Title: OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling
Venue: NeurIPS 2025
Accepted: yes
Keywords: Optimization Modeling

Operations research

Large language models
Abstract: Optimization modeling is one of the most crucial but technical parts of operations research (OR).
  To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives.
  However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance.
  To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems.
  Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts.
  Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts.
  Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10% improvements on the challenging benchmarks.

OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling

Abstract

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-theart, achieving over 10% improvements on the challenging benchmarks. The code is released at https://github.com/MIRALab-USTC/OptiTree/tree/main .

1 Introduction

Optimization models are fundamental in operations research (OR) with a wide range of critical applications in route planning [33], production planning [4], economics [23], and so on. Typically, real-world OR problems are presented as natural language descriptions that must be manually converted into optimization models before developing solver codes (e.g., Gurobi [14] and Pyomo [6, 16]) to solve. However, the modeling process is highly technical and time-consuming, requiring extensive human expertise and domain knowledge [28]. Modeling experts often engage in thorough discussions with clients to fully grasp the problem scenarios and context. This is followed by a lengthy iterative process to refine and improve the models, enhancing their accuracy and efficiency.

To reduce the time and cost spent in optimization modeling, recent advances have leveraged large language models (LLMs) to automate this process, leveraging the rich domain knowledge learnt by LLMs [39, 1, 17]. Given an OR problem, the LLMs take a natural language description as input and generate both the optimization model and the corresponding solver code. Existing works on LLM-based optimization modeling include the prompt-based modeling methods [39, 1, 2] and the fine-tuned LLM modeling agents [17, 21]. The prompt-based methods typically break down modeling tasks into sequential steps for generating variables, constraints, and objectives [1, 2]. However, this

Variable

𝒙

Constraints

𝑨𝒙 ≤ 𝒃

Objective

𝒎𝒊𝒏

𝒙

𝑓(𝒙)

Subproblem

Subproblem

CVRP

Problem Description

Each vehicle has to

supply customers, and

has a limited capacity,

for each vehicle. Each

customer has an

associated demand,

that must be satisfied

within the customer-

specific time window.

Problem

Description

Hierarchical Modeling Thoughts

for Subproblems

Global Modeling

Thoughts

1) Problem Decomposition

Enhancement

Modeling Tree

3) Modeling Thoughts

Construction

Variable

Construction

Constraint

Construction

Objective

Construction

𝐦𝐢𝐧𝒙 𝑓(𝒙)

s.t

.

𝒈 𝒙

≤ 𝟎

Existing

Prompt-based

Methods

Our OptiTree

Pipeline

𝐦𝐢𝐧𝒙 𝑓(𝒙)

s.t

.

𝒈 𝒙

≤ 𝟎

rigid decomposition does not account for problem complexity, making it particularly challenging for more complex problems and potentially leading to suboptimal modeling accuracy. Our analysis of a challenging dataset reveals that a substantial portion of errors arises from incorrect variable definitions, particularly in the hard modeling problems (please see Motivation 1 in Section 3).

Therefore, a natural question arises: how can we adaptively decompose a problem into simpler subproblems? For each OR problem, we introduce the concept of modeling subproblem , which is defined as parts of the original problem with reduced modeling complexity (please see Section 4.1 for a formal definition). For example, the standard vehicle routing problem (VRP) can serve as a subproblem for more complex variants such as the capacitated VRP (CVRP) and the VRP with time windows (VRPTW). From the perspective of OR, these subproblems share the same taxonomy as the original problems and exhibit similar modeling structures, but their lower complexity makes them easier to model. When modeling a VRP with time windows, we might begin by constructing a standard VRP model and then incrementally integrate the time window constraints. We have observed that these patterns of subproblem decomposition are prevalent across a wide range of complex problems. While most complex problems do not fit neatly into standard OR categories, they often encompass simpler standard OR subproblems (please see Motivation 2 in Section 3). For further understanding, we provide several examples in Appendix C.

In light of this, we propose a novel approach called OptiTree, designed to enhance modeling accuracy by adaptively decomposing complex problems into a series of simpler subproblems. The core of OptiTree is to distill prevalent decomposition patterns from various problems and apply the most suitable ones for unseen complex problems . Specifically, as illustrated in Figure 1, we develop a modeling tree that organizes a diverse range of OR problems according to their taxonomy and complexity. Each node in the modeling tree represents an OR problem, with problems of parent nodes corresponding to the subproblem of their children. We store relevant modeling thoughts in each tree node to enhance the modeling accuracy for each subproblem. Given a problem to solve, we 1) recurrently search for suitable subproblems to decompose, 2) retrieve high-level modeling thoughts for each subproblem, and 3) synthesize global modeling thoughts by adaptively integrating the hierarchical thoughts. To ensure the scalability and reliability of the modeling tree, we dynamically update and refine the subproblems and thoughts across a wide range of OR problems. The notable feature of OptiTree is that it transfers the search into the highly structured subproblem space, significantly reducing the search space while fully leveraging the modeling thoughts associated with the subproblems. Experiments demonstrate that our method achieves state-of-the-art performance, significantly improving modeling accuracy by over 10%.

2 Related Work

LLM-based Optimization Modeling LLM-based optimization modeling has emerged as a promising approach to reduce the time and expertise required during the modeling process [7, 22]. Existing methods in this field can be categorized into prompt-based and fine-tuned methods. Prompt-based methods involve the careful design of modeling prompts for pre-trained LLMs, such as GPT-4o and DeepSeek-V3. Notable works in this area include CoE [39] and OptiMUS [1], which utilize

multi-agent cooperation workflows to iteratively construct models and solver codes. Additionally, [2] employs Monte Carlo tree search to explore the space of variables, constraints, and objectives step by step, identifying the best components for model construction. In contrast, another line of research focuses on fine-tuning LLMs with extensive operations research and modeling knowledge. Examples include ORLM [17], Evo-Step [37], LLMOPT [21], OptMATH [25], and OptiBench [41, 35]. These methods typically generate large modeling datasets to train specialized modeling language models. In this paper, we focus on the prompt-based methods and aim to fully exploit the reasoning capabilities of pre-trained LLMs. Unlike existing approaches that decompose tasks into fixed steps for generating variables, constraints, and objectives, we propose an incremental modeling strategy that involves modeling simpler subproblems.

LLM Reasoning and Retrieval-Augmented Generation LLMs have shown promising performance across various reasoning tasks [43]. However, they are prone to generating false, misleading, or fabricated information-a phenomenon known as hallucination. Consequently, researchers have explored several methods to mitigate these hallucinations [18]. Early approaches, such as Chain-ofThoughts (CoT) [36] and Tree-of-Thoughts (ToT) [42], break down complex problems and solve them step-by-step. The Buffer-of-Thoughts (BoT) [40] method stores a meta-buffer of modeling thoughts, instantiating relevant templates to construct reasoning processes. Recent advances in reasoning LLMs such as OpenAI-o1 [30] and DeepSeek-R1 [8] have gained significant popularity. Additionally, researchers have focused on leveraging external knowledge to further reduce hallucinations [44, 10, 13]. Retrieval-augmented generation (RAG) involves querying vector or text databases for relevant documents and integrating this retrieved information into the generation process, thereby producing more accurate responses [12, 3]. In our work, we search for relevant modeling thoughts for each subproblem and dynamically combine them to generate global modeling thoughts.

3 Motivated Observations

In this section, we present key observations that motivate our decomposition method. (1) The standard fixed-step decomposition approach often fails in complex problems, as accurately identifying variables remains a significant challenge. (2) Most complex OR problems contain subproblems of standard OR problems. (3) The performance of LLMs can benefit from the subproblem decomposition. The experiments in this part are conducted in the modeling dataset IndustryOR [17], which classifies problems into three difficulty levels: Easy, Medium, and Hard.











































































Motivation 1: The Drawbacks of Existing Methods We evaluate CoT [36] on this dataset, breaking the problems down into steps involving variables, constraints, and objective generation. We find that a significant portion of errors arise from incorrect variables, particularly in Medium and Hard problems (over 70%, please see the left subfigure of Figure 2). This indicates that existing decomposition methods are not well-suited for complex problems.

Motivation 2: Prevalent Subproblem Decomposition Patterns We first collect the optimization models in the textbook [1] as a ground-truth model for the 50 standard problems. For a problem in IndustryOR to formulate, we use LLM to identify whether the problem contains subproblems

in the 50 standard OR problems. If a subproblem is identified, we augment the LLM's prompt for optimization modeling by integrating the relevant ground-truth model of the subproblem as hints. As shown in the middle subfigure of Figure 2, the LLM identifies subproblems for 69% of the problems. Upon manual verification, we find that over 63% of problems are associated with correct subproblems. These results underscore the prevalence of subproblem decomposition and demonstrate that LLMs are effective in identifying relevant subproblems with high identification accuracy.

Motivation 3: LLMs Perform Better with Vanilla Subproblem Decomposition We leverage the set of 50 standard OR problems as subproblem candidates to guide the modeling process. For each problem in IndustryOR, we decompose the process into two steps. First, we use LLM to select a suitable subproblem from the candidates. If a relevant subproblem is identified, we provide the ground-truth models for that subproblem before proceeding to model the original problem based on it. We evaluated the performance of LLMs using this two-step approach and present the results in the right subfigure of Figure 2. Our findings indicate that modeling based on a subproblem reduces task complexity and has the potential to enhance performance.

4 OptiTree: Hierarchical Thought Generation with Tree Search

The overall framework of OptiTree is illustrated in Figure 3. The core is to organize modeling knowledge through a hierarchical tree structure that captures both prevalent decomposition patterns and thoughts for various problems (Section 4.2). We utilize tree search for efficient retrieval of subproblems along with their hierarchical modeling thoughts, adaptively integrating these thoughts to construct comprehensive global modeling thoughts (Section 4.3). To ensure scalability and reliability, we construct the modeling tree using a real-world modeling dataset, dynamically managing both subproblems and modeling thoughts. This enhances the tree's capacity to distill more decomposition patterns and thoughts, allowing it to generalize effectively to unseen complex problems (Section 4.4).

