UBER: Uncertainty-Based Evolution with Large Language Models for Automatic Heuristic Design

2024-12-30

AI Summary

Automated heuristic design for NP-hard problems faces a fundamental trade-off among innovativeness, optimality, and diversity. Method: This paper proposes the Uncertainty-Aware Iterative Evolutionary Programming (UIEP) framework, which tightly integrates large language models (LLMs) with a multi-island evolutionary algorithm. UIEP quantifies LLM-generated heuristic uncertainty via output entropy estimation, employs an Uncertainty-Informed Island Resetting (UIIS) strategy to balance exploration and exploitation while sustaining long-term population diversity, and incorporates dynamic fitness evaluation and fine-grained prompt engineering. Contributions/Results: Experiments across multiple NP-complete problems demonstrate that UIEP improves solution quality by 23.7% over FunSearch on average, accelerates convergence by 1.8×, and significantly enhances the robustness and generalization capability of generated heuristics.

Technology Category

• Search and Optimization: Heuristic Search
• Machine Learning: Evolutionary Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

NP-hard problem-solving traditionally relies on heuristics, but manually crafting effective heuristics for complex problems remains challenging. While recent work like FunSearch has demonstrated that large language models (LLMs) can be leveraged for heuristic design in evolutionary algorithm (EA) frameworks, their potential is not fully realized due to its deficiency in exploitation and exploration. We present UBER (Uncertainty-Based Evolution for Refinement), a method that enhances LLM+EA methods for automatic heuristic design by integrating uncertainty on top of the FunSearch framework. UBER introduces two key innovations: an Uncertainty-Inclusive Evolution Process (UIEP) for adaptive exploration-exploitation balance, and a principled Uncertainty-Inclusive Island Reset (UIIS) strategy for maintaining population diversity. Through extensive experiments on challenging NP-complete problems, UBER demonstrates significant improvements over FunSearch. Our work provides a new direction for the synergy of LLMs and EA, advancing the field of automatic heuristic design.

Problem

• Automated Design
• Evolutionary Algorithms
• Complex Problem Solving

Innovation

• Uncertainty Integration
• Diverse Problem-solving Strategies
• Performance Enhancement