Surrogate-Assisted Evolutionary Multi-Objective Optimization of Medium-Scale Problems by Random Grouping and Sparse Gaussian Modeling

Gaussian processes (GPs) are widely employed in surrogate-assisted evolutionary algorithms (SAEAs) because they can estimate the level of uncertainty in their predictions. However, the computational complexity of GPs grows cubically with the number of training samples, the time required for constructing a GP becomes excessively long. Additionally, in SAEAs, the GP is updated using the new data sampled in each round, which significantly impairs its efficiency in addressing medium-scale optimization problems. This issue is exacerbated in multi-objective scenarios where multiple GP models are needed. To address this challenge, we propose a fast SAEA using sparse GPs for medium-scale expensive multi-objective optimization problems. We construct a sparse GP for each objective on randomly selected sub-decision spaces and optimize a multi-objective acquisition function using a multi-objective evolutionary algorithm. The resulting population is combined with the previously evaluated solutions, and k-means is used for clustering to obtain candidate solutions. Before real function evaluations, the candidate solutions in the subspace are completed with the values of the knee point in the archive. Experimental results on three benchmark test suites up to 80 decision variables demonstrate the algorithm's computational efficiency and competitive performance compared to state-of-the-art methods. Additionally, we verify its performance on a real-world optimization problem.