A Kriging-Assisted Evolutionary Algorithm Using Feature Selection for Expensive Sparse Multi-Objective optimization

The Pareto sets of many real-world multi-objective optimization problems in engineering and computer fields are high-dimensional but sparse. Such multi-objective optimization problems are called large-scale sparse multi-objective optimization problems. A sparse evolutionary algorithm has also been raised and verified effective on benchmark problems. However, in practical applications, it needs a large number of expensive function evaluations. Although surrogate-assisted evolutionary algorithms are common solutions to deal with expensive optimization problems within limited computation resources and especially Kriging-assisted evolutionary algorithms are widely used, they cannot cope with large-scale expensive sparse multi-objective optimization problems due to the inaccurate surrogate models on high-dimensional problems. Therefore, we first propose a feature selection operator based on non-dominated sorting to choose the non-zero decision variables in the Pareto set. Then, the dimension of the original problem is reduced and a Kriging-assisted multi-objective evolutionary algorithm is employed to solve the reformulated problem. Finally, the selected zero decision variables are added to the obtained optimal solutions as the result of the original problem. The experimental results on benchmark problems show that our proposed algorithm outperforms the existing algorithms.