13) are reported in [4,5].\n\nCombiMOTS could be adapted by:\n- Searching compounds maximizing CDK7 activity and minimizing off-target activity.\n- Narrow the search space on known active scaffolds/warheads.\n- Post-hoc filtering (medicinal chemistry, in-silico validation). While preliminary and beyond the scope of our current work, repository statistics summarize this workflow.\n\nOther Questions\n-\n>1. Additional Baselines\n\nWe thank the reviewer for suggesting references to integrate in future versions. We note distinctions with CombiMOTS:\n- DrugSynthMC [6] generates drug-like molecules using n-grams but lacks support for protein target setting.\n- ParetoDrug [7] extends PMCTS to protein-specific generation via atom-based, Lmser transformer models. Though cited, this method remains single-target (no multi-target code).\n- Mothra [8] is PMCTS-based but limited to single-target RNN decoding.\n- MolSearch [9] tackles on dual-target optimization rather than de novo generation by combining PMCTS with fragment-based \"design moves\".\n\nWe adapt Mothra and MolSearch to the GSK3B-JNK3 task. Repository metrics/plots show CombiMOTS's superiority across all metrics, likely due to:\n- Mothra relying on single token additions.\n- MolSearch's dependence on learned augmentation rules\n    - Both require extensive sampling for Pareto convergence (see reply `H` to **pmFQ**).\n- In contrast, CombiMOTS's node structure leads to products in a single reaction, leading to faster convergence.\n\n>2. Efficiency & 7. Runtime\n\nOne CombiMOTS tree traversal runs in $O(1)$ time, with hash table lookups (precomputed scores) being the main overhead when creating child nodes. However, oracles are called whenever a product is found: the computational overhead is bounded by the slower operation between $O(n_{children})$ and $\\text{Oracles(product)}$.\n\nRuntimes of all evaluated models are in the repository. Notably, competing PMCTS methods are significantly slower.\n\n>3. Interpretable compounds.\n\nIn Fragment-Based Drug Design, it means explaining molecular property through the fragments it is built upon. Here, FGIB helps find more dual-actives (see reply `4` to **6Myy**)\n>5. Error rates of Table 1. \n\nWe update Table 1 with error rates, p-values, and separate evaluation of baselines for dual-active generation. CombiMOTS, as a search algorithm, returns all found products, making comparisons with generative models irrelevant.\n\n>6. Toxicity Optimization\n\nWe add plots in repository for the corresponding ablation study to conclude on CombiMOTS's ability to optimize non-toxicity.\n\nReference\n-\n[1] Genheden et al., *J. Cheminform.*, 2020\n\n[2] Swanson et al., *Nat. Mach. Intell.*, 2024\n\n[3] Wahab and Gershoni-Porane, *PCCP*, 2024\n\n[4] Constantin et al., *Br. J. Cancer*, 2023\n\n[5] Olson et al., *Cell Chem. Biol.*, 2019\n\n[6] Roucairol et al., *J. Cheminform.*, 2024\n\n[7] Yang et al., *Commun. Biol.*, 2024\n\n[8] Suzuki et al., *JCIM*, 2024\n\n[9] Sun et al., *KDD'22*, 2022", "claims_and_evidence": "1. The paper provides strong evidence that CombiMOTS generates molecules with better docking scores, diversity, and novelty. However, synthetic accessibility is not discussed in detail. The authors report SA scores, which are calculated based on the molecular structures, but do not include a retrosynthesis validation study to check if the proposed molecules can truly be synthesized.\n\n2. The authors demonstrate that CombiMOTS consistently outperforms existing methods, however it seems that several important baselines are missing. Additionally, it is not quite clear how the proposed approach compares to baselines in terms of efficiency.", "methods_and_evaluation_criteria": "The proposed CombiMOTS method, real-world cases and evaluation criteria (originality and quality) do make sense for the problem of dual-targeting molecule generation. However, it is not quite evident how the proposed methodology compares to other existing approaches.", "theoretical_claims": "Not applicable.", "experimental_designs_or_analyses": "1. In Table 1 error rates are missing. It would be interesting to see how consistent CombiMOTS is and how it compares to other models in terms of stability of metrics.\n2. The authors evaluate their approach in terms of toxicity of generated molecules. It would be more informative to evaluate the impact of toxicity optimization in an ablation study.\n3. Although synthetic accessibility score is a common metric to estimate synthetic complexity of a compound, there are more advanced metrics capturing not only structural features of a molecule, but also possible retrosynthetic pathways (e.g., BR-SAscore and RAscore). Authors should consider calculating these metrics if they claim that synthetic accessibility of generated molecules increases.", "relation_to_broader_scientific_literature": "The issue of multi-objective fragment-based molecular optimization has been investigated in various studies. The use of Pareto MCTS for molecular generation was studied in [1]. The novelty of the proposed approach lies in the application of Pareto MCTS for dual-targeting molecule generation.\n\n[1] Yang, Yaodong, et al. \"Enabling target-aware molecule generation to follow multi objectives with Pareto MCTS.\" Communications Biology 7.1 (2024): 1074.", "essential_references_not_discussed": "FREED++ framework [1] was not cited, although it performs fragment-based molecule generation using RL and was reported to outperform REINVENT in certain scenarios. There are several models for multi-objective drug optimization that use MCTS [2-5] which were not cited. The authors should also consider adding these models as baselines. There is also one recent paper that introduces Pareto optimization for drug design [6].