A Surrogate-Assisted Evolutionary Algorithm with Multi-Perspective Infill Sampling for Expensive Super-Many-objective Optimization Problems

Surrogate-assisted many-objective evolutionary algorithms (SAMaOEAs) have become a pivotal method for solving expensive many-objective optimization problems (EMaOPs), where the cost of objective evaluations is computationally prohibitive. Training a surrogate model for each objective function is an intuitive approach, as it effectively approximates the landscape of that objective function. However, this approach tends to suffer from error accumulation as the number of objective functions increases. In this modeling approach, a straightforward way to mitigate error accumulation is to further add appropriate training samples for the surrogate model of each objective function. Due to the heterogeneous characteristics of different objective functions, identifying and adding informative training samples requires a substantial number of objective evaluations. Therefore, we propose a surrogate-assisted evolutionary algorithm with multi-perspective infill sampling (MP-SAMaOEA), in which only a small number of solutions are selected for objective evaluations to enhance the predictive ability of the surrogate model. A multi-perspective infill sampling is first presented in MP-SAMaOEA. Specifically, angle and Euclidean distance are adopted to estimate the performance of solutions in the objective space and the decision space, respectively. The non-dominated sorting is then conducted based on the above two indicators, and a subset of non-dominated solutions is selected. Additionally, a k-means-assisted diversity enhancement strategy is proposed in the surrogate-assisted optimizer to balance diversity and convergence. Experimental results on the WFG and DTLZ benchmark suites, as well as a real-world application, demonstrate that MP-SAMaOEA outperforms the comparative algorithms, particularly in solving expensive super-many-objective optimization problems.