4.1 Subproblem Definition and Identification

Given an OR problem P , we specialize the corresponding optimization model as follows,

where f denotes the objective function, x is the decision variables, g i represents the the i th constraint function, and β i is the parameters in the i th constraint. Suppose that we partition the variables into two groups x = (˜ x 1 , ˜ x 2 ) , the objective and constraints has the decomposition f ( x ) = f 1 (˜ x 1 ) + f 2 (˜ x 2 ) + f 3 (˜ x 1 , ˜ x 2 ) , and g i ( x i , β i ) = g i, 1 (˜ x 1 ; ˜ β i, 1 ) + g i, 2 (˜ x 2 ; ˜ β i, 2 ) + g i, 3 (˜ x 1 , ˜ x 2 ; ˜ β i, 3 ) . We define another OR problem ˜ P as a subproblem of P , if the optimization model takes the following form,

where β i k ,j is the parameter, and the optimization model (2) can be viewed as part of the original optimization model (1). However, we need to identify a subproblem through the natural language descriptions, as the ground-truth optimization models are unavailable in practice. Directly comparing two problem descriptions can lead to hallucination issues for LLMs, so we adopt a clear and comprehensible format. We first use a LLM to distill and summarize the problem description into a set of atomic high-level statements C P = { c 1 , c 2 , · · · , c n P } , called statement thoughts, where each thought c i summarize a feature or requirement related to optimization modeling. We then use the LLM to identify a subproblem ˜ P of P , if statement thoughts of ˜ P are semantically contained within those of P (denoted by C ˜ P ⊆ S C P ). With slight abuse of notation, we write ˜ P ⊆ S P to indicate that ˜ P is a subproblem of P . Due to the limited space, please see Appendix J.1 and J.2 for examples of statement thoughts and detailed meta-prompts for subproblem identification.

Now we formulate the modeling process using subproblem decomposition as follows. We decompose the OR problem as a series of subproblems [ P (1) , P (2) , · · · , P ( M ) ] , where M is the subproblem number and P (1) ⊆ S P (2) ⊆ S · · · ⊆ S P ( M ) . We then build the optimization model incrementally.

Structure of Modeling Tree

Modeling Thoughts Generation

Update of the Modeling Tree

DVRP

VRP

CO

𝐦𝐢𝐧𝒙 𝑓(𝒙)

subject to

𝒈 𝒙

≤ 𝟎

CVRP

VRP

CO

3) Optimization Model Generation

Modeling

& Solving

Answer: 49

Optimization Modeling

Thought Generation

Global Modeling Thoughts

DVRP

VRP

CO

1) Subproblem Decomposition

2) Modeling Thoughts Construction

Subproblem

Problem Type:

VRPTW

Statement Thoughts

:

Vehicle Capacity, Time Windows, Single

Visit, Depot Start/End, Travel Time and

Service Time, Route Continuity.

Modeling Thoughts

:

•

Define Variables

•

Binary

for vehicle travel,

•

𝑠𝑖

for arrival time

•

𝑞𝑖

for vehicle load.

•

Define Objective Function

•

Define Constraints

•

Flow Conservation

•

Time Window Constraints

•

Time Linkage

•

Load Constraints

•

Depot Constraints

•

Gurobi

Template

1) Problem Verification

DVRP

CVRP is a

subproblem

but not for

DVRP

2) Node Expansion

3) Verification

Maximum

Subproblem

Answer: 60

Modeling

& Solving

Schema

Distillation

Original

Problem

Validation Problem (CVRP)

Schema

4.2 Modeling Tree for Problem Decomposition

We propose the concept of modeling tree for problem decomposition. We also utilize the modeling thoughts, distilled from the real-world modeling process for each subproblem, to effectively guide LLMs in accurately modeling these subproblems.

Modeling Thoughts for OR Problems Most complex OR problems involve conventional modeling techniques, such as variable definition and constraint formulation, which can be implicit and pose significant challenges for reasoning. Thus, we distill these modeling techniques into high-level modeling thoughts, which serve as concise, step-by-step guidelines for the modeling process. When faced with a similar optimization problem, we can utilize these informative thoughts to enhance accuracy. Specifically, we design a comprehensible schema to efficiently retrieve and apply the modeling thoughts (Please see the left of Figure 3 for the schema). Each schema contains three critical elements: (1) the name of problem category, (2) statement thoughts C P for problem identification, and (3) modeling thoughts T ( P ) to guide the modeling process. These modeling thoughts include concrete reasoning steps for variable definition, constraint formulation, objective formulation, and Gurobi code templates. Unlike static examples, these thoughts are flexible and can generalize to various complex problems with similar mathematical structures.

Modeling Tree of OR Problems While existing prompt-based and fine-tuned methods consider each OR problem individually, our method fully recognizes the relationships between different OR problems and organizes them into a taxonomy tree known as the modeling tree. In this structure, each node represents an OR problem along with its corresponding schema of modeling thoughts. The root node represents an abstract class of combinatorial optimization problems. Each parent node is a subproblem of its child nodes; that is, if the node P i is a child of P j , then P j ⊆ S P i . Child nodes inherit fundamental constraints and variables from their parent nodes while adding specialized components. For example, the VRP branch might split into dynamic VRP (DVRP) and VRP with time windows. The top tier of the tree consists of simpler, foundational OR problems that are easier to model, while deeper levels feature increasingly complex variations. This structure organizes similar problems into the same branch and facilitates an efficient search for the subproblems. Please see the left of Figure 3 for the structure of the modeling tree. We formally define this structure as follows.

Definition 4.1. The modeling tree is called subproblem order-preserving if for any problem P i that is the ancestor of problem P j , it holds that P i ⊆ S P j .

4.3 Modeling Thoughts Searching and Construction

Tree Search for the Subproblems and Modeling Thoughts Given an OR problem P to model, we search the modeling tree for suitable subproblems for decomposition. We employ an LLM to extract the statement thoughts C P and compare C P with the statement thoughts at the tree node to identify relevant subproblems. Starting from the root node, we search for the first subproblem in the first tree level, i.e., P (0) 1 , P (0) 2 , · · · , P (0) T . We select the subproblem that best matches P based on the highest similarity,

where I is the indication function with I ( a ) = 1 if the condition a is true and I ( a ) = -∞ otherwise. SimLLM represents the similarity score provided by the LLM, measuring the similarity between two problems. We select the child problem P (1) and continue the search process on the corresponding tree node. If none of the children qualify as subproblems of P (with similarity score 0), we terminate the search. If the search halts at the root node, we do not provide modeling thoughts. Please see Appendix J.2 for meta-prompts for the tree search.

Global Modeling Thought Construction We obtain a series of identified subproblems P (1) , P (2) , · · · , P ( M ) of increasing complexity. Notably, the modeling thoughts of the problem P ( M ) encompass those of the preceding subproblems. Thus, we call P ( M ) the maximum subproblem . We retrieve the corresponding modeling thoughts of P ( M ) , i.e., T ( P ( M ) ) . Subsequently, we combine these modeling thoughts with the problem description of P to synthesize the global modeling thoughts T ( P ) , thereby enhancing the modeling process (for meta-prompts, please see Appendix J.3).

4.4 Construction of the Modeling Tree

Tree Construction The tree construction and updating process is fully automated and does not require human curation. To ensure the problem coverage and reliability, we construct the modeling tree from scratch using a dataset that includes problem descriptions and their corresponding groundtruth optimization models. This allows us to distill decomposition patterns and modeling thoughts effectively. In practice, we choose parts of the OR-Instruct 3K dataset, which is the training dataset of ORLM [17] covering a wide range of OR problems. We sequentially add tree nodes to enhance the capacity of the modeling tree. For each problem in the dataset, we evaluate whether it should be integrated into the tree. First, we conduct a tree search for subproblems and identify the maximum subproblem P ( M ) , which has the greatest depth. We then construct global modeling thoughts using T ( P ( M ) ) to guide the modeling process and solve the model for the final answer. If this final answer matches the ground-truth answer, no update to the tree is necessary, indicating that the modeling tree can successfully handle this type of problem. Conversely, if the answers differ, it suggests the emergence of new decomposition patterns or modeling thoughts, necessitating an update to the tree using the failed problem P .

Node Expansion We aim to expand the tree node with the problem P by following carefully designed rules to maintain the subproblem order-preserving structure. Due to the search process, P should be a child node of P ( M ) , as P ( M ) is the maximum subproblem. We first distill the modeling schema ( problem type , C P , T ( P )) for the failed problem. Next, we verify the subproblem relationships between P and the children of P ( M ) , denoted as, P ( M ) 1 , P ( M ) 2 , · · · , P ( M ) T M .

If P ⊆ S P ( M ) k , we insert P as a child of P ( M ) and as a parent of P ( M ) k .

Otherwise, we insert P as a child of P ( M ) and as a sibling of P ( M ) k .

Proposition 4.2. The modeling tree remains subproblem order-preserving during the update process.

Please refer to Appendix F for the proof. After adding a new node, we conduct the decomposition and modeling process again to verify the correctness of the new nodes, continuing this until the problem P can be correctly modeled.

5 Experiments

5.1 Experiment Setups

Dataset We consider seven modeling datasets to evaluate our method and the baselines. (1) NL4Opt [32] is from NL4Opt competition in NeurIPS 2022, composing 289 elementary-level linear programming problems. (2) MAMO EasyLP [20] contains 652 easy linear programming problems. (3) MAMO ComplexLP [20] consists of 211 more complex optimization problems. (4) ComplexOR [39] has 19 challenging problems derived from academic papers, textbooks, and real-world industry scenarios. (5) IndustryOR [17] contains 100 real-world problems from eight industries with different difficulty levels: Easy, Medium and Hard. Finally, (6) OptiBench [41] contains 605 problems, and (7) OptMATH [25] dataset has 166 challenging problems. The work OptMATH [25] proposed a data generation process for optimization modeling; OptMATH can be referred to both the testing dataset and the model trained on the training set.

Baselines OptiTree is a prompt-based model for LLM-based optimization modeling. We compare our method mainly with seven prompt-based baselines. The five prompt-based methods are as follows. (1) Standard is the direct output of pre-trained LLMs. (2) Chain-of-Thoughts (CoT) breaks the problem into reasoning steps. (3) Chain-of-Expert (CoE) [39] is a multi-agent workflow for modeling, with agents focusing on interpreting the problems, formulating the problems, writing and debugging the solver codes. (4) OptiMUS [1] is an improved multi-agent workflow with structured problem input. (5) MCTS [2] employs Monte Carlo tree search to search for variables, constraints and objective sequentially in different search depths. We also compare our method with (6) DeepSeekR1 [8] and (7) OpenAI-o1 [30]. For completeness, we also report the results of fine-tuned OR LLMs. The fine-tuned models, (8) ORLM [17] (using LLaMA-3-8B as backbone), (9) Evo-Step [37] (using LLaMA-3-8B as backbone), (10) OptMATH [25] (using Qwen2.5-32B as backbone) and (11) LLMOPT [21] (using Qwen1.5-14B as backbone). Notice that the trained model of OptMATH and Evo-Step have not been released, the results of these two baselines follows those in the original papers [37] and [25].

