  This paper introduces an approach that integrates self-adaptive Evolution
Strategies (ES) with Large Language Models (LLMs) to enhance the explainability
of complex optimization processes. By employing a self-adaptive ES equipped
with a restart mechanism, we effectively navigate the challenging landscapes of
benchmark functions, capturing detailed logs of the optimization journey. The
logs include fitness evolution, step-size adjustments and restart events due to
stagnation. An LLM is then utilized to process these logs, generating concise,
user-friendly summaries that highlight key aspects such as convergence
behavior, optimal fitness achievements, and encounters with local optima. Our
case study on the Rastrigin function demonstrates how our approach makes the
complexities of ES optimization transparent. Our findings highlight the
potential of using LLMs to bridge the gap between advanced optimization
algorithms and their interpretability.
