### Voronoi-based Estimation of Distribution Algorithm for Multi-objective Optimization

Abstract

The distribution of the Pareto-optimal solutions often has a clear structure. To adapt evolutionary algorithms to the structure of a multi-objective optimization problem, either an adaptive representation or adaptive genetic operators should be employed. In this paper, we suggest an estimation of distribution algorithm for solving multi-objective optimization, which is able to adjust its reproduction process to the problem structure. For this purpose, a new algorithm called Voronoi-based Estimation of Distribution Algorithm (VEDA) is proposed. In VEDA, a Voronoi diagram is used to construct stochastic models, based on which new offspring will be generated. Empirical comparisons of the VEDA with other estimation of distribution algorithms (EDAs) and the popular NSGA-II algorithm are carried out. In addition, representation of Pareto-optimal solutions using a mathematical model rather than a solution set is also discussed.