Metric and Implementation Following existing works [39, 1, 17, 2, 21], we use solving accuracy to evaluate the performance, i.e., whether the optimal objective of the generated optimization models equals to ground-truth values. To demonstrate the generalization of our method, we conduct experiments on GPT-4o [29] and DeepSeek-V3 [9]. We construct the modeling tree using 400 randomly selected problems in the OR-Instruct dataset [17], which is part of the training dataset for ORLM and contains 3,000 problems. We run across problems in the dataset to update the modeling tree, where the statistical information of the tree can be found in Appendix B.





























































 















































5.2 Main Results

We evaluate OptiTree against the competitive baselines on five modeling datasets using the DeepSeekV3 and GPT-4o models. The results, presented in Table 1, highlight three key findings. (1) High Accuracy . Our method significantly outperforms the baselines, achieving approximately a 10% improvement on the challenging datasets MAMO ComplexLP, ComplexOR, and IndustryOR. (2) Strong Generalization . Using only 400 problems, the constructed OptiTree has shown strong generalization ability across both easy and challenging benchmarks. (3) Adaptation to Different LLMs . Built on top of different LLMs, OptiTree consistently adapts well and exhibits impressive performance. Furthermore, it outperforms state-of-the-art reasoning LLMs, including DeepSeek-R1 and OpenAI-o1. OptiTree also outperforms the fine-tuned modeling LLMs. In Appendix A.1, we also report the proportion of codes generated by the methods that can be executed successfully.

5.3 Analysis on the Subproblem Decomposition

Coverage: Can we find a subproblem in the search process? We present the success rate of identifying subproblems, excluding the root node, in the left subfigure of Figure 4. The results demonstrate that OptiTree can successfully identify subproblems for an average of 88% of the problems. This observation suggests that, despite the diversity and complexity of OR problems, there are prevalent decomposition patterns and modeling techniques that generalize effectively across various problems. The modeling tree successfully captures these patterns.

Reliability: Does the obtained subproblem correctly match the original problem? Werandomly sample twenty problems from each dataset (nineteen from ComplexOR) where LLMs can identify at least one subproblem. We manually verify whether the selected subproblems are suitable and relevant. We compare OptiTree with its variant, OptiTree w/o Statement Thoughts, which relies solely on problem descriptions for subproblem identification. The results in the right subfigure of Figure 4 demonstrate that OptiTree achieves a high accuracy in subproblem identification, while OptiTree w/o Statement Thoughts suffers from a severe drop in accuracy.

Efficiency: What about the time cost of the searching process? We analyze the average time cost for each problem, comparing OptiTree with other prompt-based baselines in Table 2. We (1) use tree search to find an appropriate problem and (2) perform optimization modeling, combining the modeling thoughts from the problem. The two parts of time (Tree search and modeling) refer to these two steps. We also provide the average time to solve all the problems across the benchmarks. For the baselines, the time is just the average inference time, and for OptiTree, this is the average of the one-time cost of the tree construction and inference time. Specifically, the one-time cost across the benchmarks is under three hours . The execution time for the solver code is under a second, which can be considered negligible. OptiTree exhibits the highest efficiency compared to baselines. While the search and modeling time increases for more complex problems (such as MAMO ComplexLP, ComplexOR, and IndustryOR), we find that the majority of the time is spent on modeling, indicating that the search process itself is efficient.

To understand why OptiTree is more efficient, we analyze on the following two factors. First, OptiTree explores a much smaller search space. OptiTree searches predefined candidate subproblems, requiring only the identification of the most suitable subproblem within a finite set, instead of the

variable space or constraint space that can grow exponentially large for more complex problems. Second, OptiTree has fewer iterations in the workflow. While the multi-agent-based baselines often use a manager to automatically decide the agent calls, OptiTree avoids the useless agent calls with a more streamlined workflow.

5.4 Ablation Studies

Impact of the Tree Search We first investigate the impact of the tree search on modeling performance. The modeling tree organizes subproblems within its nodes. We compare this approach with a method that does not utilize a tree structure or tree search for problem decomposition, referred to as OptiTree w/o Tree Search. In this variant, LLMs directly select suitable subproblems from a pool at each step, rather than utilizing a structured modeling tree. The subproblem pool is also collected from the same dataset as the modeling tree. As shown in the left subfigure of Figure 5, OptiTree w/o Tree Search exhibits a decline in modeling accuracy. This degradation occurs because the modeling tree effectively reduces the search space and mitigates hallucinations for LLMs at each step.

Impact of the Modeling Thoughts We conduct ablation experiments on the impact of the modeling thoughts. We implement a variant of OptiTree, called OptiTree w/o Modeling Thoughts, which models the corresponding subproblems step by step without utilizing modeling thoughts. The results are presented in the right subfigure of Figure 5. We observe a significant performance drop in this method, particularly on the challenging datasets. This highlights the crucial role of modeling thoughts in guiding the modeling of subproblems.

Impact of the Search Depth To better understand the tree search process, we also conduct experiments on different depth limitations of the tree search process. The depth represents the number of decomposed subproblems in the modeling process, with greater depth allowing for more decomposition subproblems. OptiTree operates without depth restrictions, while we implement two variants-OptiTree (depth=1) and OptiTree (depth=3)-which limit the tree search depths to 1 or 3, respectively. The results in Table 3, demonstrate that a deeper search depth enables the identification of more suitable subproblems for decomposition, resulting in improved modeling performance. OptiTree (depth=3) still achieves promising results, underscoring the effectiveness of the tree search.

Impact of the Statement Thoughts The statement thoughts distilled from OR problems provide a clear and comprehensible format for subproblem identification. To investigate the effects, we implement a variant that disables statement thoughts for subproblem identification, instead relying on the problem descriptions, referred to as OptiTree w/o Statement Thoughts. As shown in Table 4, we observe a significant performance decline without statement thoughts, accompanied by an accuracy drop in subproblem matching in the right subfigure of Figure 4. This decline occurs because the statement thoughts summarize the modeling-related information to reduce hallucinations for LLMs.

6 Conclusion

This paper introduces a novel LLM-based optimization modeling method called OptiTree, which decomposes complex problems into a series of simpler subproblems to enhance modeling accuracy.











 

















































































 







































































OptiTree dynamically updates a modeling tree to store decomposition patterns and modeling thoughts for these subproblems, employing a tree search to identify suitable subproblems at each step. Experimental results demonstrate the superiority of OptiTree, consistently outperforming baseline methods across several challenging modeling datasets.

Acknowledgments

The authors would like to thank all the anonymous reviewers for their insightful comments and valuable suggestions. This work was supported by the National Key R&D Program of China under contract 2022ZD0119801, and the National Nature Science Foundations of China grants U23A20388, 62021001 and 624B1011.

References

Ali Ahmaditeshnizi, Wenzhi Gao, and Madeleine Udell. OptiMUS: Scalable optimization modeling with (MI)LP solvers and large language models. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st International Conference on Machine Learning , volume 235 of Proceedings of Machine Learning Research , pages 577-596. PMLR, 21-27 Jul 2024.

Nicol ´ a s Astorga, Tennison Liu, Yuanzhang Xiao, and Mihaela van der Schaar. Autoformulation of mathematical optimization models using llms. In International Conference on Machine Learning, ICML , Proceedings of Machine Learning Research, 2025.

Mariam Barry, Gaetan Caillaut, Pierre Halftermeyer, Raheel Qader, Mehdi Mouayad, Fabrice Le Deit, Dimitri Cariolaro, and Joseph Gesnouin. GraphRAG: Leveraging graph-based efficiency to minimize hallucinations in LLM-driven RAG for finance data. In Genet Asefa Gesese, Harald Sack, Heiko Paulheim, Albert Merono-Penuela, and Lihu Chen, editors, Proceedings of the Workshop on Generative AI and Knowledge Graphs (GenAIK) , pages 54-65, Abu Dhabi, UAE, January 2025. International Committee on Computational Linguistics.

S. Belil, S. Kemmoé-Tchomté, and N. Tchernev. Milp-based approach to mid-term production planning of batch manufacturing environment producing bulk products. IFAC-PapersOnLine , 51(11):1689-1694, 2018. 16th IFAC Symposium on Information Control Problems in Manufacturing INCOM 2018.

Yoshua Bengio, Andrea Lodi, and Antoine Prouvost. Machine learning for combinatorial optimization: a methodological tour d'horizon. European Journal of Operational Research , 290(2):405-421, 2021.

Michael L. Bynum, Gabriel A. Hackebeil, William E. Hart, Carl D. Laird, Bethany L. Nicholson, John D. Siirola, Jean-Paul Watson, and David L. Woodruff. Pyomo-optimization modeling in python , volume 67. Springer Science & Business Media, third edition, 2021.

Hao Chen, Gonzalo E. Constante-Flores, and Can Li. Diagnosing infeasible optimization problems using large language models, 2023.

DeepSeek-AI. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025.

DeepSeek-AI, Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, Damai Dai, Daya Guo, Dejian Yang, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Han Bao, Hanwei Xu, Haocheng Wang, Haowei Zhang, Honghui Ding, Huajian Xin, Huazuo Gao, Hui Li, Hui Qu, J. L. Cai, Jian Liang, Jianzhong Guo, Jiaqi Ni, Jiashi Li, Jiawei Wang, Jin Chen, Jingchang Chen, Jingyang Yuan, Junjie Qiu, Junlong Li, Junxiao Song, Kai Dong, Kai Hu, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Lei Xu, Leyi Xia, Liang Zhao, Litong Wang, Liyue Zhang, Meng Li, Miaojun Wang, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Mingming Li, Ning Tian, Panpan Huang, Peiyi Wang, Peng Zhang, Qiancheng Wang, Qihao Zhu, Qinyu Chen, Qiushi Du, R. J. Chen, R. L. Jin, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, Runxin Xu, Ruoyu Zhang, Ruyi Chen, S. S. Li, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shaoqing Wu, Shengfeng Ye, Shengfeng Ye, Shirong Ma, Shiyu Wang, Shuang Zhou, Shuiping Yu, Shunfeng Zhou, Shuting Pan, T. Wang, Tao Yun, Tian Pei, Tianyu Sun, W. L. Xiao, Wangding Zeng, Wanjia Zhao, Wei An, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, X. Q. Li, Xiangyue Jin, Xianzu Wang, Xiao Bi, Xiaodong Liu, Xiaohan Wang, Xiaojin Shen, Xiaokang Chen, Xiaokang Zhang, Xiaosha Chen, Xiaotao Nie, Xiaowen Sun, Xiaoxiang Wang, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xingkai Yu, Xinnan Song, Xinxia Shan, Xinyi Zhou, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, Y. K. Li, Y. Q. Wang, Y. X. Wei, Y. X. Zhu, Yang Zhang, Yanhong Xu, Yanhong Xu, Yanping Huang, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Li, Yaohui Wang, Yi Yu, Yi Zheng, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Ying Tang, Yishi Piao, Yisong Wang, Yixuan Tan, Yiyang Ma, Yiyuan Liu, Yongqiang Guo, Yu Wu, Yuan Ou, Yuchen Zhu, Yuduan Wang, Yue Gong, Yuheng Zou, Yujia He, Yukun Zha, Yunfan Xiong, Yunxian Ma, Yuting Yan, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Z. F. Wu, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhen Huang, Zhen Zhang, Zhenda Xie, Zhengyan Zhang, Zhewen Hao, Zhibin Gou, Zhicheng Ma, Zhigang Yan, Zhihong Shao, Zhipeng Xu, Zhiyu Wu, Zhongyu Zhang, Zhuoshu Li, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, Ziyi Gao, and Zizheng Pan. Deepseek-v3 technical report, 2025.

