Beyond Algorithm Evolution: An LLM-Driven Framework for the Co-Evolution of Swarm Intelligence Optimization Algorithms and Prompts

The field of automated algorithm design has been advanced by frameworks such as EoH, FunSearch, and Reevo. Yet, their focus on algorithm evolution alone, neglecting the prompts that guide them, limits their effectiveness with LLMs, especially in complex, uncertain environments where they nonetheless implicitly rely on strategies from swarm intelligence optimization algorithms. Recognizing this, we argue that swarm intelligence optimization provides a more generalized and principled foundation for automated design. Consequently, this paper proposes a novel framework for the collaborative evolution of both swarm intelligence algorithms and guiding prompts using a single LLM. To enhance interpretability, we also propose a simple yet efficient evaluation method for prompt templates. The framework was rigorously evaluated on a range of NP problems, where it demonstrated superior performance compared to several state-of-the-art automated design approaches. Experiments with various LLMs (e.g., GPT-4o-mini, Qwen3-32B, GPT-5) reveal significantly divergent evolutionary trajectories in the generated prompts, further underscoring the necessity of a structured co-evolution framework. Importantly, our approach maintains leading performance across different models, demonstrating reduced reliance on the most powerful LLMs and enabling more cost-effective deployments. Ablation studies and in-depth analysis of the evolved prompts confirm that collaborative evolution is essential for achieving optimal performance. Our work establishes a new paradigm for swarm intelligence optimization algorithms, underscoring the indispensable role of prompt evolution.