HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization
This addresses the need for more rigorous and consistent evaluation of LLMs in scientific and engineering problem-solving, though it is incremental as it builds on existing benchmarking efforts.
The authors tackled the problem of evaluating LLMs in heuristic algorithm generation for combinatorial optimization by introducing HeuriGym, an agentic benchmark framework, and found that even top models like GPT-o4-mini-high and Gemini-2.5-Pro achieved QYI scores of only 0.6, well below the expert baseline of 1.
While Large Language Models (LLMs) have demonstrated significant advancements in reasoning and agent-based problem-solving, current evaluation methodologies fail to adequately assess their capabilities: existing benchmarks either rely on closed-ended questions prone to saturation and memorization, or subjective comparisons that lack consistency and rigor. In this work, we introduce HeuriGym, an agentic framework designed for evaluating heuristic algorithms generated by LLMs for combinatorial optimization problems, characterized by clearly defined objectives and expansive solution spaces. HeuriGym empowers LLMs to propose heuristics, receive evaluative feedback via code execution, and iteratively refine their solutions. We evaluate nine state-of-the-art models on nine problems across domains such as computer systems, logistics, and biology, exposing persistent limitations in tool use, planning, and adaptive reasoning. To quantify performance, we propose the Quality-Yield Index (QYI), a metric that captures both solution pass rate and quality. Even top models like GPT-o4-mini-high and Gemini-2.5-Pro attain QYI scores of only 0.6, well below the expert baseline of 1. Our open-source benchmark aims to guide the development of LLMs toward more effective and realistic problem-solving in scientific and engineering domains.