Wenqi Fan, Yujuan Ding, Liangbo Ning, Shijie Wang, Hengyun Li, Dawei Yin, Tat-Seng Chua, and Qing Li. A survey on rag meeting llms: Towards retrieval-augmented large language models, 2024.

Maxime Gasse, Didier Chételat, Nicola Ferroni, Laurent Charlin, and Andrea Lodi. Exact combinatorial optimization with graph convolutional neural networks. Advances in neural information processing systems , 32, 2019.

Zirui Guo, Lianghao Xia, Yanhua Yu, Tu Ao, and Chao Huang. Lightrag: Simple and fast retrieval-augmented generation, 2025.

Shailja Gupta, Rajesh Ranjan, and Surya Narayan Singh. A comprehensive survey of retrievalaugmented generation (rag): Evolution, current landscape and future directions, 2024.

LLC Gurobi Optimization. Gurobi optimizer. URL http://www. gurobi. com , 2021.

Qingyu Han, Linxin Yang, Qian Chen, Xiang Zhou, Dong Zhang, Akang Wang, Ruoyu Sun, and Xiaodong Luo. A gnn-guided predict-and-search framework for mixed-integer linear programming. In The Eleventh International Conference on Learning Representations , 2023.

William E Hart, Jean-Paul Watson, and David L Woodruff. Pyomo: modeling and solving mathematical programs in python. Mathematical Programming Computation , 3(3):219-260, 2011.

Chenyu Huang, Zhengyang Tang, Shixi Hu, Ruoqing Jiang, Xin Zheng, Dongdong Ge, Benyou Wang, and Zizhuo Wang. Orlm: A customizable framework in training large models for automated optimization modeling. Operations Research , 2025.

Lei Huang, Weijiang Yu, Weitao Ma, Weihong Zhong, Zhangyin Feng, Haotian Wang, Qianglong Chen, Weihua Peng, Xiaocheng Feng, Bing Qin, and Ting Liu. A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions. ACM Trans. Inf. Syst. , 43(2), January 2025.

Taoan Huang, Aaron M Ferber, Arman Zharmagambetov, Yuandong Tian, and Bistra Dilkina. Contrastive predict-and-search for mixed integer linear programs. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st International Conference on Machine Learning , volume 235 of Proceedings of Machine Learning Research , pages 19757-19771. PMLR, 21-27 Jul 2024.

Xuhan Huang, Qingning Shen, Yan Hu, Anningzhe Gao, and Benyou Wang. Mamo: A mathematical modeling benchmark with solvers. CoRR , abs/2405.13144, 2024.

Caigao JIANG, Xiang Shu, Hong Qian, Xingyu Lu, JUN ZHOU, Aimin Zhou, and Yang Yu. LLMOPT: Learning to define and solve general optimization problems from scratch. In The Thirteenth International Conference on Learning Representations , 2025.

Beibin Li, Konstantina Mellou, Bo Zhang, Jeevan Pathuri, and Ishai Menache. Large language models for supply chain optimization, 2023.

Chunyang Liu, Houzhen Ma, Hengxu Zhang, Xiaohan Shi, and Fang Shi. A milp-based battery degradation model for economic scheduling of power system. IEEE Transactions on Sustainable Energy , 14(2):1000-1009, 2023.

Haoyang Liu, Jie Wang, Zijie Geng, Xijun Li, Yuxuan Zong, Fangzhou Zhu, Jianye HAO, and Feng Wu. Apollo-MILP: An alternating prediction-correction neural solving framework for mixed-integer linear programming. In The Thirteenth International Conference on Learning Representations , 2025.

Hongliang Lu, Zhonglin Xie, Yaoyu Wu, Can Ren, Yuxuan Chen, and Zaiwen Wen. Optmath: A scalable bidirectional data synthesis framework for optimization modeling. In International Conference on Machine Learning, ICML , Proceedings of Machine Learning Research, 2025.

Wenyu Mao, Jiancan Wu, Guoqing Hu a nd Zhengyi Yang, Wei Ji, and Xiang Wang. On efficiency-effectiveness trade-off of diffusion-based recommenders. In The Thirty-ninth Annual Conference on Neural Information Processing Systems , 2025.

Wenyu Mao, Zhengyi Yang, Jiancan Wu, Haozhe Liu, Yancheng Yuan, Xiang Wang, and Xiangnan He. Addressing missing data issue for diffusion-based recommendation. In SIGIR , pages 2152-2161. ACM, 2025.

Mark Meerschaert. Mathematical modeling . Academic press, 2013.

OpenAI. Gpt-4o system card, 2024.

OpenAI. Introducing Openai o1. https://openai.com/o1/ , 2024.

Tianle Pu, Zijie Geng, Haoyang Liu, Shixuan Liu, Jie Wang, Li Zeng, Chao Chen, and Changjun Fan. RoME: Domain-robust mixture-of-experts for MILP solution prediction across domains. In The Thirty-ninth Annual Conference on Neural Information Processing Systems , 2025.

Rindranirina Ramamonjison, Timothy T. L. Yu, Raymond Li, Haley Li, Giuseppe Carenini, Bissan Ghaddar, Shiqi He, Mahdi Mostajabdaveh, Amin Banitalebi-Dehkordi, Zirui Zhou, and Yong Zhang. NL4Opt competition: Formulating optimization problems based on their natural language descriptions. In NeurIPS 2022 Competition Track , pages 189-203, Virtual, 2021.

Russ J Vander Wiel and Nikolaos V Sahinidis. Heuristic bounds and test problem generation for the time-dependent traveling salesman problem. Transportation Science , 29(2):167-183, 1995.

Jie Wang, Zhihai Wang, Xijun Li, Yufei Kuang, Zhihao Shi, Fangzhou Zhu, Mingxuan Yuan, Jia Zeng, Yongdong Zhang, and Feng Wu. Learning to cut via hierarchical sequence/set model for efficient mixed-integer programming. IEEE Transactions on Pattern Analysis and Machine Intelligence , pages 1-17, 2024.

Zhuohan Wang, Ziwei Zhu, Yizhou Han, Yufeng Lin, Zhihang Lin, Ruoyu Sun, and Tian Ding. Optibench: Benchmarking large language models in optimization modeling with equivalencedetection evaluation, 2024.

Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, brian ichter, Fei Xia, Ed Chi, Quoc V Le, and Denny Zhou. Chain-of-thought prompting elicits reasoning in large language models. In Advances in Neural Information Processing Systems 35 , pages 24824-24837, New Orleans, LA, 2022.

Yang Wu, Yifan Zhang, Yurong Wu, Yuran Wang, Junkai Zhang, and Jian Cheng. Evo-step: Evolutionary generation and stepwise validation for optimizing LLMs in OR, 2025.

Xilin Xia, Jie Wang, Wanbo Zhang, Zhihai Wang, Mingxuan Yuan, Jianye Hao, and Feng Wu. High-performance arithmetic circuit optimization via differentiable architecture search. In The Thirty-ninth Annual Conference on Neural Information Processing Systems , 2025.

Ziyang Xiao, Dongxiang Zhang, Yangjun Wu, Lilin Xu, Yuan Jessica Wang, Xiongwei Han, Xiaojin Fu, Tao Zhong, Jia Zeng, Mingli Song, and Gang Chen. Chain-of-experts: When LLMs meet complex operations research problems. In The Twelfth International Conference on Learning Representations , 2024.

Ling Yang, Zhaochen Yu, Tianjun Zhang, Shiyi Cao, Minkai Xu, Wentao Zhang, Joseph E. Gonzalez, and Bin CUI. Buffer of thoughts: Thought-augmented reasoning with large language models. In The Thirty-eighth Annual Conference on Neural Information Processing Systems , 2024.

Zhicheng Yang, Yiwei Wang, Yinya Huang, Zhijiang Guo, Wei Shi, Xiongwei Han, Liang Feng, Linqi Song, Xiaodan Liang, and Jing Tang. Optibench meets resocratic: Measure and improve LLMs for optimization modeling. In The Thirteenth International Conference on Learning Representations , 2025.

Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik R Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. In Thirty-seventh Conference on Neural Information Processing Systems , 2023.

Wang Zehao, Yang Lin, Wang Jie, Wang Kehan, Chen Hanzhu, Wang Bin, Hao Jianye, Lian Defu, Li Bin, and Chen Enhong. Logictree: Improving complex reasoning of LLMs via instantiated multi-step synthetic logical data. In The Thirty-ninth Annual Conference on Neural Information Processing Systems , 2025.

Penghao Zhao, Hailin Zhang, Qinhan Yu, Zhengren Wang, Yunteng Geng, Fangcheng Fu, Ling Yang, Wentao Zhang, Jie Jiang, and Bin Cui. Retrieval-augmented generation for ai-generated content: A survey, 2024.

NeurIPS Paper Checklist

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer:[Yes]

Justification: Please see Section 1 in the paper.

Guidelines:

The answer NA means that the abstract and introduction do not include the claims made in the paper.

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.

The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.

It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes]

Justification: Please see Appendix G in the paper.

Guidelines:

The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.

The authors are encouraged to create a separate "Limitations" section in their paper.

The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.

The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.

The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.

The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.

If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.

While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.

3. Theory assumptions and proofs

Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

Answer: [Yes]

Justification: Please see Appendix F in the paper.

Guidelines:

The answer NA means that the paper does not include theoretical results.

All the theorems, formulas, and proofs in the paper should be numbered and crossreferenced.

All assumptions should be clearly stated or referenced in the statement of any theorems.

The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.

Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.

Theorems and Lemmas that the proof relies upon should be properly referenced.

4. Experimental result reproducibility

Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes]

Justification: Please see Section 5.1 of the paper.

Guidelines:

The answer NA means that the paper does not include experiments.

If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.

If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.

Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.

While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example

(a) If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm.

(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.

(c) If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).

(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.

5. Open access to data and code

Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?

Answer: [No]

Justification: We wil release the code if the paper is accepted.

Guidelines:

The answer NA means that paper does not include experiments requiring code.

Please see the NeurIPS code and data submission guidelines ( https://nips.cc/ public/guides/CodeSubmissionPolicy ) for more details.

While we encourage the release of code and data, we understand that this might not be possible, so 'No' is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).

The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines ( https: //nips.cc/public/guides/CodeSubmissionPolicy ) for more details.

The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.

The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.

At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).

Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.

6. Experimental setting/details

Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?

Answer: [Yes]

Justification: Please see Section 5.1 in the paper.

