A New Differential Evolution for Multiobjective Optimization by Uniform Design and Minimum Reduce Hypervolume

Abstract

Differential evolution is a powerful and robust method to solve the Multi-Objective Problems in MOEAs. To enhance the differential evolution for MOPs, we focus on two aspects: the population initialization and acceptance rule. In this paper, we present a new differential evolution called DEMO^{UD}_{DV}, it mainly include: (1) the first population is constructed by statistical method: Uniform Design, which can get more evenly distributed solutions than random design, (2) a new acceptance rule is firstly presented as Minimum Reduce Hypervolume. Acceptance rule is a metric to decide which solution should be cut off when the archive is full to the setting size. Crowding Distance is frequently used to estimate the length of cuboid enclosing the solution, while Minimum Reduce Hypervolume is used to estimate the volume of cuboid. The new algorithm designs a fitness function Distance/Volume that balance the CD and MRV, which maintains the spread and hypervolume along the Pareto-front. Experiment on different multi-Objective problems include ZDTx and DTLZx by jMetal 2.0, the results show that the new algorithm gets higher hypervolume, faster convergence, better distributed solutions and needs less numbers of fitness function evolutions than NSGA-II, SPEA2 and GDE3.