DesignX: Human-Competitive Algorithm Designer for Black-Box Optimization
Authors: Hongshu Guo
Zeyuan Ma
Yining Ma
Xinglin Zhang
Wei-Neng Chen
Yue-Jiao Gong
Venue: NeurIPS 2025 poster ()
Keywords: Automated Algorithm Design
Black-Box-Optimization
Meta-Black-Box Optimization
Learning to Optimize
Deep Reinforcement Learning
Primary area: optimization
TL;DR: A bi-agent learning system tailored for automated algorithm design in black-box optimization.

Abstract: Designing effective black‑box optimizers is hampered by limited problem-specific knowledge and manual control that spans months for almost every detail. In this paper, we present DesignX, the first automated algorithm design framework that generates an effective optimizer specific to a given black-box optimization problem within seconds. Rooted in the first principles, we identify two key sub-tasks: 1) algorithm structure generation and 2) hyperparameter control. To enable systematic construction, a comprehensive modular algorithmic space is first built, embracing hundreds of algorithm components collected from decades of research. We then introduce a dual-agent reinforcement learning system that collaborates on structural and parametric design through a novel cooperative training objective, enabling large-scale meta-training across 10k diverse instances. Remarkably, through days of autonomous learning, the DesignX-generated optimizers continuously surpass human-crafted optimizers by orders of magnitude, either on synthetic testbed or on realistic optimization scenarios such as Protein-docking, AutoML and UAV path planning. Further in-depth analysis reveals DesignX's capability to discover non-trivial algorithm patterns beyond expert intuition, which, conversely, provides valuable design insights for the optimization community. We provide DesignX's Python project at~\url{https://github.com/MetaEvo/DesignX}.

DesignX: Human-Competitive Algorithm Designer for Black-Box Optimization
Hongshu Guo', Zeyuan Ma', Yining Ma²,
Xinglin Zhang', Wei-Neng Chen', Yuc-Jiao Gong'.*
South China University of Technology
2 Massachusetts Institute of Technology
{guohongshu369, scut. crw.ynicolass @gmail. com, yiningmaêmit, edu {csxlzhang, cschenwn @scut. edu. en, latyyuuaiia@gmmmll.. com
Abstract
Designing effective black-bou optimizers is hampered by limited problem-specific knowledge and manual control that spans months for almost every detail. In this paper, we present DesignX, the first automated algorithm design framework that generates effective optimizer specific within seconds. Rooted in the first principles, we identify two key sub-tasks: 1) algorithm structure generation and 2) hyperparameter control. To enable systematic construction, a comprehensive modular algorithmic space is first built, embracing hundreds of algorithm components collected from decades of research. We then introduce dual-agent reinforcement learning system that collaborates on structural and parametric design through novel cooperative training objective, enabling large-scale meta-training across 10k diverse instances. Remarkably, through days optimizers continuously surpass
given black-box optimization problem
of autonomous learning, the human-crafted optimizers by orders of magnitude, either on synthetic testbed or on realistic optimization scenarios such as Protein-docking, AutoML and UAV path planning. Further in-depth analysis reveals DesignX's 's capability to discover non-trivial algorithm patterns beyond expert intuition, which, conversely, provides valuable design insights for the optimization community. We provide DesignX's Python project at https: :/gps:///ttttt //tpttbtt.//t////////////t com//MetaEvo/eesiig..
Introduction
Black-box optimization (BBO) lies the core of scientific and industrial advances, such as electronic design automation [1], molecular design [2] and AutoMI. [3]. Yet, BBO is challenging due to unavailable objectives and derivatives, and complex, diverse properties that demand extensive expert knowledge. Evolutionary Computation (EC) is widely recognized as robust derívative-free paradigm for BBO [4]. Since the 1990s, numerous EC variants such as genetic algorithms(5), differential evolution [6], particle swarm optimization [7], and evolution strategies [8] have emerged. Despite shared core paradigm, they rely on expert-designed adaptive operators [9] and hyperparameter particular BBO class instance.
control [10] to achieve the best performance
However, manually redesigning optimizers for each new BBO problem neither scalable nor practical. Recently, emerging research avenue termed as Beta-Black-BBe -ox emerged, which automates algorithm design (AAD) through bi-level paradigm: a meta-level learns policy to guide low-level BBO optimizer. By meta-training [12] over distribution of problems, MetaBBO can generate customized algorithms for both seen and unseen instances.
Beeek--ox--pttnnnn frox-Optimizatonn (MetaBBO) [11] has
Yue- Jiao Gong is the corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Design Process of Human Exports
Optinioes
NL-SHADEE
Ope minitin Perforaace
OOO Intial Workflow
3,80
problem
workfloww
peammdir tining
sugastal
algorihm
Design'
opointieess during training
Uerran coated Opennom hervere 2011-2038 SEADE GLPSO.
Design Process of DesignX
I0700
Hianan crafied Optinezzn beswonn 2000 2010 CMA-FS JADE, PIPSO
0.62
Ihrrze-crffud Qyeiniin befo:: 2008 DE, PSO.
problem
DesignX's
peneated
DesignX's
sugeoted alporitim
Agent 1
workllow
Agens
Trantin Horaee (days)
Figure I: Left: Compared to manual design process, DesignX replaces human experts by two learn- able agents. Right: Four dashed lines denote average performances of well-known human-crafted optimizers decades. During pre-training, DesignX surprisingly discovers powerful optimizers superior to the ones crafted by human experts.
Despite the success, existing MetaBBO approaches merely focus on learning specific sub-tasks of AAD for ECC Specifically, optimizer design involves two sequential sub-tasks (see Figure I, top left): (1) determining the algorithm workflow, and (2) (dynamic) algorithm configuration. Existing work addresses the former via algorithm selectors [13-15] or workflow generators [16-19], and the latter through reinforcement learning (RL) [20] for online control [2 [21-24]. While learning single sub-task eases training, often results in sub-optimal designs and limits potential performance gains.
In this paper, we advance MetaBBO research by proposing the first unified framework that jointly learns both sub-tasks of algorithm design: workflow generation and (dynamic) algorithm configura- tion, so as to enable the discovery of human- competiio optimizers in an end-to-end fashion.
This is achieved through several key innovations. Firstly, extend and enrich the Modular-BBP BBO modularization system in [24], resulting in a more comprehensive system: Modular-EC. Specifically, since Modular-BBO is primarily constructed for Differential Evolution (DE) optimizer, Modular- EC integrates more diverse sub-modules in Evolutionary Strategy (ES), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms into sub-module library. Modular-EC now supports representing different optimizer types, enhancing the capacity of Modular-BBO. Building on the upgraded Modular-EC, develop dual-agent reinforcement learning system (see Figure 1, bottom left), where both agents are Transformer-bise valid optimizer workflows conditioned on the problem instance; 2) Agent-2 dynamically adjusts hyperparameters during optimization by incorporating real-time feedback. A novel cooperative reward scheme encourages both agents to make mutually conditioned decisions, jointly optimizing for maximum performance. We train this dual-agent system on large-scale problem set of 10k synthetic instances, and observe it consistently discovering optimizers that outperform expert-crafted baselines (see Figure right). Remarkably, through days of autonomous learning, the DesignX- generated optimizers continuously surpass human-crafted optimizers by orders of magnitude, either on synthetic testbed on realistic optimization scenarios such as Protein-docking, AutoML and UAV. Furthermore, the testing results clearly demonstrate the novelty and superiority of DesignX against up-to-date MetaBBO baselines. To summarize, the contributions of this paper are in three folds:
[25]: 1) Agent-I I autoregressively samples
To the best of our knowledge, this paper the first deep learning- framework that jointly learns workflow generation and dynamic algorithm configuration in an end-to-end fashion.
We obtain a well-performing model (DesignX) through large-scale training, capable of designing powerful optimizers for diverse, unseen, realistic problems.
Further in-depth analysis reveals the importance of the proposed novel designs, providing first-hand insights on non-trivial algorithm patterns beyond expert intuition.
2
Related Works
We review the development of Automated Algorithm Design (AAD) over the past decades. Early efforts by Schmidhuber et al. [26] applied Genetic Programming (GP) to recursively improve another GP in self-referential manner. Later, GP was applied to design full algorithm templates [27], but difficulties genotype design and expensive evaluations limited its scalability for BBO problems. Recent MetaBBO approaches integrate machine learning techniques such as reinforcement learning

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(RL) and large language models (LLMs) to develop more flexible and generalizable optimizers [11, 28]. These RL-based methods like DEDQN [14] and DEDDQN [13] focused on operator selection and hyperparameter control within fixed algorithm structures. More recent methods leverage Transformer architectures for enhanced control [23, 29), including ConfigX [24] and Q-Mamba [30], which implement online and offline RI. respectively. Other works explored Transformer-basee generation of algorithm components. SYMBOL [31] learned to compose new operators as symbolic sequences. ALDes [17] tokenized common algorithmic modules and turned workflow design into sequence generation. GLHF [32] simulated DE operators with trainable modules optimized through gradient descent. Besides these works, the lifelong learning ability of MetaBBO and its adaptability for expensive evaluation condition are also discussed in recent literature [33, 34], as well as the automatic feature learning [35] and training distribution construction [36]. Though these MetaBBO approaches use relatively small neural networks for meta-learning. they achieved tailored performance on specific algorithm design tasks. With LLM-scale models, capabilities expand further. LLMs search reward functions [37], optimize neural architectures [38], act as optimizers based on previous search trajectories [39], or generate algorithm code from problem descriptions [18, 19, 40]. However, existing work focuses on only one sub-task of AAD; either generating workflows or controlling jointly end-to-end algorithm design.
parameters. No prior method jointly addresses both, which motivates our proposed DesignX to enable
3 Methodology
3.1 Modular-EC
Existing EC optimizers commonly comprise series of algorithm modules. A massive array of novel algorithm modules have been proposed in literature for specific optimization scenarios [9, 41, 42]. is a quite natural idea to "stand on the shoulder of giants" for designing new optimizers, that is to say, construct modular algorithmic space and search for well perforeen optimizer workflow in it [43, 44]. Following such idea, ConfigX [24] proposes a comprehensive modularization system: Modular-BBO for learning universal hyper-parameter control policy in DE. It groups commonly used sub-module variants in existing DE optimizers into 9 module types: 6 of which are UNCONTROLIAA
without hyper-parameters: INITIALIZ.ATIO [45], BOUNDARY BUUNDDRY_CONTRO.. [46], SELECTION [47], NICHING [48], RESTART_STRATEEE SSTRRTERRYY [49], POPULATION __NNC_REDCCTOONN [50], and the rest 3 of which are CONTROLLABLE with hyper-parameters: MUTATION [51], CROSSOVER [52]. and COIRRRMATTONSSARRRRIA [53].
In Modular-EC, have added novel module type OTHER UPDATE [54, 55] into Modular- -BO's module library, which belongs to CONTROLLABLE namespace. We integrate popular reproduction operators of diverse ES, GA and PSO optimizers into OTHER JUDATE and also update the other module types by adding corresponding sub-modules in ES, GA and PSO. To summarize, Modular-Ed EEC supports 10 module types with 116 module variants in total. This results in millions of possible algorithm workflows, significantly enhancing the expressiveness of Modular-BBO.
For concrete module variant, Modular-EC assigns it an unique 16-bit binary code id for identify. A topology_ruu sule list is built within each module variant to indicate which module types are allowed to be placed right after this module variant, ensuring legal generation of optimizer workflow in auto-regressive fashion. We list some examples here: 1) Any EC optimizer must start with INITIAL- IZATION; 2) BOUNDARY CONTROL is not allowed placed between two subsequent reproduction modules (e.g.. MUTATION and CROSSOVER); 3) RESTARRTSTRATEETT STRATEGGY is only allowed to be placed the end of EC optimizer. We provide more details of the hierarchical architecture, module variants information of Modular-FC in Appendix A.
3.2 Dual-agent Algorithm Design System
We propose a dual-agent algorithm design system for DesignX to operate on Modular-EC. As shown in Figure 2, the system consists of two Transformer-basee RL agents: Agent-1 (Ta) and Agent-2 (Tτ), each addressing a core sub-task in automated algorithm design. 1) Algorithm workflow generation: A constructs a customized optimizer workflow based on the given problem. 2) Hyperparameter control: Agent-2 dynamically adjusts the hyperparameters during the optimization process to enhance performance. By jointly addressing both sub-tasks, DesignX offers a more complete and effective solution than methods focusing on only aspect (see Section 2).
