The Study Of Regularity Model Based Multi-Objective Estimation Of Distribution Algorithm

Using evolutionary algorithms to solve multi-objective optimization problems (MOPs) has become a hot topic in the area of computational intelligence. Based on the regularity of the structure of continuous multi-objective optimization problems'Pareto Set, some researchers proposed a regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) in 2009. Experiment results indicate that RM-MEDA is very effective to deal with continuous multi-objective optimization problems with variable linkages. However, RM-MEDA mainly has the following two drawbacks:1) during the modeling process, the probability model is not accuracy enough since RM-MEDA does not fully exploit the regularity of different kind of MOPs; and 2) the global search ability of RM-MEDA is so weak that it has difficulty to solve multimodal objective functions.This paper aims at overcoming the above two drawbacks, the main work of which could be summarized as follows:For problem of the accuracy of modeling, an improved version of RM-MEDA is proposed, called RM-MEDA-RRCO. RM-MEDA uses a clustering operator which is based on local principal component analysis to build model. Experimental results show that the number of clusters is problem-dependent and has a significant effect on the performance of the algorithm. However, RM-MEDA recommended the fixed number of clusters when solving different types of problems. Evidently, this strategy is not very reasonable. The basic idea of RM-MEDA-RRCO shows as follows. During each generation, firstly we judges whether there exist redundant clusters or not according to the clustering results, and then reduce redundant clusters to adjust the clustering number. Experimental results suggest that the proposed algorithm outperforms RM-MEDA in terms of effectiveness and efficiency.For the weak global search ability of RM-MEDA, A Global RM-MEDA is proposed. RM-MEDA only applies the macro distribution information of individuals to build model, however the local information of the individuals is usually ignored. Therefore, it does not utilize the information of individuals effectively. In addition, RM-MEDA generates new individuals based on Gauss sampling operator. It is necessary to note that Gauss sampling operator is a local search operator. As a result, the global search ability of RM-MEDA is weak. In order to make full use of the information of individuals and improve the global search ability, the Global RM-MEDA incorporates differential evolution which has strong global search ability to RM-MEDA. Finally, experimental results show that the proposed algorithm is effective.