EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models

2025-08-15

AI Summary

Acceleration cuts in integer programming traditionally rely on expert knowledge, hindering their automated generation. Method: This paper proposes the first end-to-end framework for automatic cut generation that integrates large language models (LLMs) with evolutionary search. An LLM initializes semantically meaningful and syntactically valid candidate cuts; these are then iteratively refined via an evolutionary algorithm—incorporating crossover, mutation, and selection—guided by feedback from a validation set. Contribution/Results: To our knowledge, this is the first work to leverage LLMs for cut plane construction, enabling fully automated discovery of high-quality cuts without human intervention. Experiments demonstrate that, within fixed time limits, the framework reduces solver optimality gaps by 17%–57% on average and accelerates convergence to optimal solutions by up to 4×. Moreover, solutions obtained within the same time budget exhibit significantly higher quality compared to baselines.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Integer programming lies at the heart of crucial combinatorial optimization tasks but remains challenging due to its NP-hard nature. An effective approach for practically solving integer programs is the manual design of acceleration cuts, i.e. inequalities that improve solver performance. However, this creative process demands deep expertise and is yet to be automated. Our proposed framework, EvoCut, automates the generation of acceleration cuts by combining large language models (LLMs) with an evolutionary search. EvoCut (i) initializes a diverse population of candidate cuts via an LLM-based initializer agent; (ii) for each cut empirically evaluates both preservation of the optimal solution and its ability to cut off fractional solutions across a verification set; and (iii) iteratively refines the population through evolutionary crossover and mutation agents. We quantify each cut's utility by its relative reduction in the solver's optimality gap. Our comparisons against standard integer programming practice show that EvoCut reduces optimality gap by 17-57% within a fixed time. It obtains the same solutions up to 4 times as fast, and obtains higher-quality solutions within the same time limit. Requiring no human expert input, EvoCut reliably generates, improves, and empirically verifies cuts that generalize to unseen instances. The code is available at https://github.com/milad1378yz/EvoCut.

Problem

• Automating generation of acceleration cuts for integer programming
• Reducing solver optimality gap via evolutionary language models
• Improving combinatorial optimization without human expert input

Innovation

• Combines LLMs with evolutionary search
• Initializes cuts via LLM-based agent
• Refines population through evolutionary operations