Self-Guiding Exploration for Combinatorial Problems

Large Language Models (LLMs) have become pivotal in addressing reasoning tasks across diverse domains, including arithmetic, commonsense, and symbolic reasoning. They utilize prompting techniques such as Exploration-of-Thought, Decomposition, and Refinement to effectively navigate and solve intricate tasks. Despite these advancements, the application of LLMs to Combinatorial Problems (CPs), known for their NP-hardness and critical roles in logistics and resource management remains underexplored. To address this gap, we introduce a novel prompting strategy: Self-Guiding Exploration (SGE), designed to enhance the performance of solving CPs. SGE operates autonomously, generating multiple thought trajectories for each CP task. It then breaks these trajectories down into actionable subtasks, executes them sequentially, and refines the results to ensure optimal outcomes. We present our research as the first to apply LLMs to a broad range of CPs and demonstrate that SGE outperforms existing prompting strategies by over 27.84% in CP optimization performance. Additionally, SGE achieves a 2.46% higher accuracy over the best existing results in other reasoning tasks (arithmetic, commonsense, and symbolic).

Paper

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Peer review

Reviewer 8LKr6/10 · confidence 3/52024-06-14

Summary

This paper introduces a self-guiding exploration (SGE) framework that integrates exploration-of-thought, decomposition, and refinement prompting strategies to tackle NP-hard combinatorial optimization problems (COPs). The experiments, conducted on various COPs and several reasoning tasks, demonstrate improved performance compared to existing prompt strategies. *Based on my expertise, I will evaluate this paper from the perspective of combinatorial optimization.*

Strengths

* The proposed SGE is general and innovative. * The paper is well-organized and clearly written. * The scope of empirical evaluation is extensive, including combinatorial optimization problems and various reasoning tasks. * The source code is provided.

Weaknesses

* Figure 2 is lacking in detail. A comprehensive example, including detailed prompts and outputs, should be provided. * It appears that the decomposition process cannot be parallelized across subtasks due to the dependence on preceding $T_{k-1}^n$. * Limited review of related work: * LLMs/FMs in CP: Many recent studies are missing. Please see [5] for a comprehensive review. * Learning-based methods in CP: Numerous NCO studies, especially those published in the last three years, are missing as well, please see [6]. * My main concern about this paper is the weak experiments, which significantly weaken the contribution of this paper. * This paper only considers 5-30 nodes, which is **too small** for the NCO community. I would suggest generating code, like [2-4], in the decomposition or subtask resolution stages if the performance on large-scale instances is inferior. * The optimality gap (w.r.t. the traditional solver, e.g., LKH3, OR-Tools) and inference time should be reported. * Missing baselines, such as [1-4]. Only several prompt strategies are chosen as baselines. ```tex [1] Large Language Models as Evolutionary Optimizers [2] Mathematical discoveries from program search with large language models [3] Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model [4] Large Language Models as Hyper-Heuristics for Combinatorial Optimization [5] https://github.com/ai4co/awesome-fm4co [6] https://github.com/Thinklab-SJTU/awesome-ml4co ```

Questions

N/A

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

2

Limitations

Yes, the authors discuss the limitations, such as more function calls, and the sensitivity to the used LLMs.

Authorsrebuttal2024-08-08

Thank you for your question. We used general version of EoH (that was used for Bin Packing problem). Specifically, in our case, for the Job Shop Scheduling task, EoH generated heuristics that scored the job nodes, and the algorithm then selected the job with the highest score as the next one in the schedule. However, we found out, for more complex tasks than Bin Packing (e.g. TSP), EoH is better employed with the Guided Local Search, where simple heuristics like swapping are used for local optimization, and EoH identifies a heuristic that can disturb the local optimum to explore a better region of the solution space. We believe that EoH that is built this way and is developing specific heuristic programs for each problem instance would likely perform similarly to Google OR-Tools and achieve better performance. This way it works more like a metaheuristic enhancer and will give SOTA results like in [4]. Thank you again for your question, we will add this duscussion to our paper as well.

Reviewer auHA6/10 · confidence 2/52024-07-11

Summary

The paper proposes an LLM-based solution for solving standard combinatorial search problems such as TSP and VRP. The proposed solution, called SGE, uses LLMs to (1) propose alternative approaches to solve the problem at hand, (2) decompose a chosen solution approach into subtasks, (3) identify if a given subtask is easy or hard, (4) if it’s easy, just do it, else (5) recursively call SGE to solve the given subtask. Finally, SGE also uses an LLM to integrate the results returned by the above queries. Experimental results compared to other LLM-based approaches show huge gains for SGE.

Strengths

- Solving combinatorial search problems is a core problem in AI - SGE performs well experimentally - The paper is, in general, well written - The concept of having the LLM identify if a substask is hard or not, is neat

Weaknesses

1. It is not very clear to me why would one want to use an LLM to solve combinatorial problems. 2. It seems that SGE is similar to prior work noted by the reviewers for solving these problems via intelligent prompting. The main difference I could see is the part where it checks if a task is easy or not and calls recursively afterwards, and the integration of all the results together. The authors provide reasonable responses to both concerns.

Questions

1. Did you consider comparing SGE with a fast suboptimal algorithm for solving the evaluated CPs, e.g., LNS? 2. Why is the Integrate step done by the LLMs and not directly by parsing and analyzing the answer so far?

Rating

6

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

Not releavnt.

