A regularity model-based multi-objective estimation of distribution memetic algorithm with auto-controllable population diversity

The regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) employs the local principal component analysis to split the population into several clusters, and each cluster is used to construct an affine subspace by combing the cluster center, principal components and additional Gaussian noise. However, such affine subspace greatly limits the sampling range of trail solutions, which will lead to the rapid loss of population diversity. To address this issue, an improved RM-MEDA with auto-controllable population diversity (RM-MEDA-AcPD) is suggested in this paper. In RM-MEDA-AcPD, the simplex crossover method is employed to extend the representation range of the affine subspace, the main purpose of which is to push solutions forward along the orthogonal direction of the affine subspace. In addition, a random noise model related to the evolution process is designed to replace the original Gaussian noise model, which reduces the risk of rapid loss of population diversity. In experimental studies, we have compared eight regularity property-based multi-objective evolutionary algorithms with the RM-MEDA-AcPD on benchmark problems with disconnected Pareto fronts. The experimental results demonstrate that the performance of RM-MEDA-AcPD significantly outperforms the other nine comparison algorithms in solving these test instances.