Constrained optimization by applying the α constrained method to the nonlinear simplex method with mutations

Constrained optimization problems are very important and frequently appear in the real world. The alpha constrained method is a new transformation method for constrained optimization. In this method, a satisfaction level for the constraints is introduced, which indicates how well a search point satisfies the constraints. The alpha level comparison, which compares search points based on their level of satisfaction of the constraints, is also introduced. The alpha constrained method can convert an algorithm for unconstrained problems into an algorithm for constrained problems by replacing ordinary comparisons with the alpha level comparisons. In this paper, we introduce some improvements including mutations to the nonlinear simplex method to search around the boundary of the feasible region and to control the convergence speed of the method, we apply the alpha constrained method and we propose the improved alpha constrained simplex method for constrained optimization problems. The effectiveness of the alpha constrained simplex method is shown by comparing its performance with that of the stochastic ranking method on various constrained problems.