Multilayer Perceptron Grouping and Sparse Gaussian Process-Based Surrogate-Assisted Evolutionary Algorithm for Expensive Multiobjective Optimization

Gaussian processes (GPs) have attracted considerable attention in assisting evolutionary algorithms (EAs) to solve computationally expensive optimization problems (EOPs) because they can directly provide information about the uncertainty of their predictions. However, the computational complexity of GPs grows cubically as the amount of data increases, which severely limits their computational efficiency in high-dimensional expensive multiobjective optimization problems (EMOPs). To address this limitation, we propose a surrogate-assisted evolutionary algorithm (SAEA) that integrates multilayer perceptron (MLP) grouping with sparse GPs, referred to as MLPSGP-SAEA. First, the MLP grouping selects a subspace from the original space by evaluating the impact of each decision variable on the objective functions. Then, for each objective function, a sparse GP model is employed, and the locations of pseudo-input points are optimized to enhance computational efficiency while improving model accuracy. Moreover, an adaptive sparse and diverse (ASD) infill criterion is proposed, based on the characteristics of the sparse GP model predictive distribution, to better balance exploration and exploitation. Finally, extensive experiments are conducted on four benchmark suites and an aerodynamic design optimization problem. The experimental results demonstrate that MLPSGP-SAEA exhibits significant competitive advantages over the state-of-the-art SAEAs.