# On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

## TL;DR

This paper introduces HR-CMA-ES, a hybrid restart strategy combining cNrGA's global search history with CMA-ES's local optimization, leading to improved performance on benchmark functions.

## Contribution

The paper proposes HR-CMA-ES, a novel on-line search history-assisted restart strategy that enhances CMA-ES with non-revisiting global exploration using cNrGA.

## Key findings

- HR-CMA-ES outperforms CMA-ES and cNrGA on benchmark suites.
- The approach effectively identifies regions of interest for local search.
- Synergistic cooperation improves global optimization performance.

## Abstract

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.