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The Pareto optimal set of a continuous multiobjective optimization problem shows some kinds of structure, which is called the regularity property and it has been applied to design effective offspring reproduction operators in multiobjective optimization evolutionary algorithms (MOEAs). Usually, the probability model sampling and neighbor based mating are the main strategies to implement the regularity property in designing reproduction operators. In fact, different information is used in these methods. There is no doubt that combining the global and local information will favor the search. To use more information in the offspring reproduction, in this paper, we propose a regularity assisted MOEA, RAMEA for short, that combines Gaussian sampling and neighbor based mating for offspring reproduction. In RAMEA, the <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-means clustering method is used to learn the manifold structure information and partition the population into <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> clusters. A Gaussian probability model is built with <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> mean vectors of clusters, and <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> trial offspring solutions are sampled from thus model. Moreover, these sampled trial solutions are added to each cluster as mating parents to generate other offspring solutions. In this way, the global and local information are combined to generate offspring solutions in RAMEA. The proposed approach has been executed in several test instances with complicated characteristics, and compared with seven classical or newly developed MOEAs. The results have demonstrated its advantages over other algorithms.

Combining Global and Local Information for Offspring Generation in Evolutionary Multiobjective Optimization