3

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Program Structure Tree
Agent-I: 1: Auto-regreesive Workflow Generation
Initialization
Fentures
Masked Soltmax Sampling
Misked Soltmas Sampling
Maskel Solmax Sampling
Niching
GPT2 Blocks
GPTZ Blocks
GPT-2 Blocks
PST
problem
DE DE-Mutaticn
GA- GA-Crossover
start
Token
DE-Crossower
GA-Mulation
Agent-2: Dynamic Hyper-paramcter Control
decoded
byper-params
Selection
Hyppe param
Value lead
GPT-2
Blocks
optimization
progress
Pre-order Traversal
information
workflow
The dual-agent system in DesignX processes an optimizer workflow by the pre-order traversal of its program structure tree. Top Right: Agent-l generates legal optimizer workflow in an auto-regressive fashion. Bottom Right: Agent-2 controls hyperparameters of the generated optimizer workflow by conditioning on the optimization progress information.
Figure 2:
Left:
Before we get into further technical details, we first explain the Program Structure Tree (PST) [56] of an algorithm workflow and pre-order traversal of PST. We illustrate a simple example in the left of Figure 2, where two-population tiching-based EC optimizer is represented by PST and corresponding pre-order traversal respectively. The pre-order traversal representation an optimizer workflow is primarily used in Agent-1 and Agent-2 to align with information processing logic of Transformer architecture, where each module in the traversal regarded as a token.
3.2.1 Agent-1: Workflow Generation
Agent-l's workflow is shown in the top right of Figure 2. Given the feature vector Fp of an optimization problem p. Agent-1 auto-regressively samples module variants from Modular-EC to construct a complete optimizer workflow Ap T (Fp). The architecture of Tt consists of four components: 1) a problem feature embedder Wfeature IR 13xh, where 13 is Fp 's dimension and denotes the token embedding dimension; 2) a Tokenizer Wzoken E 16 where 16 denotes the 16 bits module id: L sequential GPT-2 [57] blocks with & heads and hidden dimension h. We use MSA, to denote these attention blocks; 4) masked Softmax module Wsample E R where 117 is the numbers of tokens (116 modules in Modular-EC and an additional end token).
Problem Feature Embedding. The raw feature F, for a given optimization problem p is a 13- dimensional vector, which is further divided into parts: 1) basic properties: the dimension, allowed maximum function evaluations, upperbound and lowerbound of searching range; 2) statistical properties:
well-known optimization problem statistical analysis framework, Exploratory Landscape Analysis (ELA) [58], which provides many statistical low-level features for profiling high-level optimization properties such as multi-modalin separability, global structure, etc. Specifically, we select ELA features with both significant independence and efficient computation according to the sensitivity analysis of ELA features [59, 60). We provide a detailed elaboration on these ELA features in Appendix B. Once F, is obtained, we use Wfeature to map it to h-dimensional token, which we denote start for subsequent optimizer workflow generation.
Auto-regressive Generation. Starting from the start token for problem Agent-1 auto-regressively generates the pre-order traversal of optimizer workflow Ap. Suppose A has generated m modules {AL, AB...., ATH then the sampling distribution of (m 1)-th module Am+ is:
P( mm |start, A!.......)) ~ Softmaz(mask @ (WT eamppe -H H(())))
(1)
H = MSA + (start, Wirken AA).getiid() Wioken ATTh .get_id()))
where first get each sampled module's 's id and use the tokenizer map them tokens with h-dimension. Then all tokens including start are added with Cosine Position Encoding Pos. After going through the GPT-2 blocks M MSAi, we use Wsampie to map the output embedding (m)) for m-th module as the prediction head. Recall that we have to ensure the generated workflow is legal. To achieve this, we propose masked Softmax sampling procedure. boolean mask vector mask(AA)) ) 12 117 is obtained by checking A7 topology rule AT .get gee_rrul(] Hadamard product

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between the mask and prediction head squeezes the sampling probability of illegal modules to O. We note that the dimension of prediction head and the mask is 117, which corresponds the 116 modules in Modular-FC and the end token. Without the end token, Agent-1 has risks of generating infinite trajectory. Refer to Appendix A, Table 3 to check which modules could be placed right before end. In the rest of this paper, we use (App)))) to denote the sampling probability of a concrete workflow Ap, which is the successive multiplication of all generation steps:
To (Ap) = ((4f)sstartP((((sstarr,, A...... A A (
3.2.2 Agent-2: Dynamic Algorithm Configuration
Agent-2's workflow is shown in the bottom right of Figure 2. Once A, is generated by Agent- it is used to optimize p. During the optimization process, given some observed optimization progress information O₂ at 1-th optimization step, Agent-2 dynamically adjusts hyper-parameter values C, = Ty. (O,) for all CONTROLLABLE modules in Ap. The motivation behind Agent-2 is that: common observation in EC domain reveals that hyperparameter values in optimizer more less tradeoff [9]. An effective parameter control policy could further enhance the optimization performance of the optimizer generated by Agent-1.
impact the
To suggest per optimization step hyperparameter values for CONTROLLABLE modules in Ap. an informative optimization progress feature vector O, is first computed following the common idea of up-to-date MetaBBO approaches [23, 24, 31]. O, is a 9-dimensional vector of which each dimension is a statistical feature indicating the local/global distribution in solution/objective space, convergence progress and optimization budget usage information. We provide detailed description of these features in Appendix B.2, Agent-2 then embeds O into each module in Ap to get all module's embeddings:
Amb((A))) = Pos + Wemb [A "pe-geeid(() Ot] m = 1,2.., M
(3)
where W cmb. R255x maps the concat of module id and O to h-dimensional embeddings. The final embedding for each module is obtained by adding the h--dimensional embeddings with Cosine Positional Embedding codes, which inject relative order information, to let Agent-2 grasps the overall optimizer workflow structure. The suggested hyperparameter values optimization step is decoded by first feeding the embeddings of all modules into L sequential GPT-2 [57] blocks with k heads and hidden dimension h (denoted M SA2). Then the output decision embeddings Haec are further decoded into normal distribution parameters:
1= W.T Hdeeo
Σ ==W Háecs Haec MSA2 E....AA
(4)
where WT. E IghxNmmx and WTT E RhxNmox are network parameters of the hyperparameter value head. They map Haec the mean parameters μ Mx and covariance parameters Σ E R.MxNmar where ((())) E R.-mes and {(m) E R.Nmax denotes distribution parameters for m-th module Ap. At last, the hyperparameter values C, are sampled from the predicted normal distributions for all M modules:
C2 .C,,..,,C CM. (N((()) ((.),..,((((M) y((0)
(5)
We have to note that since different modules in Modular-Eo EC might hold different number of hyperpa- rameter values, we predefine a maximum configuration size Nmar to cover them. the number of syper--aramettrs in module is less then Nmaz, we the first few sampled values and ignore the rest. Suppose the optimization horizon for problem is T steps, Agent-2 will be asked T times for deciding the per-step hyper-paramettr values. In the rest of this paper, we use To (Cr|Ap) denote the associate probability of the hyperparameters for A, optimization step t':
M
Te (C.lAp)
II m=1
N (m). (m))
(6)
3.3 Cooperative Large Scale Training
We propose large scale mete-reinforeemeet-eemmme paradigm to ensure the pre-trained DesignX model could benefit from the harmonious cooperation between Agent-1 & 2, and capable of being generalized towards unseen problems.
We only consider sampling for modules with least one hyperparameter.
5

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Large Scale Synthetic Problem Set. We construct large scale synthetic problem set containing 12800 diverse problem instances for the ease of training generalizable DesignX model. 32 representa- tive basic problems are first collected from popular BBO benchmarks [61, 62], including Rastrigin, Schwefel, Rosenbrock, etc. We follow the steps below to generate 12800 diverse problem instances: 1) We first define three problem construction modes, "single", "composition" and "hybrid". "single" mode randomly selects one basic problem. "composition" mode randomly aggregates 2-5 basic prob- lems by weighted summation of their objective functions. "hybrid" mode divides decision variables into some subcomponents and then randomly selects a group of basic functions, which are used for different subcomponents. 2) By randomly selecting the construction modes and determining the searching range, dimension (5-50d) maximum allowed optimization budget (1 (10000-50000 maxFEs) and rotation/shift in solution space, we construct 12800 problem instances with diverse optimization properties, which aligns with the intricate problem distribution in real world. We further randomly split them into training problem set Drrain (9600 instances) and testing set Drest (3200 instances). A more detailed elaboration is provided in Appendix C.
Cooperative Training Objective. We formulate the automated algorithm design task of DesignX as a dual-agent Markov Decision Process (MDP). For each problem instance p E Diraain Agent-1 first generates legal optimizer workflow Ap with probability TH (Ap) in Eq. (2). Ap is then used to optimize p until its allowed optimization budget is used up. For each optimization step t along this optimization process (T steps in total), Agent-2 continuously dictates hyperparameters C2 with
f" f2 probability ACp in Eq. (6). We record the reward obtained at t-th step as re- -
where f denotes the optimal objective value found until I-th step (w.l.ogg. p assumed as a minimization problem), J denotes the optimal objective value of p. Then the training objective of DesignX's MDP can be formulated as:
T
Peraca Σ
J Epp
rd
Σ
rt
Derainl
which is the expected optimization performance if we use DesignX's Agent-1 1 & 2 to design optimizers for solving problem instances in Dtrain- For Agent- there is intermediate reward (delayed- reinforcement task), hence we train it by episodic reinforcement learning method REINFORCE [63]. For Agent-2, the per-step reward r, can be used hence train it by the popular PPO method [64]. We provide the pseudo code of the training procedure in Appendix D, Alg. 1.
4 Experimental Analysis
In this section, discuss the following research questions: RQ1: competioeee BBO optimizers that excel at both synthetic and realistic scenarios? RQ2: What design skills has DesignX learned? RQ3: How do the core components in DesignX contribute? RQ4: How is the scalability of DesignX in terms of the scaling law? Below, we first introduce the experimental setup and then address RQ1~RQ4 respectively.
Can DesignX automatically design
Experiments Setup. The baselines in experiments include: 1) DesignX model trained after days; 2) up-to-date MetaBBO approaches GLHF [32], DEDQN [14] and GLEET [23] that excel at workflow learning or hyper-parameter control; 3) representative human-crafted optimizers: a)
those before 2000, GA [5], PSO [7] and DE [6]. b) those in 2000-2010, CMAES [65], FIPSO [66],
SaDE [67], CLPSO [68] and JADE [69]. c) those in 2010-2020, CoDE [70]. IPSO [71], SHADE [72],
LM-CMA-ES [73] and GLPSO [74]. d) those after 2020, MadDE [75], jDE21 [76]. MMES [77] and
NL-SHADE-LBC [78]. For evaluation fairness, we train DesignX and other MetaBBO baselines on
the same Derain (see Section 3.3). We leave detailed training settings and other hyper-parameter settings of all baselines at Appendix E. & E.2. To simplify presentation, we use following tags: "MetaBBO". "'before 00', "00s", "10s" and "after 20" to tag these baselines.
