LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency

2026-07-30

AI Summary

This work addresses the critical impact of modeling formulation on the solving efficiency of constraint satisfaction problems, noting that even logically correct models may suffer from poor performance due to suboptimal representations. To tackle this issue, the authors propose an automated model reformulation method that integrates large language models with evolutionary search, iteratively optimizing model expressions for enhanced solver performance. A key innovation is the Profile-Diverse Retention strategy, which leverages maximal marginal relevance to preserve a behaviorally diverse set of high-quality reformulation attempts, thereby improving search effectiveness. Experimental evaluation across eight CSPLib benchmark problems demonstrates that the proposed approach significantly accelerates solving on held-out instances, and that the diversity-aware retention mechanism consistently outperforms baseline strategies that retain only the most recent or fastest reformulations.

Abstract

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

Problem

• constraint model reformulation
• solver efficiency
• Large Language Models
• combinatorial problems
• model performance

Innovation

• LLM-guided evolutionary search
• constraint model reformulation
• Profile-Diverse Retention
• Maximal Marginal Relevance
• solver efficiency