Reviewer zLRa8/10 · confidence 4/52024-07-13

Summary

This paper discusses "Self-Guiding Exploration" (SGE), a new prompting strategy designed to enhance the problem-solving capabilities of Large Language Models (LLMs) in addressing Combinatorial Problems (CPs). The authors demonstrate that SGE leverages the autonomy of LLMs to generate and refine solution paths, significantly improving the models' efficiency in dealing with NP-hard problems prevalent in logistics and resource management. SGE operates by generating multiple thought trajectories for each CP task, breaking these into manageable subtasks, and refining the outputs to optimize results. The proposed strategy surpasses existing methods, enhancing CP optimization performance by 27.84% and achieving a 2.46% higher accuracy in various reasoning tasks compared to the best existing results. This research marks a pioneering effort in applying LLMs comprehensively to a range of complex CPs and establishes new benchmarks in both performance and versatility.

Strengths

1. The Self-Guiding Exploration (SGE) strategy is a novel approach that significantly deviates from traditional LLM prompting methods. 2. The paper introduces a new paradigm for using AI for complex problem-solving, enabling the model to generate and refine solution paths autonomously. 3. The experiments are designed and described clearly, making the results seem replicable and understandable. The authors provide extensive empirical results demonstrating the advantages of the SGE approach over existing methods. 4. Applying this new strategy to NP-hard combinatorial problems, critical in many industrial and logistical contexts, represents a substantial advancement. 5. The method's ability to improve optimization performance by over 27% and increase accuracy in reasoning tasks by 2.46% compared to existing best results is statistically and practically significant. 6. The SGE method has potential beyond the tested combinatorial problems, given its wide adaptability over different combinatorial problems.

Weaknesses

1. Performance improvements are reported primarily in LLMs. The paper should address how the strategy scales with compact models, which are more accessible for practical applications and deployment. 2. The paper could strengthen its argument by providing a broader comparative analysis with other state-of-the-art methods, especially those using different AI approaches to solve combinatorial problems (such as approximation algorithms or heuristics). This would help validate the superiority of SGE across a wider range. 3. The paper occasionally glosses over deep technical details and assumptions within the SGE framework. More detailed explanations of the underlying mechanisms, particularly how the subtasks are autonomously generated and refined, would enhance the paper's transparency and reproducibility. 4. The computational cost of running multiple explorations and refinements on LLMs is not addressed. A detailed cost-benefit analysis would be pertinent, especially for potential adopters who are weighing the economic and environmental implications of such advanced AI techniques.

Questions

1. Can the authors elaborate on how the Self-Guiding Exploration strategy scales with varying sizes of LLMs and combinatorial problems? Specifically, how does SGE perform under constraints of lower computational resources or with compact models? 2. How robust is the SGE strategy when applied to combinatorial problems outside the tested domains, such as logistics and scheduling? Are there specific types of CPs where SGE might not perform as well? 3. While the focus has been on NP-hard problems, has there been any exploration of the applicability of SGE to problems that do not fall into this category? What modifications, if any, would be necessary to adapt SGE to such contexts? 4. Could the authors compare SGE with other AI methods (such as approximation algorithms or heuristics) currently considered state-of-the-art in solving similar combinatorial problems?

Rating

8

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

1. The strategy's effectiveness relies heavily on large language models' capacities and specific configurations. This dependency could limit the applicability in environments where such models are not feasible due to resource constraints or accessibility issues. 2. The paper primarily presents results for specific problem sizes. It would be beneficial to include an analysis of how well the SGE strategy generalizes across a broader range of problem sizes, particularly large state spaces common in real-world applications. 3. While the paper provides quantitative improvements, the experimental setup could be expanded to include more diverse datasets and problem scenarios to validate the SGE method's robustness and consistency. 4. A significant limitation is the lack of a detailed analysis of the computational, environmental, and operational costs of implementing SGE. 5. The paper does not discuss how the SGE strategy adapts to evolving data or dynamic environments, which is critical for applications in rapidly changing fields such as logistics and real-time scheduling.

Authorsrebuttal2024-08-05

One limitation response that did not fit into the rebuttal

__Comment:__ The paper should address how the strategy scales with compact models. __Response:__ Thank you for highlighting this important consideration. Regarding this comment, we already evaluated the scalability of our strategy with more compact models in our paper. Specifically, we included experiments with the LLaMA models, as detailed in Figure 4 (paper). To clarify your comment further, we presented results for both the LLaMA-2-70B model, which requires around 140 GB of VRAM, and the LLaMA-2-7B model, which operates on just 14 GB of VRAM. Additionally, the LLaMA-2-7B model, when quantized, achieves a 4x reduction in VRAM requirements, allowing it to run on a single NVIDIA RTX GPU. This demonstrates the model's suitability for both the research community and practical deployments. We hope this answers your concern regarding the scalability of our strategy with compact models. However, if you are referring to even smaller models, as mentioned in the paper and noted in the limitations section, SGE heavily depends on the underlying LLM, and smaller models like 1B do not exhibit strong performance. Once again, we appreciate your attention to this aspect of our work.

Reviewer 8LKr2024-08-08

Thanks for your responses. It is surprising that SGE can outperform EOH (Table 4), which is the current SOTA based on code generation. Could the author elaborate on why this might be the case?

Reviewer auHA2024-08-12

Thanks! many aspects have been clarified

I am pretty satisfied with the authors' responses. The comparisons to suboptimal solvers is especially exciting to me, and I think it must be in the paper.

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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