4.1 Performance Comparison (RQ1)
In In-distribution Generalization. All baselines are tested on our proposed Drest (see Section 3.3), with 51 independent runs for each problem instance. Due to the space limitation, we present the absolute optimization performance of all baselines on 20 of the 3200 tested instances in Table 1. These 20 instances are randomly selected to showcase their diversity in: a) optimization properties,

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Table I:
The in in-disrribttion generalization performance in terms of absolute optimization performance
results on Diest The best is labeled in green and the second best is labeled in red.
before 00
Ods
10s
after 20
MctaBBO
DesigX
13,74E-00 + 1.64x000
6.60=-00
1.27
5.32F
20E0
2.89F-01
MAIL SOD, 30000 Fls
1164E+00
14,41E.01
13,70E+00
+
10,00E+00
13993-01
F79
1988=00
+ 3.70F000
5.385000
9.95--01
3.68E-022
UAIL, SD, 50000 FEs
19.95E.01
11,1E+00
14.05E-01
1183
+ 10.00E+00
1177
F125
L39E-03
3.50E-06
148E44
1,69-005
LOSE-M
4.81E-07
UAH, LOD, 40000 FEs
+1,386-03
+ #3 50E-00
+1.336-04
+7,998-06
+ +0,00+000
-266E-07
F154
135E-03
144E403
138E403 +
1446+03
5.47E-02
6,99E+I2
UAH, SOD. 10000 FEs
+2,268402 + +3.45E+02
+2,405-02
+6. 56,172
+ =0,00+00
+7455+01
F2I1
6.55-01
8.44-011
264E:0T
1,285-01 +
1.99-011
7.28E-022
MAH, SD, 40000 FEs
12,922.01
+
16.999.01
19.96E-02
12243.002
10.00E+00
6.56F-02
F240
6.39E-00
8.72E400
8245000
3.774000
20S5+000
1.27E-011
MWL, 20D, 20000 FEs
14,25E400
+1.1E+00
42,19E-00
43,31E400 +
+0.00E
2
F326
L10E-00
115E400
2,47E400
7.66E-01
123E+00
5.84E-11
UAL, 10D, 40000 FEs
+1.22E-01
+4.53E-01
14.648-01
=5.10E-02
+0.005400
=1666+00
F411
2.50E-01
4.07E-01
2688:41
1,28E-01
187E:001
7,91E-02
UAL. 10D, 50000
+9,11E-02
+9.27F-02
+741E.02
+1,110022
+0.00F
4.835-02
F545
2,98--00
1495400
3.365400
844Е-11
1998400
261E-08
UWI,, SD, 40000 FEs
49,94F-01 +
+4977-01
46,23F-11
+1.54F.01
+0.00F+00
6.48F-01
FIUSS
7.33--02
4. 4,205402
2.29:422
1.71E+02
9.21
167E-02
40000 FES
11.684400
+147E+02
16.066-01
10,004400
+006
FT139
LI6E-01
3.955400
K90ER00
2.774400
LI9ER0I
1.9.4
L0D,
+100E+01
#167E+00
11,548-00
11,15E000
10,004000
F1200
TA7E-00
1,144400
LISE400
1.35-01
L27E+00
1,09-000
MAL, S0D, 40000 FEs
+6,29F400
+7 +7.00F-03
+2.56F-02
+1,22F401
+0.00000
+2.12F-02
F1556
3.99E-02
2,03E402
2.73+01
LA8E401
9448+000
101E+01
MAH, LOD, 40000 FFs
+3.75E402
+1,76F402
+7.635400
+7.13F-01
+0.00F400
+1,3F4022
FIRST
LS51-001
2.53EH0T
2721+01
L8SE+01
L69E+01
MAHL 20D 10020 FEs
+1,538+00
27,11E-01
17.28E-01
12,56E400
10,0E400
23477400
F1687
K.981-00
2.07E401
4.91.111
2041-01
1940:00
2.241.002
MAL, S0D, 40000 FES
16. 66.60B+00
+107E+01
12.38E-01
1281E401
10.0E400
29099+00
F2068
3.79E-01
2.328400
1.46+01
L655+01
3.724+01
5.16E-01
MWH, 20D 20000 FEs
+6,53B400 +
13113--1
+1 -1,404001
+
+1415401
+0.005000
+ +106F401
F2390
3.93--00
2,785400
6,344400
L548+00
2.044001
185E-03
MAL, 1OD, 30000 FEs
+5,150
+0.000000
+9.035-01
105400
+0.005000
+ +0
F2473
LIDE-00
398E01
6.89101
1426.01
1610.01
MAL, 10D, 20000 FES
19.06E-02
+
16 16.880-02
11 11.80E-02
12.53E
10,00+000
11,59B-01
F2895
190E-01
4,345:00
498E400
1,99=0000
MWL, 10D, 50000 FEs
+3.89E400
+ +1 66660000
+5.35B-00
+ +5,26E-01
+
+0.004000
=334E+00
F2986
4.37E-02
4.93E402
160E+02
2.518403
LOIE+02
8,90-=01
MAL, S0D, 10000 FEs
+1.71E+02
+ +3.74E+02
46438-01
+
+2,42E+03
+
+0.00E400
21.5E=01
Normalized Averaged
2.94E-01
196E-01
1.54-001
1466-01
1.3E-01
8.26E-022
Objective
11.015+00
+
11621E+00
12.11001
12.35E +
17.36-01
11.5E-01
DeigoX
lefre
00
McaBBO
Prolcin-Docking
HPOS
LAV
0.97
Noeeiized Objjeevve
0.6
0.20
0.974
0.72
0.15
0.970
0.4
0.5
10000
5000
10000
4000 6000
5030
10000
FIEs
Figure 3: The generalization performance of baselines on realistic scenarios.
"U/M" for unimodal/multi-moottt modal "A/W" for adequate or weak global structures and "L/H" for low high conditioning; b) problem dimensions, 5D-50D; c) allowed optimization budget in terms of the number function evaluations (FEs). We additionally average the baselines in each tag ("before 00". "00s" and etc.) for the ease of presentation.
The results in Table reveal that: 1) The human-crafted BBO optimizers achieve progressive advancement through the expert-level designs proposed over the past decades. However, they are sill restricted by no-free-lunch theorem. 2) By incorporating learning paradigm into BBO optimizers, MetaBBO approaches are capable of boosting the low-level optimizers on some problem instances. 3) The optimization performance of DesignX surpasses both MetaBBO and hand-crafted BBO baselines, ranking the first place on almost all tested instances with diverse properties. Through learning the bi-agent system across a large scale problem distribution (Dtrain). DesignX intelligently designs powerful and customized optimizers for different problems. To the best of our knowledge, this is the first time RL system successfully learns how automatically design BBO optimizers.
Generalization. For marning-assisterd optimization techniques, the problem shifts in realistic scenarios might challenge their generalization ability in practice. To this end, we
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test DesignX and MetaBBO baselines trained on synthetic Deroin on three diverse realistic BBO testsuites: a) Protein-Dockinn [79]. a collection of 280 protein-docking instances, featured by intricate landscapes; b) HPO-B [80], which comprises 86 ill-conditioning AutoMI. instances; c) UAV [81], 56 diverse conflict-free UAV path planning scenarios featured by implicit constraints multiplier in objective space (see Appendix E.3 for detail). We illustrate in Figure 3 the average optimization curves of all baselines, which is averaged within each tag and across 51 independent runs. The results show that: 1) DesignX generally shows superior optimization behavior to human-crafted optimizers from different decades, designing desirable optimizers robustly for diverse realistic problems it never saw during training; 2) DesignX consistently outperforms MetaBBO approaches, which demonstrates the novelty our proposed bi-agent algorithm design system. By integrating two RL agents for both algorithmic workflow generation and hyper-parameter control, DesignX achieves better superior generalization performance to those MetaBBO baselines for single sub-task.
4.2
What has DesignX Learned?
Dimensson
maxFEs
Range
plaera paein
conaeeboo comaraa-end
Modality
Global Siructure
Condituning
30
OU PR
Figure Left: Normalized importance factors different module types for various problem characteristics. Right: Two look-into cases for interpreting design pattern learned by DesignX.
Insightful Design Skills (RQ2). Before delving into the analysis. we first abbreviate the 10 module types in Modular-EC simplify the presentation: INITIALIZATION ("T'), NICHING ("N"), MU- TATION ("M"), CROSSOVER ("C"), OTHER_ UPDATE ("OU"), BOUNDARY CONTROL ("BC"), SELECTION ("S"",, POPULATION REDUCTION ("PR"), RESTART STRATEGY ("RS") and INFOR- MATION SHARING ("IS"). The following analysis aims to investigate design principles DesignX has learned based on statisties gathered from the optimizer workflows generated for the 3200 problem instances in Diest- We list several key observations we found as below:
1) In the left of Figure 4, we summarize the relative importance of different module types in Modular- EC when considering various optimization problem characteristics: Dimension, maxFEs, Search Range, Modality, Global Structure, Conditioning. To compute the relative importance, we provide a example here. Suppose we consider the relative importance of "M" (mutation) for Modality, we first divide problem instances in Drest into those unimodal ones and those multimodal ones. Then based on the optimizer workflows generated by DesignX for these problem instances, the relative importance can be calculated as the KL-divergence of the sub-module occurence distributions of "M" in unimodal problems and multimodal problems (see Appendix E,4 for more clarification). The relative importance factor reflects how DesignX thinks when designing an optimizer for a problem with certain property. As shown in Figure 4: a) for problems with different modalities, DesignX leans to design different DE mutation strategies for the generated workflow; b) for problem with different search ranges, DesignX leans to focus more the selection of "PR" (population reduction mechanism). c) DesignX thinks designing initialization strategies has very limited impact on the final performance! These unique findings are non-trivial and deserve further analysis.
2) To investigate the above novel design principles interpreted from DesignX, we further look into the concrete sub-module occurence distributions in the first two cases. We illustrate them in the right of Figure 4. The results could clearly demonstrate DesignX's intelligent design policy: a) for unimodal problem, it smartly choose greedy-fashion mutation operators to reinforce the optimizer's exploitation, and dictates composite mutation strategy for multimodal problems to address exploration and exploitation tradeoff. b) population reduction is an effective mechanism to upgrade an optimizer's local search ability. DesignX thinks for problems with relatively smaller searching range, population reduction should be applied to accelerate the convergence. c) we examine the finding of DesignX on Initialization by replacing the designs in existing optimizers with different ones. The results validate the correctness of DesignX and is shown in Appendix F.I.
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Accumulued Rewanl
22.8%
12.35
6 layer GPT-2
layer GPT2
#oAlig Al
Deijex
Training Problem Set
Figure 5: Ratios of se- lected module types.
Figure 6: Averaged perfor-
Figure Performance comparison across model sizes and training sizes.
mance of ablation baselines.
3) Another interesting design principle of DesignX is its unique taste on different optimizer types (DE, PSO, GA, ES). To illustrate this, we count the number of optimizers generated by DesignX which contain module variants derived from these four optimizer types, and then present their distribution in Figure 5. The results indicate that the DE-related algorithm sub-modules is primarily considered by DesignX to achieve aforementioned robust optimization performance. We provide several novel and very competitive DE optimizers discovered by DesignX in Appendix F.2.
4.3 In-depth Analysis
Ablation Study (RQ3). DesignX automates BBO optimizer design through the cooperation between Agent-1 and Agent-2. We hence investigate what extent the two agents contribute DesignX's final performance. Concretely, we introduce three ablations: 1) w/o Al+A2: randomized Agent-1 & without training: 2) w/o Al: only Agent-2 is trained; and 3) w/o A2: only Agent- 1 is trained. We also include two additional baselines for systematic analysis: 1) SBS: retrain DesignX without instance/observation features (set as zero vector), making Agent-1 learn static algorithm workflow; 2) CMA-ES. We present the reversed normalized objective values (higher is better) of the ablations and DesignX Diest and three realistic problem sets in Figure 6. Detailed results for each problem set are provided in Appendix E.3. The results reveal following insights: 1) we could at least conclude that generating correct optimizer workflow might be more important than controlling the hyper- parameters (w/o A2 v.s. w/o A1); 2) By training DesignX via our proposed cooperative learning objective, achieves better performance than sub-task agent, which further validates the effectiveness of our method. 3) The static optimizer workflow found by SBS cannot perform very well, validating the necessity of generating customized workflows for each problem.
Scaling Law (RQ4). We further investigate the scalability of DesignX in terms of model capacity and training data scale. Due to our limited computational resources, preliminary study is conducted here. Specifically, we investigate three different model sizes: 1,6 and 12 layers GPT-2 blocks for both A and Agent-2, and five training problem set sizes: 500, 2000, 5000, 10000 and 20000. We train DesignX under the corresponding 15 combinations and report their testing performance on Drest in Figure 7. y-axis denoted the average learning objective across all tested problem instances and 51 independent runs. In general, we observe that when problem set scale is small, lager model might encounter overfitting issues hence underperforms on unseen problems. In contrast, for training- instance-rich scenario, larger model's learning ability continuously scales, while smaller ones might suffer from low capacity. However, in practice, might consumes exponentially more resources for stable training in large models and training scales, hence in this paper, we select DesignX with 1 layer and 10k training scale as the final model. We additionally provide comparison of DesignX and popular LLMs in terms of their design ability in Appendix E.4.
4.4 Additional Discussion
Position of DesignX. We discuss the differences of our DesignX with several related AAD fields: 1) Learning to Optimize (L20) [82]: L20 commonly addresses gradient-based optimization, while MetaBBO such as DesignX addresses gradient-free ones; 2) Programming by Optimisa- tion (PbO) [83]: PbO is tailored for specific target scenario while DesignX aims at generalization ability for diverse optimization problems; 3) Combined Algorithm Selection and Hyperparameter optimization (CASH) [84]: CASH is more general AutoML concept which focuses on selecting MI. algorithms and determining static algorithm configuration. DesignX is capable of "creating" new ones and provides DAC capability.

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Table 2: The detailed breakdown of DesignX's 's training time per training step.
