EALG: Evolutionary Adversarial Generation of Language Model-Guided Generators for Combinatorial Optimization

TL;DR

EALG introduces an innovative framework that uses large language models and evolutionary adversarial techniques to automatically generate challenging problem instances and adaptive solvers for combinatorial optimization, surpassing existing benchmarks.

Contribution

The paper presents a novel co-evolutionary approach combining LLM-guided instance generation and solver synthesis, advancing automated combinatorial optimization methods.

Findings

EALG produces significantly harder problem instances than existing benchmarks.

Synthesized solvers by EALG generalize well across various combinatorial tasks.

The framework achieves state-of-the-art performance in problem difficulty and solver adaptability.

Abstract

Generating challenging instances is crucial for the evaluation and advancement of combinatorial optimization solvers. In this work, we introduce EALG (Evolutionary Adversarial Generation of Language Model-Guided Generators), a novel framework that automates the co-evolution of optimization problem instances and their corresponding heuristic solvers using large language models (LLMs). EALG leverages a mutation-based adversarial approach that dynamically evolves instance generation procedures to create increasingly difficult problems, while simultaneously synthesizing adaptive heuristic algorithms through interactions with LLMs guided by algorithmic structure. Unlike existing approaches that focus solely on static benchmark creation or manual solver design, EALG provides a seamless pipeline from instance generation to solver synthesis. Experimental results demonstrate that EALG generates significantly harder instances than current benchmarks, and its synthesized solvers generalize effectively across a broad spectrum of combinatorial tasks. This work explores a new paradigm for combinatorial optimization that integrates instance generation with solver design, resulting in state-of-the-art performance.