\n\n[1] Telepov, Alexander, et al. \"FREED++: Improving RL Agents for Fragment-Based Molecule Generation by Thorough Reproduction.\" arXiv preprint arXiv:2401.09840 (2024).  \n[2] Suzuki, Takamasa, et al. \"Mothra: Multiobjective de novo molecular generation using monte carlo tree search.\" Journal of Chemical Information and Modeling 64.19 (2024): 7291-7302.  \n[3] Roucairol, Milo, et al. \"DrugSynthMC: An Atom-Based Generation of Drug-like Molecules with Monte Carlo Search.\" Journal of Chemical Information and Modeling 64.18 (2024): 7097-7107.  \n[4] Sun, Mengying, et al. \"Molsearch: search-based multi-objective molecular generation and property optimization.\" Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining. 2022.  \n[5] Qian, Hao, et al. \"AlphaDrug: protein target specific de novo molecular generation.\" PNAS nexus 1.4 (2022): pgac227.  \n[6] Yang, Yaodong, et al. \"Enabling target-aware molecule generation to follow multi objectives with Pareto MCTS.\" Communications Biology 7.1 (2024): 1074.", "other_strengths_and_weaknesses": "Strengths:\n1. The research in generation of dual-targeting molecules is topical and important for the broad scientific community.\n2. The paper is easy to follow. The plots and figures are visually attractive.\n\nWeaknesses:\n1. It seems that the idea of using Pareto MCTS for molecule generation is not novel. Although generating dual-targeting molecules is a more complex task, it is very similar to the conventional multi-objective molecule optimization.\n2. Some aspects of experimental design and analyses need improvements, e.g., inclusion of more baselines and experimental studies on robustness and efficiency of the presented approach.\n3. Not all the relevant papers on this topic were cited suggesting that the authors might not be aware of many significant developments in the field.\n4. Some claims are not supported with clear evidence or just vague  (e.g., about the proposed method generating interpretable compounds or the better synthetic accessibility of the generated molecules).", "other_comments_or_suggestions": "1. The experiment reported in section C.1.1 of the Appendix demonstrates that Pareto optimization leads to better-balanced trade-offs than a naive scalarized reward function. It would be also interesting to investigate how adding Pareto optimization impacts the computational costs required to generate molecules.\n2. Comparison of CombiMOTS to baselines in terms of time was not reported, although given the complexity of multi-objective drug optimization, it would be interesting to see how much time is required for the proposed approach to achieve a certain quality of molecules.\n3. Exploring the aspect of selective molecule generation could be beneficial, as technically the idea remains the same, while expanding the scope of the study. Additional case studies to this point would strengthen the work by better demonstrating its practical utility.", "questions_for_authors": "1. Why were only the three baselines considered? Why not consider other SOTA models that use MCTS, Pareto optimization and/or diffusion?\n2. The reported 11s/rollout time means that full runs take days. How does this compare to the other methods in terms of efficiency?\n3. What does “interpretable” compounds in line 96 mean? What are the statistically solid results supporting that claim?\n4. Is it possible to provide a retrosynthetic evaluation of the generated molecules?\n5. Is it possible to calculate standard deviations for metrics in Table 1 (e.g., after several runs with different random seeds)?\n6. Is it possible to compare CombiMOTS with and without toxicity optimization to see the differences more clearly?\n7. Is it possible to compare CombiMOTS with baselines in terms of time?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes CombiMOTS: a method utilizing Pareto MCTS to search for molecules simultaneously optimizing affinity towards two targets. To ground the generations in a synthetically accessible space, the authors project target-specific fragments to available building blocks, and then use those to assemble final molecules.

After a fruitful rebuttal period that lead to several score increases, all reviewers were voting to accept this paper, although weakly so. On the positive side, reviewers enjoyed the good quantitative performance of CombiMOTS, as well as its solid motivation and practical design. On the negative side, reviewers asked for further ablations, statistical analyses, and discussion of theoretical underpinnings, all of which were subsequently discussed by the authors. Some reviewers also noted somewhat limited novelty, with CombiMOTS mostly being a combination of pre-existing techniques; however, this point is itself of limited importance in the applications track, where practicality is the main concern.

After reviewing all available information and reading the paper in detail, I believe this manuscript is a decent contribution to ICML's program. Although not highly innovative, CombiMOTS could be interesting to practitioners. Therefore, I (weakly) recommend acceptance of this paper. My main reason for not going for a stronger recommendation is that CombiMOTS may not be as widely applicable as some other methods, thus perhaps interesting to a slightly narrower audience than an average ICML-accepted paper in the field of AI for Science. Finally, I would encourage the authors to incorporate reviewer feedback into the final version of their paper, and spend some extra time polishing the text and LaTeX notation; having read the work myself I believe it would be nice to make the reading experience a bit smoother.
Decision: Accept (poster)