Agent
Agent-1 (7.5k steps)
Agent-2 (2.2M steps)
Problem Ieature
Workflow
BBO
Learning
Optimization progress
Parameter values
BBO
Learning
Process
computation
generation
process
update
feature computation
inference
process
update
Runtime
2s
0.95s
20.01s
0.0.5
0.001s
0.02s
0.04s
0.0%s
Computational Overhead. We present a running time decomposition analysis of DesignX's training in Table 2, where the per-learning-teee running time for each sub-process in the two agents' training is provided. To summarize, the true computational bottleneck of DesignX is not its deep learning framework, instead, the inherent simulation cost in BBO optimization loop. This is also one of the major reason we train DesignX with CPUs, since BBO optimizers comprises many sequential logics that can not benefit from GPU's matrix and parallel acceleration support. Besides, we put agents on GPU and the BBO process in CPU, the CPU-GPU communication overhead is also too much. When being used solve a problem instance, DesignX consumes 5.5s on average and existing advanced optimizer such as CMA-ES consumes 5.0s, which indicates our DesignX would not increase the actual inference overhead. We also note that DesignX automatically "design" algorithm for users. Considering for user with limited optimization knowledge, this could save much more time and lower the development difficulty.
Comparison. In our major comparison ex- periment (Table I), to showcase the evolution path of our DesignX during its days of training and also to provide an intuitive perspective on its generalization performance under knotty problem distribution, we use average perfor- mance as a major evaluation factor show that DesignX has superior performance to those advanced optimizers in history. The conclusion may vary a little bit if we concen- trate on the rank-based performance significance testing among all baselines. In Figure 8, we illustrate such per- spective, where the critical difference diagram based the same rollout data of Table is provided. We can observe that when considering relative ranks across baselines, CMA-ES and DesignX performs almost equally and outperform the others signifi- cantly. This on the one hand demonstrates DesignX has learned robust policy, on the other hand, also outlines further improvement is still required.
GL107
Capc
J.JAAADE LBG
1951
GLERT
Figure The rank-based comparison.
Potential Limitations. While DesignX serves as an effective end-to-end learning framework for AAD, it holds certain limitations and anticipates more future research efforts. In this paper, the primary optimization domain is restricted within single-objective optimization. However, optimiza- tion domains such multi-objective optimization requires more complex algorithm modules and corresponding training problems, which challenges the extensibility of DesignX. Thanks to the uniform interfaces have developed in Modular-EC system, complex modules in such optimization domain can be integrated, and life-long learning/continall learning techniques might be a promising way to make DesignX embrace diverse optimization domains. Besides, have note that the training efficiency of DesignX is not very ideal. It still takes us 6 days to train DesignX on high- performance PC. Further improvement such Multi-GPU parallel mechanism, proximal training objective, architecture simplification//isiillaaao could be regarded as important future works.
5 Conclusion
In this paper, we propose DesignX as the first end-to-end MetaBBO approach which presents human- competitive end-to-end designing ability for BBO problems. We propose a novel dual-agent system with two RL agents for optimizer workflow generation and hlpee--araamtee control respectively. To effectively train DesignX, we construct a large scale synthetic problem set with 10k optimization problems with diverse characteristics. A cooperative learning objective is used to harmoniously learn optimal design policies for the two RL agents. Surprisingly, a DesignX model with merely two simple GPT-2 blocks continuously surpass popular human-craficn designs along the training. We have validated the generalization ability of DesignX on both synthetic and challenging realistic scenarios. More importantly, non-trivial design principles learned by DesignX are interpreted, which provides valuable design insights back to the community. We believe DesignX could serve as a pivotal step towards fully end-to-end foundation models for automated algorithm design.
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Acknowledgments and Disclosure of Funding
This work was supported in part by National Natural Science Foundation of China (Grant No. 62276100), in part by Guangzhou Science and Technology Elite Talent Leading Program for Basic and Applied Basic Research (Grant No. SL20024004013611, in part by the Guangdong Provincial Natural Science Foundation for Outstanding Youth Team Project (Grant No. 2024B1515040015 and in part by the Fundamental Research Funds for the Central Universities (Grant No. 20252YGX2R027),
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Figure 9: Left: The hierarchical Python inheritance in Modular-EC to support intricate polymorphism in EC modules. Right: Legal/M[legal algorithm workflow examples in Modular-EC.
Hierarchical Inheritance. As illustrated in the left of Figure 9, MMMdular-EC is designed as a Polymor- phism system via multiple levels of Python inheritance. Such design allows maintaining diverse EC modules (the bottom ones in Figure 9) via universal interface encapsulation. In specific, Modular-FC holds three levels of inheritances: 1) High-level: All modules in Modular-EC stem from the abstract base class MODULE, which declares properties and methods shared by all modules. In high-level inheritance, two sub-classes inherit from MODULE: UNCONTROLLABLE and CONTROLLABLE These two sub-classes divide all possible EC modules into those without/with hyper-parameters. For CONTROLLABLE, we add a config_space property as its hyper-paramettr space, which for now is void until concrete EC module is created at the low-level inheritance; 2) Middle-level: We have summarized several major EC module types from existing literature, which are widely adopted in many EC optimizers. In this inheritance level. UNCONTROLLABLE and CONTROLLABLE are further divided into these EC module types. Considering that legal (or rational) EC optimizer workflow should comprises correctly ordered modules, we add and specify a topology_rut r_llee property for each module type to indicate which module types could be placed right after it. topology_ parllooyyruleeoooo plays a key role in DesignX's i dual-agent algorithm design system to ensure legal generation of optimizer workflow in auto-regressive fashion. 3) Low-level: In low-level inheritance, the concrete variants of each EC module types are created, which are collected by us from existing EC literature where they serve as common choices for many EC optimizers. For a concrete low-level module variant, we assign it unique id property as its identifier in Modular-EC, specify config space dictionary of its all hhper--ppeeeee hyper-parameters parameters (if it inherits from CONTROLLABLE), and re-write exec() method by how processes the solutions during optimization.
Summary of Maintained EC Modules. There are 6 UNCONTROLLABLE module types without hyper-parameters grouped in Modular-FC:
1. INITIALIZATION [45], which initialize a population of solutions to kick start a BC opti- mizer. We have maintained 5 initialization variants in the low-level inheritance (e.g., Sobol sampling [94], LHS sampling [95]).
2. NICHING [48], which divides the population into several sub-populations. We have main- tained 3 niching variants in the low-level inheritance (Random [96], Ranking [97] and Distance [98]).
3. BOUNDARY __CNN_OOL [46], which ensures that the values of solutions in the population are all controlled in the bound. We have maintained 5 boundary control variants in the low-level inheritance (c.g., Clip [46], Reflect [46]).
4. SELECTION [47], which selects better solutions from parents/offsprings. We have main- tained 6 variants of this type the low-level inheritance (e.g., DF-Crowding [76], GA- Roulette [5]).
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Table 3: The list of the practical variants of CONTROLLABLE and UNCONTROLLABLE modules.
(a) The CONTROLLABLE modules.
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RESTARTTSTRATEEGY [49], which re-initializes the population when it converges or stagnates. We have maintained 4 restart strategy variants in the low-level inheritance (e.g.. Stagnation [99], Obj Moj_eennveeeece [76]).
6. POPULATION REDUCTION [50], which reduces the population size to perform exploitative optimization. We have maintained 2 variants of this type in the lowelevel inheritance (Lin- car [100] and Non-Linear [101]).
For CONTROLLABLE modules, we introduce four types:
1. MUTATION [51], which introduces stochastic local search for each solution. We have maintained 49 mutation variants in the low-level inheritance (e.g., GA-gaussian [5], DE/rand/1 [6]).
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(b) The UNCONTROLLABLE modules.
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2. CROSSOVER [52], which encourages global optimization by exchanging two solution's 's information. We have maintained 17 crossover variants in the low-level inheritance (e.g.. GA-SBX [5], DE-binomial [6]).
3. OTHER_ OTHER_UPDATE, which denotes other population update paradigm in PSO/ES variants. We have maintained 10 variants of this type in the lovelevel inheritance (e.g.. ES-CMA [65],
ES-Diagonal [92], PSO-normal [7]).
4. INFORMATION SHARING [53], which takes the best solution in the target aub-population to replace the worst solution in current sub-population to perform information sharing between sub-populations.
Additionally, advanced evolutionary computation (EC) methods often integrate multiple candidate operators to dynamically select operators during optimization. To accommodate such scenarios, we introduce MULTI SULLI_STTRATESS STRATEGY modules, which contains 2-5 candidate sub-modules of the same type (e.g., mutation operators) and expose an additional operator selection parameter in their configuration space (config_spenl sonnfe_spacee...... For categorization, Multi-Strateg, modules inherit the type of their constituent sub-modules. For example, a BULTI_STRATEGE module containing DE mutation operators is classified under the MUTATION category.
Module's ID. The unique identifier id of module variant a 16-bit binary code of which: 1) the first bit is 0 or 1 to denote if this variant is UNCONTROLLABLE CONTROLLABLE; 2) the 2-nd to
27

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7-th bits denote which one of the 11 module types this variant belongs to; 3) the last 9 bits denotes its id within that module type.
Module's Topology Rule. A key property in module variant is its topology_rite rule, which is a list of module types indicating which module types are allowed to be placed right after this module variant. A very simple example is illustrated in the right of Figure 9, where in EC optimizer, selection modules are not allowed to be placed before crossover modules. We list some other examples here: 1) Any EC optimizer must start with INTIIALIZATINN; 2) BOUNDARY CEUNDDRY_COOSEE CONTROL is not allowed placed between two subsequent reproduction modules (e.g., MUTATION and CROSSOVER); 3) RESTART SSTAATETRTTYYYY is only allowed to be placed at the end of a EC optimizer.
In total, we have created 116 module variants in the low-level inheritance to cover commonly used techniques in existing EC literature. Besides, an end token is included to indicate the end of the algo- rithm generation. We provide a complete information table about these module variants in Table 3a Cconfigspaace
and Table 3h, including their names, types, original papers and syper-parametee Such a comprehensive module space in Modular-EC could express BBO optimizers with diverse workflow structures, hence allows learning for effective (even optimal) algorithm design policies.
B Feature Design
B.1 ELA Features for Agent-1
In this paper for each problem we introduce a 13-dimensional feature vector Fp comprising two components: the 4-dimensional basic problem information and the 9-dimensional ELA features. The basic information includes the problem dimension (D), maxFEs (marFEs), upper bound (ub) and lower bound (lb). Since the scale of these values could vary, we normalize the feature of problem dimension FD = log D and the feature of maxFEs FFES 10 log ma. Es. For the upper and lower bounds we use Fub ub/100 and Fi,. lb/ 100 respectively. For the 9-dimensional ELA features which are significant independence and efficient computation according to the sensitivity analysis of ELA features in [59, 60), we present them Table 4. These features profile the optimization properties of the problem such as modality, Skewness, global structures, etc.
Table 4: The list of the ELA features for Agent-1.
Fentures
Deseription
ela faammetalinn lin, simple imeeccett ela jaa_metaqqadd simple simple _di_r2
The intercept of the linear regression model approxmmting the problem.
Adjusted coefficient of desermination of the quadratic regression model without variable interactions.
ela, meta.lin Interact.adj_.r
Adjusted coefficient of determination the linear regression model with variable interactions.
The initial partial infomution from the Information Content Hiness Sequences (ICoHiS) approach [109]
hch max
The maximum information content from ICaFiS.
secpp ratio
The hall patial information sensilixity from ICoFiS. arithmetic
distances among nearest neightbrrs
better neighbors.
ubc. distdiitittioooo cooloo.oocf_eeee. var
The coefficient of variation of the distance ratios.
ela, nisber of peaks
The estimation of the number of peaks in the distribution of the function values.
B.2 Statistical Features for Agent-2
The statistical feature O E R summarized below:
1. The first feature is the minimum objective value in the current (sub-)population indicating the achieved best performance of the current (sub-) hoppuapopulttin:
Sc O., min{ fo. fo.-- )iEL.NN (ecl,NNPaaa Procai]
(8)
It is normalized by the difference between the best objective value at initial optimization for* step and the global optimal objective value of the optimization problem f", so that the scales of the features from different tasks are in the same level. which hence stabilizes the training. N Procal is the (sub-)population size.
2. The second one is the averaged normalized objective values in the current (sub-)population, indicating the average performance of the subb)ppopulation:
ft f0.* - f ]iE[ Prncatl
O mean
(9)
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3. The variance of the normalized objective values in the current (sub- puubb))opulation, indicating the variance and convergence of the (sub- )population
ft 0 = std{ f f
Jie JiE J.
