PDE-PEDA: A New Pareto-Based Multi-objective Optimization Algorithm

Xuesong Wang (China University of Mining and Technology, China)

Minglin Hao (China University of Mining and Technology, China)

Yuhu Cheng (China University of Mining and Technology, China)

Ruhai Lei (China University of Mining and Technology, China)

Abstract: Differential evolution (DE) algorithm puts emphasis particularly on imitating the microscopic behavior of individuals, while estimation of distribution algorithm (EDA) tries to estimate the probabilistic distribution of the entire population. DE and EDA can be extended to multi-objective optimization problems by using a Pareto-based approach, called Pareto DE (PDE) and Pareto EDA (PEDA) respectively. In this study, we describe a novel combination of PDE and PEDA (PDE-PEDA) for multi-objective optimization problems by taking advantage of the global searching ability of PEDA and the local optimizing ability of PDE, which can, effectively, maintain the balance between exploration and exploitation. The basic idea is that the offspring population of PDE-PEDA is composed of two parts, one part of the trial solution generated originates from PDE and the other part is sampled in the search space from the constructed probabilistic distribution model of PEDA. A scaling factor Pr used to balance contributions of PDE and PEDA can be adjusted in an on-line manner using a simulated annealing method. At an early evolutionary stage, a larger Pr should be adopted to ensure PEDA is used more frequently, whereas at later stage, a smaller Pr should be adopted to ensure that offspring is generated more often using PDE. The hybrid algorithm is evaluated on a set of benchmark problems and the experimental results show that PDE-PEDA outperforms the NSGA-II and PDE algorithms.

Keywords: Pareto differential evolution, Pareto estimation of distribution algorithm, multi-objective optimization, offspring generation scheme

Categories: G.1.6, I.1.2, I.2.8