Claude and Gemini Design Metaheuristics: A Cooperative Multi-LLM Approach

Abstract

In this entry to the GECCO 2026 Competition on LLM-Designed Metaheuristics, three large language models (GPT-5.4 Thinking, Gemini 3.1 Pro, Claude Opus 4.6) were independently prompted to design a metaheuristic for the GNBG benchmark (24 problems, hence the /24 scoring scale). Each reached a per-model ceiling (GPT 19.82, Claude 21.08, Gemini 23.29) and could not improve further on its own. Handing the best design (Gemini's) to the second-best model (Claude) for refinement produced, within four iterations, EO-BIPOP-CMA-CDR, which ranks first in the full 24-algorithm field at 23.30/24 and outperforms the source design head-to-head by three score points. A single cross-model handoff yielded more progress than five further self-refinement iterations by the source model. We argue that model diversity is a usable, low-cost resource for LLM-driven algorithm design.