A Constrained Multiobjective Evolutionary Algorithm Based on a Hybrid Constraint Handling Technique Using Population Trimming Strategy

Abstract

For constrained multiobjective optimization problems (CMOPs), one of the fundamental issues faced by researchers is how to make comparisons between individuals within the population that results in a balanced selection of better individuals. The selection of better individuals need to be balanced between elitism, diversity and feasibility. In this paper, we propose a hybrid constraint handling technique of population trimming strategy and adaptive penalty function for multiobjective evolutionary algorithm NSGA-II to solve CMOPs. In our approach, a method of objectivization of constraint violations and proportional reduction is used to compare two individuals and trim the population, and as a result the new parent population consisted of the optimal feasible individuals and good infeasible individuals is obtained. To our knowledge, the distant matrix in proportional reduction procedure is firstly proposed for comparison and maintaining diversity in infeasible individuals. Furthermore, an adaptive penalty function method is utilized to give the fitness of individuals in parent population. Numerical simulations indicate that the proposed algorithm outperforms the current state-of-the-art algorithms, e.g. NSGA-II-CD, NAGA-II-WTY, in both convergence and diversity.