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Self-Guiding Exploration for Combinatorial Problems (2405.17950v1)

Published 28 May 2024 in cs.AI

Abstract: 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).

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Summary

  • The paper presents the Self-Guiding Exploration (SGE) approach that enhances LLM performance in combinatorial problems by 27.84% through sequential subtask breakdown and refinement.
  • It demonstrates a 2.46% accuracy improvement over existing methods in diverse reasoning tasks, confirming SGE's robustness and versatility.
  • The research pioneers LLM application to NP-hard combinatorial problems, setting a new benchmark and foundation for future advancements in the field.

The paper "Self-Guiding Exploration for Combinatorial Problems" addresses a significant gap in the application of LLMs to Combinatorial Problems (CPs), which are crucial in complex fields such as logistics and resource management. Combinatorial Problems are known for their NP-hardness, making them challenging for conventional algorithms and requiring innovative methods to achieve efficient solutions.

LLMs have shown their effectiveness in various reasoning tasks, utilizing prompting techniques like Exploration-of-Thought, Decomposition, and Refinement. Despite these advances, their application to CPs has been largely unexplored. This paper introduces a novel prompting strategy termed Self-Guiding Exploration (SGE), which aims to enhance LLM performance in solving CPs.

SGE is designed to operate autonomously, generating multiple "thought trajectories" for each CP task. These trajectories are broken down into manageable subtasks, which are executed sequentially. The results are then refined to ensure optimal outcomes. This process significantly improves the LLM's ability to navigate the solution space of CPs efficiently.

Key findings and contributions of the paper include:

  1. Performance Optimization: SGE outperforms existing prompting strategies by an impressive 27.84% in terms of CP optimization performance. This highlights the effectiveness of the self-guiding mechanism in improving LLM's capability to solve complex combinatorial problems.
  2. Accuracy Improvement: Beyond optimization, SGE demonstrates a 2.46% higher accuracy over the best existing results in other reasoning tasks, including arithmetic, commonsense, and symbolic reasoning. This showcases the general applicability and robustness of the SGE strategy across different domains.
  3. Novelty and Scope: The research is pioneering in its application of LLMs to a broad range of combinatorial problems. This sets a foundation for future work exploring the utility of advanced prompting strategies in CPs.

Overall, the paper presents a compelling advancement in leveraging LLMs for combinatorial problems. By introducing the Self-Guiding Exploration approach, it not only addresses a critical gap but also sets new benchmarks for performance in this challenging domain.

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