(10)
4. The next feature the maximal distance between the solutions in (sub-)population, normal- ized by the diameter the search space, measuring the convergence:
| 23112 12
O
max
| /b|l2
(11)
where ub and lb are the upper and lower bounds of the search space.
5. The dispersion difference [110] feature is calculated the difference of the maximal distance between the top 10% solutions and the maximal distance between all solutions in (sub-)popullaton:
| xzylb
0,55
max 1, Procal)
[ub lb|l2 2
(12)
max 1.J Ptecal
Iub lb|12
It measures the funnelity the problem landscape: single funnel problem has a smaller dispersion difference while the multi-funnel landscape has larger value.
6. The fitness distance correlation (FDC) [111] describes the complexity of the problem by evaluating the relationship between fitness value and the distance of the solution from the optimum.
Ptocal ExP
P (f: - fdd d²)
O var( {d] (E((L.N varl Ve
(13)
where the f is the averaged objective value in suub-)population, d; || xx ||2 is the distance between 2; and the best solution x², d' = mean (eran(d IiE(I,N is the averaged distance,
var(-) is the variance.
7. The found global best objective among all (sub-) hob-))population, indicating the achieved best performance of the overall optimization:
O,, minf fa. - f hEELNND
(14)
8. This feature is the FDC feature for the overall population:
O NP E (Ji (d;
(15)
var( (E)) var (a(((i)ee(.NN)))
9. The last feature is the remaining optimization budget, indicating the optimization progress:
Oryy ma.: F.s FEs
(16)
FarFEs
where maxFEs Es is maximum allowed function evaluations and F Es is the number of consumed function evaluations.
C Synthetic Problem Set Generation
To construct the large scale synthetic problem set, we first collect 32 representative basic problem functions from popular benchmarks [61, 62], which are listed in Table 5. Given solution E RR., a shift vector E RDD and rotation matrix M E DxD the objective value of a D-dimensional basic problem with problem function fs is formulated as Fo(x)) = fs(MT(x o)). Then to enhance problem diversity, we borrow the idea from CEC benchmarks [61] and construct the "composition" and "hybrid" problems.
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Table 5: Overview of the basic problem functions.
1D
Functions
Modality
Global Structure
Conditioning
Sphere
Unimodal
Adequate
Low
2
Schwefel F12
Unimodal
Adeeuutte
7
Eliipoiiall
Unimodal
Adequite
Low
4
Ellipsiidal high condition
Unimodal
Adequate
High
Bent cigar
Unimodal
Adequate
High
16
Discus
Cnimodal
Adequate
High
Different Powers
Unimodal
Adequate
High
88
Rosenbrock
Unimodal
Adequate
Low
Ackley
Multimdal
Adequate
High
10
Weierstrass
Multmmdal
Weak
High
Griewank
Multimodal
Weak
Low
Rastrigin
Multimodal
Weak
High
Buche Rastrigin
Unimodal
Adequate
High
14
Modified Schwefel
Multimodal
Weak
High
16
Katsuura
Multimoaal
Weak
High
16
Compostie Gniewank-Koeebrrock Function F8F2
Unimodal
Adequatc
Low
17
Escafter' ' F6
Multimodal
Adequate
High
18
Happycat
Multimodal
Weak
Low
19
Hghat
Unimodal
Adequate
Low
20
Lumacek bi- Rustriinn
Multimodal
Weak
High
f21
Zakharov
Unimodal
Adequute
Low
f22
Levy Scaffer's s F7
Multimodal
Weak
High
12
Multimodal
Weak
Low
Sasp-Rattrigin
Multimodal
Weak
Low
155
Linear Slope
Unimodal
Adequate
126
Attractive Sector
Unimodal
Adeeuutte
High
f27
Slep-Ellipsoidal
Multimodal
Weak
Low
128
Shurp Ridge
Unimodal
Adequate
High
129
Rastrigin's 's F15
Unimodal
Weak
Low
7a0
Schwefel
Multimodal
Weak
111
Gallagher's & Gaussian 101-me Peaks
Multimodal
Weak
Low
Gallagher's 's Gaussian 21-hi Peaks
Multimodal
Weak
Low
"composition" problems aggregate basic problems using weighted sum. It first randomly select basic problem functions as the sub-problems [fl...., ."" } where E []. Then for the i-th
sub- sub-problem we generate weight w² E (0, 1]. Finally, the composition problem F. is calculated as the weighted sum of objective values of its sub-problems Fo(x) = Σi= w² f' (M (x - o)) where
the solution, o the shift vector and M is the rotation matrix.
"hybrid" problems decomposition solutions into several segments and evaluate these segments with different sub- problems. It first randomly decomposes D problem dimensions into [2, 5) segments with each segment s² = {di....... .... ,di.D', } where d'-j E [1, D] is the index of the j-th dimension in the segment, D' is the length of the i-th segment satisfying E D D. Then basic problem functions are selected the sub-problems [ , with dimensions respectively. The evaluation of hybrid problem F3 defined as (x()) = ("
D'
To construct the 12800 problem instances, for each problem, the problem type is randomly selected from "single" (basic problem), "composition" and "hybrid". The problem dimension chosen from (5, 10, 20, 50}. the search range is sampled from ([-5.5], [-100, 10]. [020, 20), [-50, 50]} and the maxFEs is selected from [10000, 20000, 30000, 40000, 50000). If the problem type is "single", its problem function is randomly selected from the 32 basic problem functions. If the problem type is "composition" or "hybrid", 2-5 sub-problems as well as their weights or dimension decompositions are determined. After the construction of 12800 problems, we then randomly split them into a training problem set Drrain with 9600 problems and a testing problem set Drest with 3200 problems.
D Pseudo Code of Training
The cooperative training of DesignX is two-stage. Started by three initial models, the Agent-1 model Te, Agent-2 actor wa and critic Vg. we firstly train Agent-1 and freeze Agent-2 models. For each epoch and each problem p Dirain with dimension D. 100 D solutions are sampled, evaluated and then used to caleulate the ELLA features FELA of problem p. Given the feature vector Fp concatenated by basic problem information and FELA. Agent-1 auto-regressively generates the modules Ap using
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Fp mentioned in Section 3.2.1 in the main paper. Controlled by the frozen Agent-2, Ap optimizes problem p using p.maz Es function evaluations and obtains the accumulated reward Rp. which is then used to update π in REINFORCE, [63] manner. After training Agent- the well-trained model frozen and its Agent-2's turn. For each epoch and each problem p E Dirainn Agent-I generates an effective algorithm with modules Ap- For each optimization step, the Agent-2 actor Te determines the hyper-parametent of the CONTROLLABLE modules in A, according to the current state O, The controlled Ap optimizes for one step and obtains the next state O++1 and reward Tr. For each nstep optimization, the actor тe and critic by are updated for kepoch learning steps PPO [64] manner. The pseudo code is shown in Alg. 1. We omit the batch processing for better readability.
The pseudo code of the training of DesignX Input: Training problem set Drrains Modular-EG -CC M, initial Agent-1 model Tg. Agent-2 actor and critic Vip.
Algorithm 1:
Output: Well trained Th, T and Up.
// Training for Agent-1;
Freeze mg;
for epoch to Epoch do
for each p E Derain do
Sample solutions XELA RR 1xp.0p..xp.DD and evaluate them YELA p(XELA):
Obtain the ELA features FELA = ELA(XELA: YELA):
Get the feature vector F, =Concat(p.D) D...caatp....mma......... p.maFFE....
p.ub, p.lb, FELA):
Auto-regressively generate the optimizer Ap T (F. M) following Section 3.2.1;
Initial state Oz=1 = Ap.lopiimize()) Rg = 0:
while Termination condition is not met do
0r (Ot):
O++1, Ap.optimize((e. p);
Rp Rp + rri
end
Update To by in REINFORCE [63] manner;
end end
// Training for Agent-2;
Freeze No:
for epoch to Epoch do
for each p & Drrain do
Generate the optimizer Ap Lines 1~~0;
Initial state O,=1 = Ap.oplimizeel
while Termination condition is not met do
for step = 1 to nssep do
ar (O,);
O Oz+1, Ap ww.oopiiize(a,.
Record transition St, Ge, St41, Ft >;
end
for h = 1 to kepoch do
Update actor ny and critie uy in PPO [64] manner;
end
end end
end
E Experimental Setup
E.1
Training Setup
In this paper, we set the embedding dimension h = 64 and the number of attention head k: 4 for both Agent-1 1 & 2. The number of blocks L is 1 for Agent-1 and 3 for Agent-2. The maximum number
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of modules M is 64 and the predefined maximum configuration size Nmar = 12. The training of both agents on Draain lasts for Epoch 100 epochs with fixed learning rate 0.0001. Agent-1 is trained with a batch size of 128. During the training of Agent-2, for a batch of 64 problems, PPO [64] method used to update the policy and critic nets for kepoch = 3 times for every nstep = 10 rollout optimization steps. All experiments are run on two Intel(R) Xeon(R) 6458Q CPUs with 488G RAM. All baseline configurations align with their original papers.
E.2
Objective Value Normalization
Since the objective value scales of different problems vary, averaging them directly is not fair, it cannot reflect the true performance of baselines. To normalize the values to the same scale, we the best objective value found by random search fp. Rs on problem p. Concretely, for problem p randomly sample p-max F Es solutions in the search range [p.lb, p.ub] and take the best sampled objective value as J p.ns- In the experiment, for the found best objective value f,.,, of baseline in
fedss Then average the normalized objective test run i on problem p, normalize it by p.b. p.
values of baseline b on all problem and all runs as the normalized averaged objective value in Table 1 in the main paper: fo = 1-5 EpeD.... Eis f2.... The similar procedure is conducted on the three realistic benchmarks. We also reversed normalized averaged objective value formulated as 1 fo in the ablation study in Section 4.3.
E.3 Realistic Benchmark
1. Protein-Docking Benchmark [79], where the objective is to minimize the Gibbs free energy resulting from protein-proted interaction between a given complex and any other conformation. We select 28 protein complexes and randomly initialize 10 starting points for each complex, resulting in 280 problem instances. To simplify the problem structure, we only optimize 12 interaction points in a complex instance (12D problem).
2. HPO-B Benchmark [80] an AutoMI MaMMMMILyyprpppa hyper-parameter optimization benchmark which includes wide range of hyperparameter optimization tasks for 16 different model types (e.g., SVM, XGBoost, etc.), resulting in a total of 935 problem instances. The dimension of these problem instances range from 2 to 16. To save evaluation time, we adopt the continuous version of HPO-B, which provides surrogate evaluation functions for time- consuming machine learning tasks. We also note that HPO-B represents problems with ill-conditioned landscape such as huge flatten.
3. UAV Path Planning Benchmark [81] provides 56 terrain-based landscapes as realistic Unmanned Aerial Vehicle (UAV) path planning problems, each of which is 30D. The objective is to select given number of path nodes (x.y.z coordinates) from the 3D space, so the the UAV could fly as shortly as possible in a collision-Fi -fee way.
E.4 Relative Importance Calculation
Taking the relative importance of mutation ("M") modules on modality divide problem instances Drest into those unimodal ones and those multimodal ones. Next we collect the mutation modules used in optimizers generated for unimodal and multimodal problems respectively. We count the occurence of each mutation sub-modules in the two mutation module collections as the histogram shown in the top right of Figure 4 in the main paper. Considering the occurence probabilities of different sub-modules in the two collections for unimodal and multimodal two distributions, the KL-divergence between the two distributions. For characteristics with more than two properties such as dimension, maxFEs and search range, use the maximum KL-divergence among the distributions. Finally, to highlight the relative importance different modules to the same problem characteristic, conduct the mean-std standardization. Given the importance Iw,p of module w E Ω to characteristic the standardized importance is I/ap Iw.e- (n which is shown in the sid (Z
example, we first
then measure the relative importance of mutation modules to modality as
left of Figure 4 in the main paper.
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14
$,025
Revered 1pe--
B.x.
DAY
9/020
8.A.
0.2
Unitum
Sahal
Lis
Halia
Normal
Unitbem
Sobal
Halion
Normal
Unilirm
Sibel
Lits
Halion
Normat
Uniferm
Sabut
Liis
Hallon
Nomal
Figure 10: The performance of optimizers with 5 different initialization modules on Diest and three realistic benchmarks.
