Adaptive landscape-aware repelling restart covariance matrix adaptation-evolution strategy for multimodal and global optimization

Abstract

In multimodal optimization using Covariance Matrix Adaptation-Evolution Strategy (CMA-ES), redundant restarts are caused by repeated convergence to previously explored local basins, which leads to significant computational resource waste. To address this problem, previous research proposed the concept of Repelling Restart and developed RR-CMA-ES, but issues remain regarding rigid repulsion and gradient information of local basin structures. Building on this foundation, we propose an Adaptive Landscape-aware Repelling Restart CMA-ES (ALR-CMA-ES) that enhances the original RR-CMA-ES through three key improvements: 1) A fitness sensitive dynamic exclusion mechanism that adaptively adjusts tabu region radius based on local optimality and convergence frequency, prioritizing avoidance of high-quality basins; 2) A covariance matrix mechanism preserving convergence history to geometrically align hyper-ellipsoidal exclusion regions with explored local basin landscapes; 3) A Boltzmann-like probabilistic acceptance scheme incorporating exclusion regions, permit- ting controlled exploration near tabu boundaries. Experiments on the BBOB benchmark demonstrate that ALR-CMA-ES outperforms RR-CMA-ES in 90% of tested problems spanning 2D to 50D. This method provides a practical solution for expensive black-box optimization by systematically integrating landscape topology awareness into tabu mechanisms, while proposing a new solution for multimodal optimization problems.