Differential evolution improvement by adaptive ranking-based constraint handling technique

Differential evolution (DE) is known among the best methods for solving real-world optimization problems owing to its simple and efficient nature. Since almost all real-world applications are constrained optimization problems, constraint handling techniques are required for differential evolution algorithms. Conventional constraint handling techniques for DE mainly focus on discarding or devaluing the infeasible solutions, leading to an information loss of the infeasible region. To strike the balance between the explorations of the feasible region and the infeasible region, we look into the bi-objective space constituted by the objective function and the total constraint violation, and define the infeasible solution which has the lowest degree of constraint violation and lies in the Pareto front as the best infeasible solution. We discuss how the best infeasible solution help improve the current best solution. Based on this, we propose an improved differential evolution algorithm with adaptive ranking-based constraint handling technique (AR-DE). First, we start by identifying the best feasible solution and the best infeasible solution of the current population. Second, to guide the population evolving toward these solutions, different mutation and selection operators are proposed. Third, we design the adaptive control to automatically choose the operators to fit different stages of the evolution and various situations of the population. We conduct experimental studies by comparing with other widely used constraint handling techniques based on the cardinal version of differential evolution for fair competition. Standard test problems and five well-known engineering constrained optimization design problems are used to evaluate the effectiveness of AR-DE. Statistical outcomes show that the overall results of AR-DE are better than those of the other comparing methods. We also investigate the ability of AR-DE to obtain feasible solutions, and tune the parameters to achieve better performance.