Elite-driven surrogate-assisted CMA-ES algorithm by improved lower confidence bound method

To relieve the computational burden and improve the global optimizing ability of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for real-world expensive problems, an elite-driven surrogate-assisted CMA-ES (ES-CMA-ES) algorithm by the improved Lower Confidence Bound (ILCB) method is proposed in this paper. Firstly, the ILCB method is established by introducing the step size, which captures the trend of exploration and exploitation in CMA-ES, to control the uncertainty term of the ILCB formula adaptively. Next, based on the ILCB method, a novel model management consisting of the efficient pre-screening strategy and the competitive chaotic operator is developed. In each generation of ES-CMA-ES, a large number of candidate points are sampled first, and then a few of them with better ILCB predicted values are screened out by the efficient pre-screening strategy, aiming to enhance the sampling quality and accelerate the optimization convergence. Moreover, the local search is performed on the best-performing screened sample points utilizing the competitive chaotic operator, with the purpose of increasing the diversity of populations in ES-CMA-ES and avoiding being trapped in the local optima. By means of the above procedures of the model management, the elite sample points are finally obtained which will be evaluated by true fitness function in each generation of ES-CMA-ES. To verify the effectiveness of ES-CMA-ES, five known black-box optimization algorithms are employed to make a comparison. Firstly, seven typical numerical examples of 10-dimensional and 20-dimensional benchmark functions are carried out, respectively. Furthermore, a 20-dimensional engineering example of the aerospace variable-stiffness composite shell under combined loadings is studied. Results indicate the outstanding efficiency, global optimizing ability and applicability of the proposed ES-CMA-ES compared to its counterpart algorithms.