Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme

Abstract

One of the most important issues in developing an evolutionary optimization algorithm is the proper handling of any constraints on the problem. One must balance the objective function against the degree of constraint violation in such a way that neither is dominant. Common approaches to strike this balance include implementing a penalty function and the more recent stochastic ranking method, but these methods require an extra tuning parameter which must be chosen by the user. The present paper demonstrates that a proper balance can be achieved using an addition of ranking method. Through the ranking of the individuals with respect to the objective function and constraint violation independently, we convert these two properties into numerical values of the same order of magnitude. This removes the requirement of a user-specified penalty coefficient or any other tuning parameters. Direct addition of the ranking terms is then performed to integrate all information into a single decision variable. This approach is incorporated into a ( μ, λ) evolution strategy and tested on thirteen benchmark problems, one engineering design problem, and five difficult problems with a high dimensionality or many constraints. The performance of the proposed strategy is similar to that of the stochastic ranking method when dealing with inequality constraints, but it has a much simpler ranking procedure and does not require any tuning parameters. A percentage-based tolerance value adjustment scheme is also proposed to enable feasible search when dealing with equality constraints.