HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

2026-09-28

AI Summary

This study addresses the challenge of synergizing computational allocation with structural optimization in hybrid heuristic algorithms under time constraints by proposing HeurEvo, a novel framework that introduces a pioneering "plan-code-component" co-evolution mechanism. By integrating agent-based techniques, island models, and large language model (LLM)-driven automated code generation with feedback analysis, HeurEvo enables the joint evolution of algorithmic structures and low-level implementations, thereby transcending the limitations of conventional approaches that merely fine-tune individual components or configurations. Experimental results demonstrate that HeurEvo consistently yields high-quality solutions within strict time budgets, achieving performance comparable to or even surpassing that of state-of-the-art solvers operating over significantly longer durations.

Abstract

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.

Problem

• mathematical optimization
• time-critical constraints
• hybrid heuristics
• agentic heuristic design
• combinatorial optimization

Innovation

• Agentic Evolution
• Co-evolution Framework
• Hybrid Heuristics
• Mathematical Optimization
• Multi-Agent System