A Fast Two-objective Differential Evolutionary Algorithm based on Pareto-optimal Set

Abstract

The two-objective differential evolution with Pareto-optimal set, which is researched in this paper. Firstly, it is found that there are some redundant computations in the classic multi-objective evolutionary algorithm, such as the NSGA-II. Then, based on the concept of Pareto-optimal set, the non-dominated solution sorted and its potential features, the authors propose a ranking method for solution that only handles the highest rank individuals in current population. The highlight of the proposed method is that during the ranking process, the individuals can be chosen into the next generation meanwhile. When the individuals of next generation population are obtained the algorithm is broken out. Both the number of individuals for sorting process and the time complexity are reduced. Furthermore, a method of uniform crowding distance calculation is provided in this work. Finally, the authors incorporate the introduced ranking method and uniform crowding distance method into differential evolution, a fast two-objective differential evolution algorithm is obtained. For verifying the proposed method, they use the classical optimal problems ZDTl~ZDT4 and ZDT6 for tesing. Simulation results show that the authors' method has greatly improved in terms of time complexity and performance than other algorithms.