An Equivalent Penalty Coefficient Method: An Adaptive Penalty Approach for Population-Based Constrained Optimization

The penalty function method has been widely used for solving constrained optimization problems. In the method, an extended objective function, which is the sum of the objective value and the constraint violation weighted by the penalty coefficient, is optimized. However, it is difficult to control the coefficient properly because proper control of the coefficient varies in each problem. In this study, the equivalent penalty coefficient value (EPC) is proposed for population-based optimization algorithms (POAs). EPC can be defined in POAs where a new solution is compared with the old solution. EPC is the penalty coefficient value that makes the two extended objective values of the solutions the same. Search that gives priority to the objective value is realized by selecting a small EPC. Search that gives priority to the constraint violation is realized by selecting a large EPC. The adaptive control of the penalty coefficient can be realized by selecting an appropriate EPC. The proposed method is introduced to differential evolution and the advantage of the proposed method is shown by solving well-known constrained optimization problems.