Halse
Hadkas Intnkiates
Niching
comne Andivr
Mali-Sinlegy
Hull-SSnkogy
Recrral Cheazeer
Missios
Mistinn
Bioanal Croenver
Bisanaal Cuommer
Heandary Crandd
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Beardar Cormol
BE like
Selectin
Selecton
Scedkin
Popelateen Rodution
Papelvire Rodution
Nr
Vis
Vio
(a)
(b)
Figure 11: Two examples of DesignX generated DE optimizers.
F Additional Experimental Results
F1
Insightful Design Skills in Initialization
In Section 4.2 of the main paper, we observed that certain modules (e.g., Initialization) contribute minimally to optimizer performance. To validate this finding, we replace the Initialization modules in existing optimizers with five sampling methods: Uniform sampling [45], Sobol sampling [94], Latin-hypereube sampling (LHS) [95], Halton sampling [103] and Normal sampling [ [104]. The per- formance of optimizers with different Initialization modules on Diest and three realistic benchmarks are demonstrated in Figure 10. The results show that different Initialization modules have limited impact the optimization performance, which validates the correctness of DesignX: The influence of different initialization methods might be diminished by subsequence more important optimization modules such as mutation modules.
F.2 Examples of Generated DE Optimizers
In this section we provide two examples of the competitive DE optimizers discovered by DesignX in Figure 11. Figure Ila is simple DE/current-to-rande -atirmmm-tt-raannd///iiilaaallla optimizer with an archive for eliminated individuals. It could perform efficiency exploitative optimization on unimodal problems. Figure 1lb is a relatively complex DE optimizer with two sub-populations split by Distance-based Niching module which enhances the population diversity. The two sub-popule sub-populations both use mutation multi-strategy module containing DE mutations: rand2, current-to-r -oadd and current- to-best, followed by the Binomial crossover. The composite mutation modules not only address exploration and exploitation tradeoff but also provide Agent-2 more decision flexibility. Besides, linear population reduction modules are introduced to accelerate the convergence at the end of optimization. These designs make the optimizer superior in solving multimodal problems. The two examples validate the intelligence and effectiveness of DesignX.
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F.3 Additional Results of Ablation baselines
In this section we demonstrate the detailed ablation study results for Diest and the three realistic benchmarks in Figure 12. The results validate that generating optimizer workflow (w/o A2) is more important than hyper-parameter control (w/o Al) general cases. On the other hand, is quite obvious that training Agent-1 and Agent-2 in cooperative way results in better optimization performance. We also observe that the ablated models and the final DesignX model perform equally in HPO-B B tasks, this might reveal that the generalization of DesignX on extremely ill-conditioned BBO scenarios is still limited. This might addressed by some RL-based fine-tuning on specifically constructed ill-conditioned problem set.
0.80
Rosmsed HPn-a 2u
Lo
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acco
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Noo AZ
Devigot
Wo A2
Deugat
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moo Al
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DesignX
Figure 12: Detailed performance of ablation baselines on Drest and three realistic benchmarks.
Table 6: Normalized averaged performance of DesignX and LLMs on synthetic and realistic problems.
GPT-4 Turbo
Gemini-I.S
Deepseek-RI
DesignX
2.211-01
2.08I-0I
2.311-01
8.26E-02
Dreat
17.68E-02
+1.22E-01
#7.26E-02
+1.75E-01
Protein
9.72E-01
9.72E-01
9.71E-01
9.69E-01
Docking
+2.57E-06
12.44E-06
+2.51E-06
12.43E-06
3.78E-01
3.95E-01
4.36E-01
3.44E-01
HPO-B
+1.89H-02
+2.10F-02
+1.98F-02
+1.85E.02
1,28F-01
1.11-00
1,25F-01
1.17E-01
UAV
+1.20E-02
+1.79E-02
+1.23E-02
+2.30E-02
F.4 Comparison to LLMs
We would like to note that Large Language Models (LLMs) also capable of designing algorithms for diverse tasks [18, 19]. In the context of Optimization, however, the potential and expertise level of existing general LLMs may not be very ideal. To demonstrate this, in this section, we consider three LLM baselines: GPT-4 Turbo [1 12], Gemini- 1.5 [113] and Deepseek- R1 [114], and compare their algorithm design ability with our DesignX model on Drest and three realistic problem sets. For each tested problem instance we prompt the LLMs with design requirement: "You are expert in Black-Box Optimization, given a problem instance with following matheraaical form: xxx, and given its dimension IOD, search range as [-10, 10], optimization budget as 10000 function evaluations. Please generate an optimizer with executable code for this problem. Do not generate explanations!". Then execute their generated optimizer code to optimize the problem. The averaged results shown in Table 6. DesignX significantly outperforms LLMs across all benchmarks. While LLMs is demonstrated with powerful general-task-see -tas--sllviingg capability, the results here clearly indicate their lacks optimization aetimizatin-ddmmin-eoo domaain-seeeiffi knowledge. By checking the codes these LLMS generated, found that these general LLMs only capable of recognizing current task is optimization task, while ignoring the specific problem characteristics behind. A direct demonstration that they lean generate specific kind of optimizer: Vanilla DE, for almost all tested problem instances. In contrast, DesignX trained specifically to tailor desired optimizers for diverse optimization problems. Through its learning from Modular-FCC, valuable expert-level knowledge from human experts are effectively injected into the two agents. The cooperative large-scale training enables DesignX's A and Agent-2 learn optimal workflow generation policy and parameter control policy respectively, resulting in state-of-the-art performance.
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Reviews:
[{"review_id": "T5QZRQenJg", "reviewer": "Reviewer_kkQ7", "summary": "This paper presents designX, which is an automated algorithm design benchmark that can learn optimizer for BBO problem efficiently. The authors created a comprehensive algorithmic space that incorporates hundreds of potential related tasks / questions. Then,  a two-agent reinforcement learning approach is proposed to learn from the generated algorithmic space. The proposed learning agents achieve effective performance improvement on the designated benchmarks.", "questions": "- What is the effect of using non-transformer architectures? Any rationale here?\n\n- Maybe I am wrong, but how is the dual-agent system being able to learn on two CPUs system? Shouldn't it be a mixture of GPU + CPU since the agents are GPT-2 like transformers. The author should clarify on this point.", "limitations": "Author didn't mention limitation. \nQuoted\"The limitations of the work are not discussed due to page limitation.\"", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strength\n+ Idea looks pretty interesting, consideration of designing dual-agent looks logical and reasonable.\n+ the efforts on designing the algorithmic space should be helpful for the community.\n+ results seem to be effective. \n+ some of the observation of what DesignX was learned is interesting.\n+ good efforts on open sourcing.\n\nWeakness\n- the design space can still be further extended. In fact, I might interpret the maximum # of action (12?) and # of operation (16?) through the code, but it seems like the author doesn't claim much on the reason to pick certain action or operation pools and to clarify the coverage of their choice is good. If the author mentioned in supplementary materials, I would encourage them to clearly point it out, if not, I think this part needs to be further justified. The authors should also discuss the potential extendibility of the proposed work, especially when the targeted problem is much more complex that the existing operations might not  be enough to serve as a support design choice pool.\n- parts of the illustration of the agent design is somewhat hard to understand. For example, in Figure 2, are the GPT-2 blocks shared by both agents? The same color used might cause such confusion. From the code it seems like they are separate models, but I wonder is the design of these 2 agents share any similarities / differences?\n- The claim said designing such optimizers requires up to month sounds like an overclaim, especially considering all experiments were conducted on two CPUs. The authors can clarify on this.\n- didn't mention limitation", "was_revised": true, "final_justification": "The authors provided a comprehensive rebuttal to my questions. After the discussion, the authors promised to provide revision to the comments I made. These revisions would presumably solve most of my concerns. Therefore, I recommend to accept this paper.", "rebuttal": "We sincerely appreciate the reviewer for your insightful comments and valuable suggestions. For your concerns, we provide following point-to-point responses to address them.\n\n**[W1, Design Space Extendibility and Coverage]**\n\n- Coverage of Modular-EC: we would like to clarify that the operator pool choice and action length choice have provided a wide coverage over existing single-objective optimizers. For operator pool, the 116 submodules are carefully collected by us from decades of literatures and representative BBO optimizers. We provide two DE examples below to showcase Modular-EC could express either simple structure or very complex modern optimizers:\n    1. a simple 1997 DE/rand/1/bin combines: \n        1. Uniform initialization module\n        2. rand/1 mutation module\n        3. binomial crossover module\n        4. Clip boundary control module\n        5. DE-like selection module\n    2. a very advanced and complex 2022 NL-SHADE-LBC optimizer uses:\n        1. Uniform initialization module\n        2. current-to-pbest/1 with archive mutation module\n        3. binomial crossover module\n        4. Halving boundary control module\n        5. DE-like selection module\n        6. Non-linear population reduction module\n    \n    For action length choice (12), we believe it is enough for existing or any potential operators, e.g., even the latest DE algorithms such as  NL-SHADE-LBC (winner of IEEE CEC Congress) holding 3-4 parameters per module.\n    \n- Extendability for Outlier Problems: On the one hand, thanks to our proposed universal interfaces and inherentance architecture in Modular-EC, we believe extending it to embrace other novel algorithmic modules is quite easy to achieve. On the other hand, the 16-bit binary module ID spans a huge module space, many of which are still reserved for future module extension. We agree with the reviewer that extending (or more specifically fine-tuning) DesignX for complex optimization domains still require efforts such as novel fine-tuning strategy. For such point, we cite the paper ConfigX [1], where life-long learning ability of similar modular system has been validated. We will regard this as an important future work to enhance the scalability of DesignX.\n\n**[W2, Agent Model Comparison]**\n\nAgent-1 and Agent-2 use separate GPT-2 models without shared parameters. We will clarify this in the revised paper. \n\n1. Similarity: the internal GPT-2 blocks share same architecture.\n2. Difference: First, the input and output of the two agents differ with each other: for Agent-1, input is the problem feature, output is the softmax distribution of submodules; for Agent-2 input is the concat of submodule-id and optimization status, output is the sample distribution of hyper-parmeter values. Second, the feedforward logics are different: for Agent-1, the GPT-2 auto-regressively output submodules; for Agent-2, it is a self-attention among submodules in the generated workflow.\n\n**[W3, Designing Time]**\n\nWe would like to clarify that when we claim “designing such optimizers requires up to month”, we mean that for humans, designing an optimizer and fine-tune its hyper-parameters to achieve maximal perforamence gain on the target problem might consume days to months. Humans may select a BBO optimizer suitable for the target problem according to their expert-knowledge on optimization, design optimizer’s workfow, fine-tune the hyper-parameters and evaluate the optimizer on the target problems. Such process would repeat over and over again until the optimizer achieves desired performance on the target problem, which is really time-consuming. \n\nIn contrast, our trained DesignX only consumes seconds to infer an algorithm and optimize the given problem. If we understood your question wrongly, please give us timely feedback so we can discuss with you more on this issue.\n\n**[W4&Limitations, Discussion on Limitation]**\n\nWe appreciate your careful reading and constructive suggestion. We will replenish a limitation discussion section into the appendix of the revised paper to enhance this paper’s scientific integrity.\n\n> While Designx has been validated as an effective and novel framework to learn automated algorithm design policy, it still hold two limitations and anticipates further efforts in the future to address them.\n> \n\n> 1. In this paper, the primary optimization domain is restricted within single-objective optimization. However, optimization domains such as multi-objective optimization requires more complex algorithm modules and corresponding training problems, which challenges the extensibility of DesignX. Thanks to the uniform interfaces we have developed in Modular-EC system, complex modules in such optimization domain can be easily integrated, and life-long learning/continual learning techniques might be a promising way to make DesignX embrace diverse optimization domains.\n> \n\n> 2. The training efficiency of DesignX is not very ideal. It still takes us 6 days to train DesignX on high-performance PC. Further improvement such as Multi-card parallel mechanism, proximal training objective construction, architecture simplefication/distillation could be regarded as important future works.\n> \n\nWe hope the above discussion could address your concerns. We will refine such discussion into the revised paper.\n\n**[Q1, Rationale of Transformer Architecture]**\n\nLet us explain the rationale behind our Transformer choice for you. First, we actually have conducted prelimary experiments on other neural network architectures, to be specific, MLP and LSTM architectures. Four experiments were conducted:\n\n- Agent-1 (MLP), Agent-2 (MLP): this experiment fails since MLP can not generate algorithm workflow in an auto-regressive fashion.\n- Agent-1 (MLP), Agent-2 (LSTM): same as above, fails.