Guidelines:

The answer NA means that the paper does not include experiments.

The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.

The full details can be provided either with the code, in appendix, or as supplemental material.

7. Experiment statistical significance

Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?

Answer: [Yes]

Justification: Please see Section 5 in the paper.

Guidelines:

The answer NA means that the paper does not include experiments.

The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.

The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)

The assumptions made should be given (e.g., Normally distributed errors).

It should be clear whether the error bar is the standard deviation or the standard error of the mean.

It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.

For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).

If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.

8. Experiments compute resources

Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?

Answer: [Yes]

Justification: Please see Section 5 in the paper.

Guidelines:

The answer NA means that the paper does not include experiments.

The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.

The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.

The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).

9. Code of ethics

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines ?

Answer: [Yes]

Justification: The research conducted in the paper conforms, in every respect, with the NeurIPS Code of Ethics.

Guidelines:

The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.

If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.

The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).

10. Broader impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?

Answer: [Yes]

Justification: Please see Appendix I in the paper.

Guidelines:

The answer NA means that there is no societal impact of the work performed.

If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.

Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.

The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.

The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).

11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [NA]

Justification: The paper poses no such risks.

Guidelines:

The answer NA means that the paper poses no such risks.

Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.

Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.

We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.

12. Licenses for existing assets

Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?

Answer: [Yes]

Justification: We have cited the datasets in Section 5.1.

Guidelines:

The answer NA means that the paper does not use existing assets.

The authors should cite the original paper that produced the code package or dataset.

The authors should state which version of the asset is used and, if possible, include a URL.

The name of the license (e.g., CC-BY 4.0) should be included for each asset.

For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.

If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.

For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.

If this information is not available online, the authors are encouraged to reach out to the asset's creators.

13. New assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?

Answer: [NA]

Justification: The paper does not release new assets.

Guidelines:

The answer NA means that the paper does not release new assets.

Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.

The paper should discuss whether and how consent was obtained from people whose asset is used.

At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.

14. Crowdsourcing and research with human subjects

Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?

Answer: [NA]

Justification: We do not include experiments with human subjects.

Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.

According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.

15. Institutional review board (IRB) approvals or equivalent for research with human subjects

Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?

Answer: [NA]

Justification: The paper does not involve crowdsourcing nor research with human subjects. Guidelines:

The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.

Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.

We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.

For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.

16. Declaration of LLM usage

Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.

Answer: [Yes]

Justification: We have include the prompt of LLMs in Appendix J.

Guidelines:

The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.

Please refer to our LLM policy ( https://neurips.cc/Conferences/2025/LLM ) for what should or should not be described.

Table of Contents for Appendix

A Additional Experiments

A.1 The Code Pass Rate for Each Dataset

We present the code pass rates of various methods across the benchmarks. Following the definition in [39], the code pass rate refers to the proportion of solver code that can be executed without encountering any errors. The results in Table 5 demonstrate that our method achieves the highest code pass rate across all datasets, demonstrating the high quality of the codes generated by our approach.

A.2 The Greatest Search Depth

We report the greatest search depth across different datasets. For the harder datasets, the search depth tends to increase, indicating that more complex problems feature more sophisticated subproblem structures.

A.3 More Evaluation Results

The objective metric is standard in the LLM-based optimization modeling literature [39, 1], and in subsequent works ORLM, LLMOPT, OptMATH, OptiBench. However, defining a robust 'partial credit' metric is a significant challenge. Most existing benchmarks only contain labeled optimal value and do not contain annotated ground-truth optimization model , making the partial credit metric difficult to design. Even with ground-truth models, simple text-based or structural comparisons can be unreliable. A model may have minor syntactic differences from the ground truth but be semantically equivalent. Conversely, a model might be nearly identical yet contain a critical error, such as a misplaced inequality sign.

For further evaluation, we find that the training set in OptMATH has annotated models. We use 100 problems for evaluation. As our method and the baselines were not trained on this dataset, the comparison is safe and fair. We present the percentages of LLM-generated models that align with the ground-truth models based on statistical information, including the number of variables, binary variables, integer variables, constraints and objective values. Note that all the statistical information is just a reference, as the mismatch of variables and constraints does not imply the model is incorrect . Notably, OptiTree exhibits the highest matching ratio with the ground-truth model, underscoring its reliability.

A.4 Built OptiTree on More Models

We conduct experiments to build OptiTree on (1) stronger models, including GPT-o1 and DeepSeekR1; (2) weaker models, including Qwen-2.5 7B and Llama3-8B. The results in Table 8 demonstrate that OptiTree can significantly improve the performance of the LLMs.

A.5 Constructing Modeling Tree with Different Datasets

We investigate the robustness of the datasets for tree construction. (1) For the first variant, we use 100 problems from MAMO EasyLP and 100 from ComplexLP, which we refer to as OptiTree (MAMO). (2) For the second variant, we use 100 problems from the OR-Instruct 3K dataset, representing only 25% of the problems used in our main experiments. We call this variant OptiTree (100 OR-Instruct). We evaluate performance on three challenging benchmarks: MAMO ComplexLP, ComplexOR, and IndustryOR. Unlike the OR-Instruct 3K dataset, the MAMO datasets do not include a ground-truth modeling process for tree construction; we rely solely on the final answers for this purpose. The results presented in Table 9 reveal two key findings. (1) Despite utilizing easier problems without a ground-truth modeling process, OptiTree (MAMO) achieves high performance, with only a slight drop compared to the original OptiTree. (2) OptiTree demonstrates data efficiency, as OptiTree (100 OR-Instruct) exhibits performance comparable to that of the full OptiTree. These findings suggest that common decomposition patterns and modeling techniques are widely applicable across OR problems, and the modeling tree effectively captures this general knowledge across different datasets.

B Subproblem Identification Analysis

We analyze the structure of the modeling tree, where the statistical information of the tree is presented in Table 10. We also examine the problems represented within the modeling tree. We also analyze the subproblem matching distribution in different datasets. We find significantly different distributions of the sbuproblems on different datasets. The consistent superior performance of OptiTree across the datasets demonstrates the strong generalization ability across different problems from various scenarios and difficulty levels.

Resource Allocation Problem

ILP Production Planning with Resource and Demand Constraints

Sales and Inventory Optimization with Profit Maximization

ILP Production Planning with Time and Resource Constraints and Minimum Demand Requirements

Cost-Minimizing Resource Allocation with Capacity Constraints

Product Mix Optimization

Transportation Problem

Land Use Optimization Problem

ILP Production Planning with Resource, Environmental, and Energy Constraints

Blending Problem

Integer Linear Programming for Resource Allocation with Multiple Constraints

Vehicle Routing Problem (VRP)

Binary Budget Allocation Problem with Ratio and Selection Constraints

Budget-Constrained Market Promotion and Education Allocation Problem

Integer Linear Programming (ILP) Production Planning Problem

Multi-Category Capacity Allocation Problem with Proportional and Absolute Constraints

ILP Agricultural Land Allocation with Crop Rotation Constraints

Integer Linear Programming for Resource Allocation with Proportional and Range Constraints

Resource Allocation Problem with Demand Satisfaction

Budget Allocation Problem with Minimum Investment Requirements

Budget-Constrained Biometric System Allocation Problem with Quantity Maximization

Integer Linear Programming for Budget Allocation

Multi-Venue Reservation Optimization Problem with Cost and Fairness Constraints

Bounded Knapsack Problem

Capacitated Facility Location-Allocation Problem with Fixed Costs and Variable Costs

ILP Power Generation Scheduling Problem

Green Vehicle Routing Problem

School Bus Routing Problem

Fixed-Charge Transportation Problem

Knapsack Problem

Multi-Product Inventory Optimization with Relative Demand Constraints

Event Scheduling Optimization

1

10

40

Number of Matched subproblem

Integer Linear Programming for Resource Al ocation with Proportional and Range Constraints

Integer Linear Programming for Resource Al ocation with Multiple Constraints

Capital Budgeting Problem

Discrete Budget Al ocation Problem with Pairwise Constraints

Integer Linear Programming for Urban Planning with Budget Constraints

Budget Al ocation Problem with Minimum Investment Requirements

ILP Production Planning with Resource and Demand Constraints

Land Use Optimization Problem

Resource Allocation Problem

Discrete Budget Al ocation Problem with Multiplicative, Pairwise, and Range Constraints

Cost-Minimizing Resource Al ocation with Capacity Constraints

Transportation Problem

Integer Linear Programming for Resource Al ocation in Construction

Integer Linear Programming (ILP) Production Planning Problem

Integer Linear Programming for Budget Al ocation

Staff Rostering Problem

Integer Linear Programming for Agricultural Resource Al ocation with Yield and Area Constraints

Integer Linear Programming for User Group Service Al ocation

Integer Linear Programming for Staff Al ocation with Service Capacity and Cost Constraints

ILP Production Planning with Time and Resource Constraints and Minimum Demand Requirements

Integer Linear Programming for Emergency Resource Al ocation

Budget-Constrained Market Promotion and Education Al ocation Problem

Multi-Product Inventory Optimization with Relative Demand Constraints

Budget Al ocation Problem with Cost Minimization

ILP Multi-Plant Power Generation Cost Minimization Problem

Integer Linear Programming for Product Launch Optimization

Integer Linear Programming for Service Al ocation with Demand and Staffing Constraints

Multi-Product Inventory Al ocation with Demand and Space Constraints

Single-Period Inventory Optimization with Capacity Constraints

Multi-Product Demand Al ocation Problem with Integer Constraints

Sales and Inventory Optimization with Profit Maximization

Assignment Problem

ILP Power Generation Scheduling Problem

Integer Linear Programming for Energy Consumption Optimization

Integer Linear Programming for Energy Device Operation Optimization

Investment Portfolio Optimization with Proportional and Risk Constraints

Job hop Scheduling

Multi-Objective Capital Budgeting Problem with Weighted Objectives

Product Mix Optimization

Project Scheduling (PERT/CPM)

Public Facility Resource Al ocation Problem with Cost Minimization

Research Funding Al ocation Problem with Cost Minimization

Resource Al ocation Problem with Demand Satisfaction

Resource Al ocation with Service Level Constraints

Safety-Centric Budget Al ocation Problem with Coverage Requirements

Water Resource Al ocation Problem with Recovery Rate Maximization

10 0

10 1

10 2

Number of Matched subproblem

Maximum Flow Problem

Capacitated TSP

Facility Location-Allocation Problem

Transportation Problem

Uncapacitated Facility Location Problem with Transportation Costs

Production Planning Problem

Transshipment Problem

Balanced Transportation Problem

Staff Rostering Problem

Lot Sizing Problem

Blending Problem

Gate Assignment Problem

Set Covering Problem

Product Mix Optimization

Capital Budgeting Problem

1

10

40

Number of Matched subproblem

Transportation Problem

Capacitated Facility Location Problem

Integer Linear Programming Problem

Flow Shop Scheduling

Cutting Stock Problem

Material Blending Optimization Problem

Lot Sizing

Job Shop Scheduling Problem

Vehicle Routing Problem with Time Window (VRPTW)

