Efficient Constraint Handling based on the Adaptive Penalty Method with Balancing the Objective Function Value and the Constraint Violation

Abstract

Real world problems are often formularized as constrained optimization problems (COPs). Constraint handling techniques are important for efficient search, and various approaches such as penalty methods or feasibility rules have been studied. The penalty methods deal with a single fitness function by combining the objective function value and the constraint violation with a penalty factor. Moreover, the penalty factor can be flexibly adapted by feeding back information on search process in adaptive penalty methods. However, keeping the good balance between the objective function value and the constraint violation is very difficult. In this paper, we propose a new adaptive penalty method with balancing the objective function value and the constraint violation and examine its effectiveness. L-SHADE is adopted as a base algorithm to evaluate search performance, and the optimization results of 28 benchmark functions provided by the CEC 2017 competition on constrained single-objective numerical optimizations are compared with other methods. In addition, we also examine the behavioral difference between proposed method and the conventional adaptive penalty method.