\n- Agent-1 (LSTM), Agent-2 (MLP): we observe two issues in this experiment, during training of Agent-1, the LSTM encounters gradient explosion due to the MDP of Agent-1 is an reward-delayed one, hence the policy gradient might be too much for LSTM. The parameter control performance of MLP-based Agent-2 is far worse due to MLP can not capture the topology dependency within an complete algorithm workflow.\n- Agent-1 (LSTM), Agent-2 (LSTM): Agent-1 still encounters gradient explosion issue while LSTM-based Agent-2 performs better than MLP-based one. However, it still underperforms DesignX.\n\nSecond, these preliminary results coherent with a recent MetaBBO work ConfigX [1], where the ablation results also reveal that Transformer architecture achieves superior modelling capabability than MLP and LSTM.\n\n**[Q2, Training Hardware]**\n\nWe indeed train our Design on 2 32-core CPUs with 488G RAM. Our primary consideration regarding GPU deployment for agents involves the trade-off between GPU acceleration of network operations and CPU-GPU transfer overhead. The total number of parameters of DesignX’s Agent-1&2 are 100k. For such relatively small models, GPU acceleration cannot offset the overhead introduced by excessive CPU-GPU transfers. Therefore we do not use CPU-GPU mixing strategy. More importantly, during the testing, for a single testing problem, 1 CPU core is enough to infer the algorithm workflow and do hyper-parameter control in the subsequent optimization episode. However, for future work involving larger training sets or models with more parameters, GPU deployment may be efficiency.\n\nWe hope the above responses could address your concerns and anticipate your timely feedback.\n\n[1] Guo, Hongshu, et al. \"Configx: Modular configuration for evolutionary algorithms via multitask reinforcement learning.\" *Proceedings of the AAAI Conference on Artificial Intelligence*. Vol. 39. No. 25. 2025."}, {"review_id": "VttRYhWLih", "reviewer": "Reviewer_CRYE", "summary": "This paper presents DesignX, an automated algorithm design framework that can automatically generate optimization algorithms to black-box optimization (BBO) algorithms. DesignX employs two agents, namely an algorithm structure generation agent (Agent 1) and a parameter tuning agent (Agent 2). Agent1 is responsible for taking the relevant features of the BBO problem and generating a program structure, while agent 2 is responsible for tuning the hyper parameters. The optimization of the two agents is formulated as a dual-agent MDP problem and trained cooperatively.\n\nThe agents are trained on an augmented BBO problem dataset and evaluated on both in-distribution test problems and realistic out-of-distribution problems. Results show that algorithms discovered by DesignX show superior or competitive performance compared to the baseline optimization algorithms, some of which are designed by expert humans. Ablation studies are conducted to test the effectiveness of both agents and additional analysis is presented to demonstrate the design principle of the automatically generated algorithms.", "questions": "1. How expandable is DesignX? If more advanced expert-designed BBO algorithms are available, would it be possible to incorporate them into the pipeline?\n2. If the user is interested in a particular type of (or even just one) BBO problem, would it be possible to train or even fine tune DesignX for their usage?\n3. The training objectives of DesignX include the “optimal objective value” (Line 218). Is this value computed and updated along the training or is it pre-computed? If it is pre-computed, how to ensure its optimality if a solution to the targeting BBO problem is not yet available?\n4. How sensitive is DesignX to the dimensionality of the BBO problems. In the training and testing set, the dimensions of the BBO problems are all under 50. What if the dimension can exceed 1,000 or even 10,000?\n5. The training of DesignX seems to require function evaluation of the BBO problems because the reward is dependent on the objective value. If so, how much slow down will DesignX incur if the BBO problem of interest requires expensive evaluation?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "## Strengths:\n1. The idea of searching for novel algorithms for BBO problems is interesting. Given the large space of BBO problems, it would be exciting to have an automated framework that can generate algorithms for them. Even if the generated algorithms might be suboptimal, it can provide the human with insights in how to design better algorithms.\n2. The presentation of the paper is clear and easy to follow. I like how Fig2 gives an intuitive and detailed overview of the framework.\n3. The experiment section gives comprehensive evaluation of the framework. The design principles revealed from DesignX that initialization is not important (according to the algorithm) is interesting.\n\n## Weakness:\n1. In addition to the training time of DesignX, I suggest presenting the compute resource required to train DesignX, so that the users have a better idea of the resource needed.\n2. Minor: DE seems to refer to Differentiable Evolution, but it is never mentioned in the main paper. I suggest mentioning the full name when it is referred to for the first time.", "was_revised": true, "final_justification": "The authors' rebuttal addressed all of my concerns and questions on this paper. This paper has reasonable technical contents and they also have a reasonable plan for the future direction. I am happy to recommend an acceptance for this work.", "rebuttal": "We appreciate the reviewer for your positive and valuable feedback. For the remaining concerns, we address them as below.\n\n**[W1, Computational Resource Requirement]**\n\nThank you for your valuable suggestion, we would clarify that the computational resources used for DesignX's training are reported in Appendix E.1: we train DesignX on two Intel(R) Xeon(R) 6458Q CPUs with 488G RAM.\n\n**[W2, Abbreviation Issue]**\n\nWe apologize for the overuse of abbreviations. We will follow your suggestion and include the full names of all abbreviations upon their first use in the revised paper.\n\n**[Q1&Q2, Extendibility and Transferring]**\n\nModular-EC is an extensible framework where modules are organized within a hierarchical inheritance architecture and universal interfaces. If more advanced expert-designed BBO algorithms are available, users can decompose algorithms into modules, integrate these modules into Modular-EC by inheriting its base classes and implementing modules using universal interfaces. This approach also works for integrating modules tailored to specific types of BBO problems, such as Bayesian optimization modules for solving expensive problems. With these new modules, similar to ConfigX [1], users can conduct life-long learning to adapt the DesignX model to new modules and solve problems of interest with advanced expert-designed BBO modules.\n\n[1] Guo, Hongshu, et al. \"Configx: Modular configuration for evolutionary algorithms via multitask reinforcement learning.\" *Proceedings of the AAAI Conference on Artificial Intelligence*. Vol. 39. No. 25. 2025.\n\n**[Q3, Optimal Objective Value]**\n\nThe training problems are synthetic problems from well-known optimization benchmarks, including the CoCo BBOB and CEC benchmarks. These problems have known optimal objective values. In this paper, these values are 0. If the optimal objective value for the target BBO problem is not yet available (e.g., for realistic benchmark problems), we use the best objective value found by all baselines across all runs as the \"optimal objective value\".\n\n**[Q4, Dimensionality Sensitivity]**\n\nIn this paper, Modular-EC integrates BBO modules tailored to low-dimensional optimization. For large-scale optimization where dimensionality can exceed 1,000 or even 10,000, DesignX with the current Modular-EC cannot handle these problems. As mentioned in the response to Q1 & Q2, Modular-EC is an extensible framework. We can integrate large-scale optimization modules and conduct transfer learning to enable DesignX to solve high-dimensional problems, which is a future work.\n\n**[Q5, Efficiency on Expensive Problems]**\n\nBBO and MetaBBO optimizers require objective values during optimization; therefore, expensive problems reduce their efficiency. Since DesignX’s reward is calculated using objective values obtained directly from the low-level optimizer without extra evaluations, its incurred slowdown is equivalent to that of both BBO optimizers and other MetaBBO optimizers. To address expensive evaluations, surrogate-based methods have been extensively studied. DesignX could integrate these optimization modules to enhance efficiency for expensive problems.\n\nWe hope the above responses could address your concerns and anticipate your timely feedback."}, {"review_id": "rfQM5kHwrU", "reviewer": "Reviewer_WYcX", "summary": "The authors propose DesignX a novel meta-learning method for the design of model-free black box optimizers. The method consists of two agents, both using transformer policies whose weights are jointly optimized using reinforcement learning on a set of synthetic optimization tasks. The first agent is used at optimization start to select the modular algorithmic workflow conditioned on characteristics of the problem (per-instance algorithm selection) and the second agent is used during every step of the optimization to dynamically determine the parameter values for each module (dynamic algorithm configuration). Authors evaluate the meta-learned reactive black box optimizer on in-distribution and out-of-distribution tasks, and present additional analyses and an ablation regarding the relative contributions of both agents.", "questions": "I have serious concerns that in my view render the manuscript as-is unsuitable for publishing. That being said, if all these concerns are fully addressed, I am open to considerably increase my evaluation score and “accept” the paper.\n\n- Improve positioning in historical AAD context. MetaBBO is a very recent movement that mainly relabels and unifies research directions that have been explored in the algorithm selection, configuration and hyper-heuristic community for decades. Also more recent trends like “learning to optimize” (https://www.jmlr.org/papers/volume23/21-0308/21-0308.pdf) are closely related. I would like to ask the authors to discuss its relation to these lines of works. Furthermore, since agent 2 “automatically learns a policy for hyperparameter tuning”, Dynamic Algorithm Configuration  (DAC, https://www.jair.org/index.php/jair/article/view/13922/26882) should be mentioned.\n- Nuance / clarify the claim that DesignX is “the first framework that jointly learns workflow generation and tuning”. In particular, they should relate this contribution to previous work in “programming by optimization” and on the “CASH” problem. \n- Improve the presentation of the results in Table 1 and Figure 3. In particular, I strongly feel $\\textit{the authors should not average results across multiple methods}$. In addition, I recommend to complement the results with rank-based statistics, ideally combined with rank-based statistical significant tests / critical difference diagrams (https://mirkobunse.github.io/CriticalDifferenceDiagrams.jl/stable/), which would give a better impression of relative performance across the heterogeneous sets. For example in Table 1, instead of picking 20 arbitrary instances, one could partition test instances based on their properties (e.g., dimensionality / modality / etc.) and compute aggregated rank-based statistics per subgroup. Similarly, in Figure 3, results are averaged across many different instances, which is susceptible to outliers and including average rank plots is best practice in these settings. Specifically for Figure 3, using a log scale for the x-axis would be more appropriate, since function evaluations (at least in AutoML) are expensive.\n- Include a baseline (e.g., CMA-ES) to put the existing ablation results into perspective. Also, if possible, include the single-best-solver (SBS) as an ablation on Agent 1. This could be done by retraining DesignX without instance/observation features, causing it to effectively learn a single algorithm template and static setting. Alternatively, a static algorithm configurator (e.g., SMAC) could be used on the Modular-EC search space.\n- Discuss limitations (see Limitations part of this review).", "limitations": "The authors do not discuss the limitations of DesignX.\n\n\nIn particular, I would like to see a discussion of these aspects of the method / evaluation:\n- Computational overhead / resource requirements: Hand-crafted optimizers, in particular evolutionary methods typically add relatively little overhead per Function Evaluation (FE). The overhead of DesignX is likely much higher, as it must query Agent 2 every iteration. The comparison in Figure 3 (#FE on x-axis) is therefore not entirely fair. Furthermore, while most evolutionary methods run of CPU, it is unclear whether DesignX requires GPU.\n- Conceptual complexity / tunability: DesignX is relatively complicated. An important benefit of evolutionary / model-free optimization methods is that they tend to be simple, and relatively easy to tune and adjust when needed. Doing the same for DesignX seems hardly trivial.\n- Evolutionary BBO: DesignX is limited to evolutionary methods. These are not state-of-the-art across all scenarios. In particular, they are known to require a lot of FEs compared to more sample-efficient, model-based optimizers such as Bayesian Optimization. \nIn settings were FEs are expensive, e.g. AutoML, one would typically use Bayesian Optimization methods to get near-optimal results in 10-100 FEs.\n- Tuning of hand-crafted baselines: It is unclear how the parameters for the hand-crafted baselines were chosen. Decades of academic literature and practice have demonstrated the importance of optimizing these for the task at hand. Comparing a method that was meta-learned for 6 days against baselines with default hyperparameter setting is arguably unfair.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 4, "strengths_and_weaknesses": "$\\textbf{Strengths:}$ The paper presents an interesting and novel approach to automated algorithm design (AAD). To the best of my knowledge, this is the first work to combine per-instance algorithm selection with dynamic algorithm configuration in an end-to-end fashion. The method is described in sufficient detail and design decisions explained and motivated. While not the first line of work in this direction, I think the use of deep-RL with modern sequence models (in this case transformers) is very promising. The evaluation, in particular the meta-learning curve shown in Figure 1, as well as the ablations, show this meta-learning approach works, at least to some extent.