Knapsack Problem ILP

Generalized Assignment Problem

Knapsack Problem

Budget-Constrained Generalized Assignment Problem

1

2

3

Number of Matched subproblem

Production Planning Problem

Lot Sizing Problem

Transportation Problem

Staff Rostering Problem

Product Mix Optimization

Capital Budgeting Problem

Integer Linear Programming (ILP) Production Planning Problem

Assignment Problem

Knapsack Problem

Multi-Product Lot Sizing with Inventory Constraints

Blending Problem

Cutting Stock Problem

Meal Planning Problem

Resource Allocation Problem

Flow Shop Scheduling

0-1 Knapsack Problem with Cardinality Constraint

Multi-Constraint 0-1 Knapsack Problem

Set Covering Problem

Military Resource Allocation Problem with Probabilistic Outcomes

Vehicle Routing Problem with Time Window (VRPTW)

Transshipment Problem

Capacitated TSP

Quadratic Assignment Problem

School Bus Routing Problem

Cost-Minimizing Resource Allocation with Capacity Constraints

Project Scheduling (PERT/CPM)

Bounded Knapsack Problem

Multidimensional Knapsack Problem

1

10

20

Number of Matched subproblem

C Common Subproblem Decomposition Patterns

In combinatorial optimization, there are commonly subproblem decomposition patterns. Here, we provide observations and examples to illustrate these patterns. First, we can expand a subproblem into more complex problems using the following patterns.

Constraint Addition introduces new constraints to model refined requirements.

Variable Expansion incorporates new decision variables.

Dimensional Replication replicates the problem structure across multiple items.

We provide the following examples to demonstrate the three decomposition patterns.

C.1 Analysis on CVPR and CVRPTW

The Capacitated Vehicle Routing Problem (CVRP) aims to determine optimal routes for a fleet of vehicles to serve a set of customers from a central depot while minimizing total travel cost or distance. The basic CVRP formulation includes constraints ensuring each customer is visited exactly once, vehicles return to the depot, and the fleet size is respected. In contrast, the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) extends the CVRP by adding temporal constraints, requiring each customer to be served within a predefined time window. This introduces additional complexity, as routes must now satisfy both spatial routing constraints and temporal synchronization.

The optimization model for CVRP is as follows. V is the set of nodes (depot 0 and customers), c ij is the travel cost from i to j . x ij is the binary decision variable for route inclusion. K is the fleet size.

̸

The optimization model for CVRPTW is as follows. t i is the service start time at node i . [ a i , b i ] is the time window for node i . s i is the service duration at i . d ij is the travel time from i to j . M is the big-M number.

Notice that CVRP is a subproblem of CVRPTW. We identify the following decomposition patterns.

Variable Expansion. The introduction of new continuous variables t i tracks service times, adding a temporal dimension to the original CVRP.

Constraint Addition: CVRPTW introduces time windows a i ≤ t i ≤ b i and synchronization constraints (time consistency), which refine feasible solutions by eliminating temporally infeasible routes.

C.2 Analysis on SCMCFP and MCNFP

The Single-Commodity Minimum-Cost Flow Problem (SCMCFP) optimizes the flow of a homogeneous good (e.g., water, electricity) through a network to meet supply/demand at nodes while minimizing costs, subject to arc capacity constraints. Its linear programming formulation tracks flow conservation and capacity limits for a single product type. In contrast, the Multi-Commodity Network Flow Optimization Problem (MCNFP) generalizes this by handling multiple distinct commodities (e.g., different goods in logistics, data streams in networks) sharing the same infrastructure. Each commodity has unique sources, sinks, and demands, coupled through shared arc capacity constraints.

The optimization model for SCMCFP is as follows. Suppose that G = ( V, E ) is the network with nodes V and directed arcs E . b i is the net supply ( > 0 ) or demand ( < 0 ) at node i . c ij is the cost per unit flow on arc ( i, j ) . u ij is the capacity of arc ( i, j ) . x ij is the flow decision variable on arc ( i, j ) .

The optimization model for MCNFP is as follows. Suppose that K is the set of commodities. s k , t k is the source/sink nodes for commodity k . d k is the demand for commodity k . c k ij is the commodity-specific arc cost. x k ij is the flow of commodity k on arc ( i, j ) .

Notice that SCMCFP is a subproblem of MCNFP, where we identify the following pattern.

Dimensional Replication: Adds commodity dimension k ∈ K to flow variables.

D Algorithm of OptiTree

E More Related Works

E.1 Machine Learning for Accelerating Mathematical Optimization Solving

Mathematical optimization finds broad applications across critical domains such as chip design [38] and optimization [31]. Driven by advances in graph models [27] and generative models [26], machine learning techniques have been widely adopted to speed up combinatorial optimization solving [5]. These efforts follow main directions: improving key modules in branch-and-bound algorithms [11, 34], and predicting high-quality solutions to warm-start solvers [24, 15, 19].

F Proof of Proposition 4.2

Lemma F.1 (Transitivity of ⊆ S ) . Given three problems P 1 , P 2 and P 3 , if P 1 ⊆ S P 2 and P 2 ⊆ S P 3 , then P 1 ⊆ S P 3 .

Proof. We prove by induction. If the initial tree contains only the root node (abstract OR problem). The property holds trivially. Assume the modeling tree is subproblem order-preserving after k insertions. We show that the tree preserves the property when adding a new node P . We Identify the maximum subproblem P ( M ) for P . For each child P ( M ) t of P ( M ) , P ( M ) t cannot be the subproblem of P . Thus, P cannot be in the descendent of P ( M ) t . We have the following two situations.

Case 1 Analysis ( P becomes parent of P ( M ) t ). By insertion rule, we have P ( M ) ⊆ S P . By assumption we have P ⊆ S P ( M ) t . Finally, the transitivity ensures all ancestors of P ( M ) satisfy P ′ ⊆ S P ( M ) t .

Case 2 Analysis ( P becomes sibling of P ( M ) t ). First, the operation maintains P ( M ) ⊆ S P and P ( M ) ⊆ S P ( M ) t . We notice that no new ancestor-descendant relationships are created between P and siblings, and existing subproblem relations are preserved through shared parent P ( M ) .

Thus, the modeling tree remains subproblem order-preserving. By induction, the proposition holds for all tree updates.

G Limitations and Failure Cases

Following OptiMUS [1], the errors mainly come from three aspects: missing or wrong constraints, incorrect modeling and coding errors. In [1], almost half of the errors come from the incorrect modeling (62.5% for ComplexOR), e.g., defining wrong binary variables in the model. We analyze the failures of OptiTree and normalize the failure rates to sum to 1. We find that most errors are from the missing constraints. OptiTree can significantly reduce the error of incorrect modeling, which mainly comes from the wrong variable definitions. The constraint errors are the main error for OptiTree. First, accurately formulating constraints requires a deep and nuanced understanding of the specific problem scenario and its domain knowledge. For highly specialized or novel OR problems, existing background knowledge may not fully capture the intricate details necessary for precise constraint definitions. The second limitation is the intrinsic reasoning ability of the base LLM . While OptiTree provides a structured framework and knowledge, the final synthesis depends on the LLM's inherent reasoning capabilities. This framework may struggle with problems requiring significant logical or relational reasoning. For instance, in the staff rostering problem, the model must allocate staff for 24-hour shifts to meet coverage constraints (with workers working 8-hour days). If it fails to recognize that the demand period from 1:00 to 2:00 AM is covered by workers who began their shifts at 8:00 PM, it will result in an incorrect constraint and ultimately a flawed model.

H Case Analysis

H.1 Example: Inventory Problem

We provide a detailed analysis of an example from the IndustryOR dataset. This example demonstrates that while OptiTree successfully corrects fundamental structural errors (what [1] terms 'Incorrect Modeling'), it still faces challenges with constraints that require deep, context-specific logical reasoning .

Problem . A factory requires a specialized tool for n planning stages. r j specialized tools are needed. At the end of this stage, all tools used within this stage must be sent for repair. There are two repair methods: one is slow repair, which is cheaper (costs b per tool) but takes longer ( p = 3 stages to return); the other is fast repair, which costs c per tool and requires q = 1 stages to return. If the tools cannot meet the needs, new ones must be purchased, with a cost of a per new tool. Determine an optimal plan to minimize the cost.

The Errors of the Standard Output Model The standard output from DeepSeek-V3 produces a structurally flawed model. It tries to fulfill demand by combining new purchases with tools returning from repair, but it completely lacks any concept of inventory tools. The model given by the Standard output of DeepSeek-V3 is as follows. Let x j ≥ 0 be the new tools purchased at stage j , s j ≥ 0 be the tools sent to slow repair at stage j , and f j ≥ 0 be the tools sent to fast repair at stage j .

Following the errors described in OptiMUS [1], the model output has the error type of Incorrect modeling , which fails to define the Inventory variables I .

The Improvement of OptiTree OptiTree correctly identifies that this problem contains an Inventory Problem subproblem. By applying the modeling thoughts, it generates a much-improved model that correctly introduces inventory variables I and a proper inventory balance constraint. The model given by OptiTree (DeepSeek-V3) is as follows. Let x j ∈ Z + be the new tools purchased at stage j , s j ∈ Z + be the tools sent to slow repair at stage j , f j ∈ Z + be the tools sent to fast repair at stage j , and I j ∈ Z + be the inventory of available tools at start of stage j . OptiTree finds a subproblem of the Inventory Problem for the original problem.

The Errors in the Model Given by OptiTree Despite the structural correction, the OptiTree model still contains a subtle error that requires common-sense logical reasoning . The model does not

account for the finite 10-stage horizon. A human modeler would reason that it is illogical to pay for a repair that will finish after the tools are no longer needed. Slow repairs (taking p = 3 stages) are disabled for the last 3 stages ( j = 8 , 9 , 10 ) since tools sent for repair at these stages wouldn't return by stage 10, and fast repairs (taking q = 1 stage) are disabled for the final stage ( j = 10 ) for the same reason. The repair requirement uses inequality

rather than equality s j + f j = r j , allowing flexibility to not repair tools when unnecessaryparticularly near the end of the horizon. Thus, the final corrected model should be

This demonstrates a limitation where OptiTree applies a general pattern correctly but misses a nuanced, context-dependent constraint. The error stems not from a lack of OR knowledge patterns but from a gap in the base LLM's logical reasoning about the problem's specific context. We believe this limitation will diminish as the underlying reasoning capabilities of LLMs continue to improve.

