Simple addition of ranking method for constrained optimization in evolutionary algorithms

During the optimization of a constrained problem using evolutionary algorithms (EAs), an individual in the population can be described using three important properties, i.e., objective function, the sum of squares of the constraint violation, and the number of constraints violated. However, the question of how to combine these three properties effectively is always difficult to solve due to the scaling and aggregation problems. In this paper, a simple addition of ranking method is proposed to handle constrained optimization problems in EAs. In this method, each individual is ranked based on the above three properties separately, resulting in three new properties which are in the same order of magnitude. Simple addition of the three new terms can then be performed and this produces a new global ranking for each individual. The algorithm was tested using 13 benchmark problems on the basis of evolution strategy and genetic algorithm. Results showed that the proposed algorithm performed well in all of the problems with inequality constraints, without requiring any parameter tuning for the constraint handling part. On the other hand, problems with equality constraints can be handled well through the addition of a simple diversity mechanism and a tolerance value adjustment scheme.