\n\n$\\textbf{Weaknesses:}$ The authors make some very strong claims (e.g., “the DesignX-generated optimizers continuously surpass human-crafted optimizers by orders of magnitude”), which combined with a lacking positioning in the historical context of AAD, the absence of a critical discussion of limitations, and questionable presentation of the main result, is prone to misinterpretations (especially given the diversity of the NeurIPS target audience).\n\n - While I regard the approach taken in this work to be interesting and novel, I am somewhat concerned about how the authors position their contribution. The related work section, despite claiming to “review the development of Automated Algorithm Design (AAD) over the past decades”  jumps from Genetic programming to recent works published in the last 5 years, ignoring over four decades of active research on the topic. \n- The main novelty claim made is that DesignX is “the first framework that jointly learns workflow generation and tuning”. \n  - First, the distinction between workflow / tuning is not that clear in AAD, parameters often affect workflow and workflow components can be seen as categorical parameters. For example, formulating the AAD as an optimization / configuration problem has been explored under the name programming by optimization (PbO: https://www.cs.ubc.ca/~hoos/Publ/Hoos10.pdf, early examples: https://www.ijcai.org/Proceedings/09/Papers/093.pdf, https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fa23d5b7d494fe40bde7417e3639c7cbd7f347ac, http://www.cmap.polytechnique.fr/~nikolaus.hansen/proceedings/2014/WCCI/CEC-2014/PROGRAM/E-14713.pdf).\n  - Second, while the classical works distinguish between algorithm selection/configuration, the combined Algorithm Selection and Hyperparameter Optimization (CASH problem) has been extensively studied (https://dl.acm.org/doi/10.1145/2487575.2487629).\n- My primary concern is about how the main results are presented. Specifically, I feel $\\textit{the presentation of results in Table 1 and Figure 3 is misleading}$: The averaging of the results of all baselines in the same decade is problematic. One poor member in the generation can easily pull down an entire generation - especially since averages are reported which are susceptible to outliers. For example, inspecting the data provided by the authors, on the first instance in Table 1, CMA-ES has 4.27E-05 (6.02E-06) while designX obtains 2.89E-01. Orders of magnitude worse (LM-CMA-ES even obtains 5.28E-12). Also, showing 20 random instances in Table 1 is not the best way of summarizing the results across the 3200 test functions and the use of rank-based statistics aggregated across all instances would be more appropriate (see Questions to authors), also in Figure 3.\n- The ablations, while interesting, are also very strong (replacing learned by random choices). For Agent 2 (DAC), it is known (and confirmed) that random can be a strong baseline, but for agent 1 (AS), improvement over random algorithm selection is arguably setting the bar too low. In particular, it is best practice in AS to include a comparison with the single best solver (SBS, see also Questions to authors).\n- Failure to discuss limitations. I do not follow the justification by the authors: “The limitations of the work are not discussed due to page limitation”. A lack of space should not be the reason not to discuss limitations. While the main limitations should arguably be mentioned in the main paper, they could have at least added an Appendix discussing these.", "was_revised": true, "final_justification": "The authors' prompt and elaborate responses have addressed most of my original concerns and assuming the promised changes are implemented, I do not see further ground for rejection. I have decided to improve my score to borderline accept (4). For a better score, I am missing a clear / consistent improvement w.r.t. e.g. CMA-ES which, given the complexity of the approach, I believe one could reasonably expect. Nonetheless, the approach is novel and interesting and further work along these lines could bring future improvements.", "rebuttal": "We want to express our deepest gratitude to the reviewer for recognizing our paper as a novel and interesting work. Besides, we also thank you for the valuable and insightful comments. For your concerns, we provide following point-to-point responses to address them.\n\n**[W1&W2&Q1&Q2, Positioning and Related Works Discussion]**  \n\nWe appreciate for the constructive suggestions and agree that key works in related areas should be replenished to enhance the paper’s scientific integrity. To this end, we provide following discussion.\n\n1. L2O:  Sharing the same meta learning paradigm, key difference between L2O and MetaBBO locates at the targeted optimization domain: L2O commonly addresses gradient-based optimization problems (so called White-Box), while MetaBBO such as DesignX addresses gradient-free (black-box) scenarios.\n2. PbO: While level-0 to level-3 PbO is closely related to some automated algorithm design concepts such as parameter selection, configuration, operator selection, algorithm selection, etc. DesignX shows great similarity with the highest level PbO (level-4): providing designs for every where of a program/workflow. However, two differences remain: a) PbO requires context-based program specification for a specific target scenario, which requires developer to provide these prototypes as much as possible, while in contrast, DesignX provides abstract modular space that includes generic operators adaptable for a wide range of scenarios. b) PbO focuses on improving performance on specific tasks, while DesignX serves as a pivotal step toward foundation model with generalization ability for diverse optimization problems.\n3. CASH: CASH methods have been proven effective in many AutoML scenarios, such as selecting machine learning algorithms and corresponding hyper-parameter values for specific tasks. In comparison, DesignX’s target scenarios are a subset of the CASH target scenarios, designing BBO optimizers. However, in terms of methodology, DesignX shows more flexibility in the design process: a) CASH focuses on selecting existing algorithms while DesignX is capable of “creating” new ones. b) CASH determines a parameter setting once for all, while DesignX supports adaptive control.\n4. Others: We also have to note that dynamic algorithm configuration, algorithm selection and hyper-heuristic are also closely related to DesignX. Thanks to the long-standing study on them, DesignX draws valuable insights from them and achieves automated end-to-end algorithm design. \n\nConsidering PbO and CASH, we decide to change our claim from “the first framework that jointly learns workflow generation and tuning” to “the first deep learning framework that jointly learns workflow generation and tuning” in the revised paper. \n\nWe hope the above discussion could address your concerns. We will refine such discussion into the related work of the revised paper.\n\n**[W3&Q3, Better Statistical Presentation]**\n\nThe aggregated results shown in Table 1 and Figure 3 are a deliberate choice to manage the scale of our comparison. Evaluating DesignX against 20 BBO/MetaBBO baselines on thousands of problems generated an immense volume of data, making it impossible to present individual results for all baselines and problems within the confines of the paper. Table 1, therefore, reports average performance on a subset of 20 randomly selected problem instances. Full, disaggregated results have been provided in an Excel spreadsheet within the anonymous GitHub repository (since the time of submission).\n\nIn addition, we appreciate the reviewer for this brilliant idea of using rank-based statistical diagrams!  Following your suggestions, we have conducted all possible partitions of the tested set. The suggested statistical validation is also conducted and the results show that CMA-ES and our DesignX dominate the other baselines with 95% confidence in all tested cases. We showcase two partitions and the corresponding ranking results of the top 10 baselines below and will add all results to the revised paper (Appendix).  \n\n**Unimodal & Multimodal**\n\n|  | DE | CMAES | SaDE | JADE | SHADE | LMCMAES | jDE21 | NL-SHADE-LBC | GLEET | DesignX |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| **Unimodal** | 10.513 | **3.850** | 5.392 | 8.743 | 9.117 | 5.518 | 8.783 | 7.332 | 9.901 | 4.276 |\n| **Multimodal** | 9.840 | 3.497 | 6.216 | 8.702 | 9.617 | 7.715 | 8.707 | 6.100 | 8.884 | **2.952** |\n\n**Adequate Global Structure & Weak Global Structure**\n\n|  | DE | CMAES | SaDE | JADE | SHADE | LMCMAES | jDE21 | NL-SHADE-LBC | GLEET | DesignX |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| **Adequate** | 9.761 | **2.771** | 6.130 | 8.959 | 9.351 | 7.184 | 8.835 | 6.351 | 8.861 | 3.544 |\n| **Weak** | 10.880 | 4.870 | 6.136 | 7.156 | 10.830 | 9.353 | 7.980 | 5.473 | 8.884 | **3.640** |\n\nWe can observe that: for easier problems such as those with unimodal or adequate global structure, CMA-ES achieves better performance due to its straightforward convergence. However, for those multimodal and weak global structure problems, our DesignX is capable of discovering more promising algorithms. We thank the reviewer for leading us to a promising way to present the advantages of our DesignX. \n\nFor Figure 3, we will provide the same ranking results in Appendix and use a log scale for the x-axis in the revised paper.\n\n**[W4&Q4, Ablation Baselines]**\n\nWe have added CMAES and the SBS as baselines according to your suggestion. We report the average performance of them in the following table. \n\n| CMAES | SBS | w/o A1+A2 | w/o A1 | w/o A2 | DesignX |\n| --- | --- | --- | --- | --- | --- |\n| 5.62E-01 | 4.92E-01 | -7.73E-02 | 1.78E-01 | 5.08E-01 | **6.91E-01** |\n\nResults show that 1) DesignX outperforms CMAES, SBS and the ablated baselines. 2) The single optimizer workflow found by SBS cannot defeat the workflows generated by Agent-1 with randomized Agent-2, validating the necessity of generating customized workflows for each problem. \n\n**[W5&Q5, Limitation Discussion]**\n\nWe apologize for the absence of the discussion of limitations. Here we discuss the limitation of DesignX from the four aspects you suggested.\n\n- **Computational overhead / resource requirements:** We report the average solving time of DesignX, traditional BBO optimizer and MetaBBO basleines below: admit that compared to traditional BBO optimizers, DesignX has higher computational overhead due to additional agents. We report the averaged runtime for one test run on one problem of DesignX, BBO optimizers and MetaBBO optimizers below.\n    \n    \n    | DesignX | BBO | MetaBBO |\n    | --- | --- | --- |\n    | 5.5s | 2.6s | 3.6s |\n    \n    Indeed, DesignX requires more computational overhead to solve a problem. However, the solving time remains at second-level. Considering that: a) DesignX achieves better optimization performance than baselines, and b) for human users who have limited knowledge of designing optimizers, the time and resources DesignX saves are actually implicit. This reveals certain advantage of our DesignX.\n    \n    For hardware requirements, training DesignX requires two 32 cores CPUs and 488G RAM, while using DesinX to infer only requires a single CPU core.\n    \n- **Conceptual complexity / tunability:** Compared with traditional optimizers, DesignX’s architecture and training paradigm are relatively complex. However, we have to clarify that this is the burden of us, DesignX’s developers, and is not in the development loop of DesignX’s users. With DesignX at hand, a user could solve optimization problems without cumbersome algorithm selection and tuning process. For the generalization aspect of DesignX, we admit more future works have to be explored such as a) improving its life-long learning/continual learning through robust fine-tuning strategy; b) in-depth study on relationship between problem space and generalization boundary.\n- **Evolutionary BBO:** Indeed, the primary focus of DesignX is currently restricted within EC methods. However, the methodology of constructing modular space, the universal interface design, and the corresponding training paradigm is generic. Take BO as an example, on the one hand, we could include algorithm modules in BO methods into Modular-EC thanks to our universal interface design. On the other hand, DesignX could also serve as an inspiration for BO developers to construct their BO version DesignX.\n- **Tuning of hand-crafted baselines:** We would clarify that we have tried two baseline settings: a) default settings, that is, following the settings in their original papers, and b) settings fine-tuned by SMAC3. In preliminary experiment we found that the fine-tuned performance is only comparable with the default settings. This is not surprising since the default choices typically have been set by the authors through careful sensitivity analysis. As a result, as stated in Appendix E.1, we use default settings for hand-crafted baselines.\n\n**[Paper Formatting Concerns]** \n\nWe apologize for any confusion. We have addressed the typos you mentioned in the revised paper. The first matrix $\\mathcal{W}\\_{token} \\in \\mathbb{R}^{13 \\times h}$ in 3.2.1 is a typo. It should be $\\mathcal{W}\\_{feature}$ indicating the problem feature embedder. The second $\\mathcal{W}\\_{token}\\in\\mathbb{R}^{16 \\times h}$ is correct, indicating the tokenizer. \n\nDeveloping DesignX is a long long challenging journey, we really hope this study could appeal more researchers to explore possibility of foundation model for optimization. We hope the above responses could address your concerns and at last turning you back to acceptance side. Thanks for taking your time reading such long long responses. If you have any further questions, we promise timely address them in the next rebuttal phase."}]

Author rebuttal:

Meta-review: DesignX presents a dual-agent RL framework that searches a modular space of black-box optimiser components. One agent proposes an algorithmic structure, the other tunes hyperparameters, and the resulting designs are evaluated across a broad suite of synthetic and applied tasks. The idea is timely, the modular search space is well motivated, and the study is substantial. Reviewers generally found the contribution credible and useful, with performance that is competitive with strong human-crafted baselines such as CMA-ES in several settings. Overall, the paper can be accepted pending incorporation of discussion-phase commitments, as well as minor presentation fixes, including unambiguous diagrams of the two-agent architecture and clear documentation of baseline tuning.
Decision: Accept (poster)