Abstract
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 $k$ -means clustering method is used to learn the manifold structure information and partition the population into $K$ clusters. A Gaussian probability model is built with $K$ mean vectors of clusters, and $K$ 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.
Highlights
I N scientific research and engineering applications, there are a large number of optimization problems with multiple criteria
Multiobjective optimization evolutionary algorithms (MOEAs) are well suited for solving multi-objective optimization problems (MOPs) as they can obtain an approximated solutions set within a single run, that population solutions are maintained during the process of
Two reasons can be made from these results of the excellent performance of RAMEA: (a) the combination of Gaussian sampling and neighbor based mating; (b) sampled trial solutions act as mating parent, as offspring
Summary
I N scientific research and engineering applications, there are a large number of optimization problems with multiple criteria. Clustering methods are used to learn the population structure information to define the neighborhood relationship among solutions, and neighbor based mating reproductions are performed for local exploitation to improve the convergence of algorithms. The manifold property is used to assist the search of RAMEA, including the Gaussian modeling and sampling, and the neighborhood relationship for mating Both the population global distribution information and individual local information are used to generate trial solutions by combining the sampling and mating reproduction. Instead of approximating the PS with models, some researchers have designed mating restriction mechanisms based on the manifold property of the PS, that clustering learning methods are used to extract the population structure information for reproduction. Input : the solution xi, and its two parent x1 and x2; Output: a new solution y;
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