I Broader Impacts

This paper focuses on the automatic optimization modeling in operations research. The traditional modeling process often demands significant human effort and specialized domain knowledge, making it both costly and time-consuming. Our work aims to enhance the efficiency and accuracy of this process. We introduce a novel tree-based method for organizing operations research problem data. Unlike existing approaches that treat each problem individually, our modeling tree leverages the relationships between different problems. During the modeling process, we can retrieve and utilize valuable modeling thoughts to improve overall effectiveness. Additionally, our research offers new perspectives on organizing, utilizing, and managing knowledge within the field of operations research.

J Prompts for LLMs

In this part, we present the meta-prompts we used in this paper.

J.1 Schema in OptiTree

J.2 Prompts for Subproblem Identification

J.3 Modeling

Modeling with Modeling Thoughts You are a mathematical formulator working with a team of optimization experts. The objective is to tackle a complex optimization problem.

You are an expert in problem analysis and can apply previous problemsolving approaches to new issues. The user will provide a specific task statement thoughts and a modeling thought. Your goal is to analyze the user's task and generate a specific solution based on modeling thought. If the instantiated solution involves Python only provide the code and let the compiler handle it. If the solution does not involve code, provide a final answer that is easy

the code, to extract from the text. It should be noted that all the Python code should be within one code block; the answer should not include more than one code block! And strictly follow the modeling thought to instantiate the Gurobi code, but you should also adjust the input parameter according to the user input! User Input: {user_input} modeling thought: {modeling thought} Please analyze the above user task statement thoughts and modeling thought, and generate a specific, detailed solution. If the solution involves Python code, only provide the code. If not, provide a clear and extractable final answer.

Code Correction

You are an excellent Python programming master who is proficient in analyzing and editing Python code, and you are also good at understanding real-world problems. Your task is: 1. Analyze the given Python code 2. Edit the input code to make sure the edited code is correct and can run and solve the problem correctly. Your response should follow the format below: '''python ## Edited code here '''

J.4 Tree Update

Statement Thoughts Distillation stopping at the root node

You are given a specific combinatorial optimization problem. Your task is to summarize the industrial scene type of this specific problem and provide a detailed statement thoughts of this type. Importantly, you must classify the problem into more precise industrial scenarios, such as the Traveling Salesman Problem (TSP), facility location problem, Parallel Machine Scheduling, and so on. Avoid using broad categories such as linear programming, mixed-integer optimization, integer optimization, Integer Linear Programming Problem, and so on. -**Specific Problem**: {specific_problem}

K Examples

To better understand OptiTree, we provide two examples of OptiTree for each of the five datasets.

K.1 NL4Opt

NL4Opt

Natural Language Description:

A patient can be hooked up to two machines to have medicine delivered, machine 1 and machine 2. Machine 1 delivers 0.5 units of medicine to the heart per minute and 0.8 units of medicine per minute to the brain. Machine 2 delivers 0.3 units of medicine per minute to the heart and 1 unit of medicine per minute to the brain. In addition however, machine 1 creates 0.3 units of waste per minute while machine 2 creates 0.5 units of waste per minute. If at most 8 units of medicine can be received by the heart and at least 4 units of medicine should be received by the brain, how many minutes should each machine be used to minimize the total amount of waste produced?

Subproblem Identification Process:

K.2 MAMOEasyLP

MAMOEasyLP

Natural Language Description:

An environmental organization is planning to invest in two projects: Project X which involves tree planting, and Project Y which focuses on waste management. The investment in each project must be a whole number due to the indivisible nature of resources. The total combined investment for both projects cannot exceed 20 units due to budget limitations. Additionally, the overall environmental impact score, calculated as twice the investment in Project X plus the investment in Project Y, should be at least 10 points to meet their objectives.Each unit of investment in Projects X and Y has an associated cost of 4 and 5 units respectively, and the organization aims to minimize this total cost while meeting all constraints.Given these conditions, what is the minimum total cost required for this scenario? Please provide your answer rounded to the nearest whole number.

Subproblem Identification Process:

MAMOEasyLP

Natural Language Description:

A tourism company is planning to allocate resources between two major services: X represents local sightseeing tours and Y represents adventure activities. The total number of services that can be offered in a month cannot exceed 200 due to resource constraints. The minimum number of local sightseeing tours ( X ) they need to offer is at least 50, and for adventure activities ( Y ), it

K.3 MAMOComplexLP

MAMOComplexLP

Natural Language Description:

Natural Languange description: Imagine you're a college student aiming to balance your diet and budget. You have identified nine different food items from your local grocery store that you can include in your menu: Chicken, Rice, Apples, Steak, Lentils, Fish, Tofu, Cheese, and Bread. Each of these foods provides varying amounts of protein, carbohydrates, and calories, and each comes with its own price. Here is the detailed nutritional content and cost for each food item: Chicken: Gives you 15 grams of protein, 18 grams of carbohydrates, and 300 calories for $4. Rice: Offers 1 gram of protein, 25 grams of carbohydrates, and 267 calories for $2. - Apples: Provide 1 gram of protein, 21 grams of carbohydrates, and 266 calories for $5. - Steak: Contains 6 grams of protein, 3 grams of carbohydrates, and 119 calories for a higher cost of $10. - Lentils: These give 3 grams of protein, 7 grams of carbohydrates, and 166 calories for just$2. - Fish: Delivers 17 grams of protein, 13 grams of carbohydrates, and 129 calories for $8. - Tofu: Offers a substantial 18 grams of protein, 27 grams of carbohydrates, and 216 calories for $10. - Cheese: Gives 12 grams of protein, 17 grams of carbohydrates, and 76 calories for $9. - Bread: Provides 2 grams of protein, a massive 30 grams of carbohydrates, and 258 calories for $4. Your daily dietary goal is to consume at least 90 grams of protein, 105 grams of carbohydrates, and 1805 calories. Your challenge is to figure out how to meet these nutritional requirements from the food options mentioned above while spending the least amount of money. So, what is the least amount of money you need to spend to meet your daily dietary requirements? Please note that the response should be a single answer, asking for only the optimal value.

MAMOComplexLP

Natural Language Description:

Consider a courier company that needs to deliver packages to five distinct cities, denoted as E, F, G, H, and I. The courier can start from any city, but they must visit each city only once and then return to the starting point. The aim is to find a route that would minimize the total delivery cost. The cost might include factors like distance, fuel expenses, or traffic conditions. Here's an outline of the delivery cost between these cities: The cost to deliver from City E to F is 50 units, to G is 48 units, to H is 99 units, and to I is 91 units. From City F, it costs 50 units to deliver to E, 57 units to deliver to G, 84 units to H, and 72 units to I. For City G, the delivery costs are 48 units to E, 57 units to F, 46 units to H, and 86 units to I. If the package starts from City H, it costs 99 units to deliver to E, 84 units to F, 46 units to G, and 29 units to I. Lastly, from City I, it costs 91 units to deliver to E, 72 units to F, 86 units to G, and 29 units to H. What is the least total delivery cost for the courier to visit each city exactly once and then return to the starting point?

Subproblem Identification Process:

{

K.4 IndustryOR

IndustryOR

Natural Language Description:

The number of salespeople required at a 24-hour convenience store in different time periods is as follows: 2:00-6:00 - 10 people, 6:00-10:00 - 15 people, 10:00-14:00 - 25 people, 14:00-18:00 20 people, 18:00-22:00 - 18 people, 22:00-2:00 - 12 people. Salespeople start their shifts at 2:00, 6:00, 10:00, 14:00, 18:00, and 22:00, working continuously for 8 hours. Determine the minimum number of salespeople needed to meet the requirements.

IndustryOR

Natural Language Description:

A wealthy noble passed away, leaving the following inheritance:

A painting by Caillebotte: $25000

A bust of Diocletian: $5000

A Yuan dynasty Chinese vase: $20000

A 911 Porsche: $40000

Three diamonds: each $12000

A Louis XV sofa: $3000

Two very precious Jack Russell racing dogs: each $3000 (will stipulates they must not be

K.5 ComplexOR

ComplexOR Natural Language Description: This problem involves optimizing the number of raw rolls cut from a stock roll to meet specific width orders using various cutting patterns. This is a cutting stock problem. Given a roll of width RollWidth and a set of NumWidths widths Widths to be cut. Each width i has a certain number of orders Orders_i. There are NumPatterns patterns and each pattern j has a certain number of rolls of each width i NumRollsWidthPattern{ i, j }. The problem aims to minimize the total number of raw rolls cut. It is constrained that for each width i , the total number of rolls cut meets the total orders. The decision to be made concerns how to decide the number of rolls cut using each pattern j . The number of widths to be cut is 5. The total number of patterns is 2. The set of widths to be cut from the roll is [2, 3, 5]. The width of the raw roll is 10. The number of orders for each width is [4, 2, 2]. The number of rolls of each width i in each pattern j is [[1, 2, 0], [0, 0, 1]]. Number of rolls cut for each width is non-negative. Total number of rolls cut for each width i must meet or exceed Orders_i. Number of rolls cut using each pattern j must be non-negative. Minimize the total number of raw rolls cut to meet the orders. Subproblem Identification Process: { "matching_problem_type": "Cutting Stock Problem", "reasoning": "The specific problem described involves optimizing the cutting of raw rolls to meet specific width orders using various cutting patterns. This is a classic example of a Cutting Stock Problem, which is explicitly listed in the provided problem types . The objective and constraints of minimizing raw material usage while satisfying order requirements align directly with the characteristics of the Cutting Stock Problem.", "belongs_to_problem_types": true } Get the Modeling Thoughts: { "Problem Type": "Cutting Stock Problem", "Statement Thoughts": "The Cutting Stock Problem is a combinatorial optimization problem commonly encountered in manufacturing and logistics. It involves determining the optimal way to cut raw material rolls of fixed length into smaller pieces of specified lengths and quantities required by customers, with the objective of minimizing the total number of rolls used and thereby reducing waste. The challenge lies in efficiently allocating the cuts to satisfy all customer demands while adhering to the physical limitations of the raw material rolls, Roll Capacity: Each raw material roll has a fixed length, and the total length of all pieces cut from a single roll must not exceed this length., Demand Satisfaction: The total number of each type of piece produced across all rolls must exactly match the customer's specified demand for that type.,

ComplexOR

Natural Language Description:

