Distributed Probabilistic Model-Building Genetic Algorithm

Algorithms where offsprings (new search points) are generated according to the estimated probability model of the good parents are called the Probabilistic Model-Building Genetic Algorithms (PMBGAs). In this paper, a new model of PMBGA, Distributed PMBGA (DPMBGA), is proposed. In the DPMBGA, the correlation between the design variables is considered by PCA when the offsprings are generated. The distribution of the offsprings is estimated as the normal distribution. The island model is also applied in the DPMBGA for maintaining the population diversity. Through the standard test functions, the effectiveness of the DPMBGA is examined. The result shows the good search ability of the DPMBGA with PCA for the test functions that have correlation between the design variables. On the other hand, the DPMBGA without PCA is good at optimizing the problems where there is no correlation between the design variables. The DPMBGA where PCA is executed in the half of the islands and not executed in the other island can find the good solutions in the problems whether or not the problems have the correlation between the design variables. The results of the DPMBGA are also compared with those of the UNDX with MGG. The results explain that the DPMBGA shows the better performance than the UNDX.