Heuristic Search as Language-Guided Program Optimization

2026-02-17

AI Summary

This work addresses the limitations of existing large language model (LLM)-driven heuristic design methods in combinatorial optimization, which often rely on manual trial-and-error or domain-specific knowledge and lack a systematic mechanism for improvement. To overcome this, the authors propose a structured framework that formalizes heuristic discovery as a language-guided program optimization process, comprising three modular phases: forward evaluation, backward feedback, and program update. This design enables an iterative and composable optimization workflow, unifying and generalizing prior approaches while allowing flexible enhancements through modularity. Empirical evaluation across four real-world combinatorial optimization tasks demonstrates that the proposed method significantly outperforms baseline techniques, achieving up to a 0.17 improvement in the QYI metric on unseen test instances.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Planning with Language Models
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Large Language Models (LLMs) have advanced Automated Heuristic Design (AHD) in combinatorial optimization (CO) in the past few years. However, existing discovery pipelines often require extensive manual trial-and-error or reliance on domain expertise to adapt to new or complex problems. This stems from tightly coupled internal mechanisms that limit systematic improvement of the LLM-driven design process. To address this challenge, we propose a structured framework for LLM-driven AHD that explicitly decomposes the heuristic discovery process into modular stages: a forward pass for evaluation, a backward pass for analytical feedback, and an update step for program refinement. This separation provides a clear abstraction for iterative refinement and enables principled improvements of individual components. We validate our framework across four diverse real-world CO domains, where it consistently outperforms baselines, achieving up to $0.17$ improvement in QYI on unseen test sets. Finally, we show that several popular AHD methods are restricted instantiations of our framework. By integrating them in our structured pipeline, we can upgrade the components modularly and significantly improve their performance.

Problem

• Heuristic Search
• Large Language Models
• Combinatorial Optimization
• Automated Heuristic Design
• Program Optimization

Innovation

• Heuristic Search
• Large Language Models
• Program Optimization
• Modular Framework
• Combinatorial Optimization