Multi-objective Estimation of Distribution Algorithm based on Voronoi and local search

Abstract

In this paper we propose an Estimation of Distribution Algorithm (EDA) equipped with Voronoi and local search based on leader for multi-objective optimization. We introduce an algorithm that can keep the balance between the exploration and exploitation using the local information in the searched areas through the global estimation of distribution algorithm. Moreover, the probability model in EDA, receives special statistical information about the amount of the variables and their important dependency. The proposed algorithm uses the Voronoi diagram in order to produce the probability model. By using this model, there will be a selection based on the area instead of selection based on the individual, and all individual information could use to produce new solution. In the proposed algorithm, considering the simultaneous use of global information about search area, local information of the solutions and the Voronoi based probability model lead to produce more diverse solutions and prevent sticking in local optima. Also, in order to reduce the data dimension, the principle component analysis is proposed. Several benchmarks functions with different complexity like linear and non-linear relationship between the variables, the continues\-discontinues and convex\non-convex optima fronts use to show the algorithm performance.