A data-driven co-evolutionary exploration algorithm for computationally expensive constrained multi-objective problems

Surrogate-assisted multi-objective optimization algorithms have attracted widespread attention due to their outstanding performance in computationally expensive real-world problems. However, there is relatively little research about multi-objective optimization with complex and expensive constraints. Hence, a data-driven co-evolutionary exploration (DDCEE) algorithm is presented in this paper for the above-mentioned problems, where Radial Basis Functions are utilized to train dynamically updated surrogate models for each objective and constraint. Specifically, a data-driven co-evolutionary exploration framework is proposed to fully utilize and mine the potential available information of RBF models, and RBF models are constantly updated to guide co-evolutionary in discovering valuable feasible regions and achieving global optimization. In co-evolutionary exploration, one population focuses on exploring the entire space without considering constraints, while the other population focuses on exploring feasible regions and collaborating by sharing their respective offspring. Reference vectors are introduced in co-evolutionary exploration to divide the objective space into several sub-regions for further selection. Furthermore, an adaptive selection of promising samples strategy is presented to reasonably utilize the information of solutions with good convergence and enhance the convergence and diversity of the Pareto front. After comprehensive experiments on constrained multi/many-objective benchmark cases and an engineering application problem, DDCEE shows more stable and impressive performance when compared with five state-of-art algorithms.