Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery

TL;DR

This paper introduces a game-theoretic co-evolution framework called ASRO for heuristic discovery using LLMs, which adaptively evolves solvers and instances to improve generalization and robustness in combinatorial optimization.

Contribution

It presents a novel game-theoretic approach for heuristic discovery that replaces static evaluation with adaptive co-evolution, enhancing out-of-distribution performance.

Findings

ASRO outperforms static training baselines in multiple domains.

It achieves better generalization on diverse and out-of-distribution instances.

The framework demonstrates robustness and adaptability in heuristic discovery.

Abstract

Large language models (LLMs) have enabled rapid progress in automatic heuristic discovery (AHD), yet most existing methods are predominantly limited by static evaluation against fixed instance distributions, leading to potential overfitting and poor generalization under distributional shifts. We propose Algorithm Space Response Oracles (ASRO), a game-theoretic framework that reframes heuristic discovery as a program level co-evolution between solver and instance generator. ASRO models their interaction as a two-player zero-sum game, maintains growing strategy pools on both sides, and iteratively expands them via LLM-based best-response oracles against mixed opponent meta-strategies, thereby replacing static evaluation with an adaptive, self-generated curriculum. Across multiple combinatorial optimization domains, ASRO consistently outperforms static-training AHD baselines built on the same program search mechanisms, achieving substantially improved generalization and robustness on diverse and out-of-distribution instances.