Enhancing evolution strategy with stratified sampling: A study on sample efficiency and convergence speed

Evolution strategy (ES) is a widely recognized evolutionary computation technique employed to address optimization challenges. Typically, ES generates candidate solutions by drawing from a multivariate normal distribution. However, due to the randomness of sampling, several samples are clustered together during every iteration, which may lead to lower accuracy and slower convergence in optimization problems. In this study, the stratified sampling technique based on the Latin hypercube sampling (LHS) mechanism is added to speed up the convergence speed to the global optimum. These sample vectors are combined to obtain the sample matrix of ES with population size, which enables the algorithm to improve the sample efficiency. Furthermore, several standard unimodal and multimodal functions are tested to evaluate the performance of the sampling strategy on covariance matrix adaptation evolution strategy (CMA-ES) with LHS and optimized LHS (OLHS) on convergence speed, search precision, and dimension scalability. Compared with the CMA-ES with random sampling, the proposed CMA-ES-OLHS achieves an average reduction of 21.8~26.5% in function evaluations across 11 benchmark functions, demonstrating that OLHS significantly improves the sample efficiency and convergence speed.