Capacitated facility location problems focus on determining the optimal placement of a certain number of facilities to serve a set number of customers in a way that minimizes the total cost, considering fixed costs, capacities, customer demands, and transport costs. Capacitated facility location problems deal with locating NumberOfFacilities facilities to serve NumberOfCustomers customers, at minimum total cost. Considering potential facility locations and customer zones as fixed points in a network, each facility has a fixed FacilityFixedCost and a FacilityCapacity. Furthermore, there exists a CustomerDemand for each customer zone, and a FacilityToCustomerTransportCost representing the cost of transport between facilities and customer zones. The number of potential facilities that can be established is 10. The number of customer zones to be served is 20. The fixed cost associated with establishing a facility is [8517, 5068, 9433, 6127, 6033, 5966, 7762, 9406, 6602, 7040]. The cost of transporting goods from each facility to each customer zone is [[80, 94, 44, 51, 190, 44, 129, 178, 129, 91, 172, 119, 177, 150, 90, 51, 53, 97, 184, 87], [139, 33, 104, 135, 50, 176, 97, 121, 47, 29, 186, 163, 149, 108, 156, 169, 100, 160, 153, 85], [153, 36, 18, 170, 18, 181, 178, 68, 171, 106, 159, 110, 21, 106, 91, 29, 144, 140, 155, 116], [103, 59, 78, 125, 14, 11, 152, 95, 76, 173, 36, 148, 75, 132, 59, 153, 113, 74, 185, 71], [193, 186, 130, 145, 114, 150, 33, 154, 20, 75, 103, 30,

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nOptiTree proposes a tree-search framework that adaptively breaks down complex operations-research problems into a sequence of simpler subproblems, navigating a “modeling tree” whose nodes store distilled hierarchical modeling thoughts for large-language-model guidance. During inference, the system selects the most relevant subproblems, assembles their thoughts into a unified modeling plan, and continually updates the tree to preserve subproblem order while capturing new decomposition patterns. Experiments on five optimization-modeling benchmarks show OptiTree lifts solving accuracy by over 10 percentage points versus state-of-the-art prompt and fine-tuned baselines.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n\n* Introduces a modeling-thought tree that stores and retrieves subproblem reasoning snippets, adding a clear structural advance over standard chain-of-thought prompting.\n* Yields double-digit accuracy gains and nearly perfect code-execution rates while cutting inference latency versus prior prompt pipelines.\n* The paper motivates its design with diagnostic analyses, intuitive diagrams, and thorough ablations that clarify each component’s contribution.\n* The method generalize well across all benchmark when the tree is constructed with different dataset.\n\n# Weaknesses\n\n* Focuses on exact objective matches (accuracy). Can provide deeper insight with measuring near-optimality, solver tolerance, or robustness—key factors in real-world optimization.\n* The link between diagnosed variable-definition errors and the chosen decomposition remedy improvements are not convincingly demonstrated.\n* Setup for efficiency comparison is unclear.\n\nQUESTIONS:\n* Can you include results when OptiTree is applied on top of reasoning LLMs (e.g., GPT-o1, DeepSeek-R1) and fine-tuned LLMs (e.g., ORLM, LLM-OPT). This would make the empirical case even more compelling.\n* What is the setup for comparing Efficiency? Because runtime is dominated by tree breadth/depth and LLM calls, does OptiTree’s speed-up stem mainly from exploring a smaller search tree (fewer iterations), or from other engineering choices? Is bigO time complexity possible to provide?  How does OptiTree scale for complex problems?\n* Since high “variable-definition failure” rates motivate the method, can you quantify how much OptiTree lowers this specific error relative to baselines—ideally with a before-and-after breakdown.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper develops a method to improve LLM-based optimization modeling through a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity. Then, they recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts. The authors perform thorough experiments to show the performance benefits of their method.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The high level concepts proposed in the paper make sense and the performance substantially improves from existing methods, especially on the MAMO complex dataset where they raise the performance from 56.8% (previous methods) to 81.5% (their methods).\n2. The authors provide a few ablation studies to justify their methods empirically.\n3. Their motivated observations in Sec. 3 seem insightful.\n\n**Weaknesses:**\n\n 1. The pseudocode provided in the appendix seems unclear and insufficient to reproduce the entire experiments. There are many things that I find confusing, and the authors should revise the pseudocode to provide more clarity:\n     - Page 19: you should explicitly refer to the exact name of the prompt you are using on each line. Just a few examples I find confusing:\n        1. I'm confused about which prompt is used to “synthesize $Tau(P)$ from $Tau(P(M))$” (Algorithm 1, Line 21) - your modeling prompts on page 25-27 does not seem to require the $Tau(P(M))$ information, so how do you generate modeling thoughts by combining information from the maximal subproblem’s modeling thought?\n        2. Algorithm 2, line 3: “modeling fails” - please make it more clear where is this executed and what does this mean.\n        3. Algorithm 2, line 4: What prompt is used to “distill schema (problem type, CP, $Tau(P)$) from P”? \n        4. Algorithm 2, Line 5: $P(M) ← MaximalSubproblem(P, T)$: is this $P(M)$ the same $P(M)$ that you get from Algorithm 1, Line 20?          \n    - Page 23: Modeling Thoughts Distillation: there seems to be two prompts (separated by “You are given a specific combinatorial optimization problem.” on page 24. what’s the difference? \n    - Page 23: Code Correction: how is this prompt used? How many code correct iterations do you do and when do you do it? How much performance benefit do you get from code correction? It seems like the authors did not mention this part at all in the main paper or in the pseudocode.\n    - What’s the difference between the Subproblem Identification prompt (Page 22) and Add New Tree Nodes prompt (Page 27)? Is it just in Page 22 you output an extra similarity score, but for Page 27 you don’t.\n    - Page 24: The “constraints” information in the statement thoughts outputs - are they used anywhere? Do you only use <the more precise of statement thoughts> as the “statement thoughts” for your subproblem matching, or you use the whole json for the matching? \n\nAs a side remark (reproducibility): I strongly encourage the authors to provide the code during the rebuttal period. It seems like this field has issue with code opensourcing, publishing papers without code or delay the opensourcing detrimentally hurt the field’s progress, especially the paper heavily depends on prompting off-the-shelf LLMs. \n\n2. The authors rely on off-the-shelf LLMs for their entire algorithm, which raises the question of robustness of their method (see question 2 for additional questions). The authors should also have a discussion regarding when their tree modeling fails, given that the reliance on the off-the-shelf LLMs.\n3. The authors should report the performance on recent benchmarks including Optmath and Optibench.\n\nQUESTIONS:\n1. While the authors see improvements using GPT-4o and deepseek-v3 to build the tree, can your method further improve (1) stronger models like the reasoning models GPT-o1/3 and deepseek-R1? (2) weaker models like qwen and llama, if they use these models to build the tree and construct solutions? \n2. I wonder if the authors proposed pipeline is sensitive to different dataset used to build the tree? Also, if the pipeline is sensitive of different seeds (do you get drastically different trees if you run the code with different seeds)?\n3. Main paper, Line 221: if $P \\subseteq P_k^{(M)}$: is this a typo, should it be the other way around $P_k^{(M)} \\subseteq P$?\n4. Figure 2: can the authors provide a few examples of the errors in IndustryOR and how their methods help the performance? \n5. Can the authors provide the entire tree built from the algorithm and a minimal script to reproduce the result so that we can examine the meaningfulness of the tree and the algorithm?\n\nLIMITATIONS:\nThe authors discussed limitations in Sec F of the Appendix.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nOptiTree is a prompt-based framework that improves LLM-driven optimization modeling by recursively decomposing a natural-language problem into a chain of simpler subproblems. It constructs an offline modeling tree that organizes OR problem types in a taxonomy; each node stores high-level statement thoughts (key features) and modeling thoughts (variable, constraint, and objective templates). At inference time, an LLM follows the tree from the root to the deepest matching node, assembles the retrieved thoughts into one prompt, and generates solver-ready code.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1.  Focuses on a long-standing bottleneck in operations research by turning LLMs into reliable optimization-modeling assistants. \n2. Constructs a Modeling Tree that stores both “statement thoughts” and “modeling thoughts”, turning prompt retrieval into a structured, hierarchical memory for LLMs.\n2. Proposes an incremental insertion algorithm that allows the tree to grow continuously without retraining.\n\nWeaknesses:\n1.  The paper lacks a clear explanation of how to construct the modeling tree. After reading it, key details remain unclear, such as how to add tree nodes or evaluate whether a problem should be integrated. Is this process fully automated?\n2.  How is the greatest search depth determined during tree traversal?\n3.  Although the paper shows that the Modeling Tree as a whole improves solution quality, it never measures how performance evolves when thoughts are aggregated level-by-level along the search path. Without such a vertical study, it is hard to verify that deeper, more-specific nodes truly add incremental value (rather than the final node alone doing all the work) and to understand the cost–benefit trade-off between prompt length and accuracy.\n4. In the experimental section, it would be beneficial to include comparisons with the latest methods, such as Evo-Step [15] and OptMATH [16].\n\nQUESTIONS:\n1. The paper briefly mentions the limitations of OptiTree. Could the authors elaborate on these limitations in more detail? Specifically, analyzing scenarios where OptiTree may underperform and discussing the potential reasons would provide a more balanced perspective.\n\nFor other questions, please refer to the weaknesses.\n\nLIMITATIONS:\nThe paper briefly mentions the limitations of OptiTree. Could the authors elaborate on these limitations in more detail? Specifically, analyzing scenarios where OptiTree may underperform and discussing the potential reasons would provide a more balanced perspective.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents OptiTree, a novel approach for improving LLM-based optimization modeling through hierarchical problem decomposition. The work addresses the challenge of automating operations research modeling, where complex problems described in natural language must be converted into mathematical optimization models. The core innovation lies in organizing OR problems into a tree structure where complex problems are decomposed into simpler subproblems, enabling more effective modeling through adaptive rather than fixed-step approaches.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper demonstrates good results with comprehensive experiments across five datasets, showing consistent 10%+ improvements on challenging benchmarks compared to both prompt-based methods and fine-tuned models. The methodology is rigorous, including proper comparisons to state-of-the-art reasoning LLMs like OpenAI-o1 and DeepSeek-R1, along with thorough ablation studies examining tree search, modeling thoughts, search depth, and statement thoughts components. \n\nHowever, the paper suffers from clarity issues and has some experimental concerns. The motivating observations lack crucial details - it's unclear which specific dataset was used for the three motivational experiments, what constitutes the \"50 standard OR problems,\" or what it means to \"provide ground-truth models for that subproblem.\" Technical details are often relegated to appendices, making it difficult to understand how statement thoughts are extracted or how the similarity function SimLLM operates. The evaluation has notable limitations, relying solely on solving accuracy (whether optimal objectives match ground truth) without analyzing partial credit. \n\nThe scalability and practical deployment aspects raise additional concerns. Tree construction seems to require human curation for new domains, and it's unclear how this approach scales or what happens when problems don't fit existing tree structures. The paper lacks analysis of tree maintenance costs over time and provides no thorough error analysis of failure cases. From a significance standpoint, \nit seems like the evaluation is limited to standard OR problem types and it may be difficult for this approach to generalize to ML more broadly.\n\nQUESTIONS:\nIn table 2, I am confused by how the compute times for tree search and modeling are calculated. My understanding is that modeling should be a 1-time cost when the tree is originally built. Is this reflected in the table?\n\nLIMITATIONS:\nLimitations could be discussed more thoroughly.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}