Constrained Multiobjective Optimization via Relaxations on Both Constraints and Objectives

Since most multiobjective optimization problems in real-world applications contain constraints, constraint-handling techniques (CHTs) are necessary for a multiobjective optimizer. However, existing CHTs give no relaxation to objectives, resulting in the elimination of infeasible dominated solutions that are promising (potentially useful but inferior) for detecting feasible regions and the constrained Pareto front (CPF). To overcome this drawback, in this work, we propose an objective relaxation technique that can preserve promising by relaxing objective function values, i.e., convergence, through an adaptively adjusted relaxation factor. Further, we develop a new constrained multiobjective optimization evolutionary algorithm (CMOEA) based on relaxations on both constraints and objectives. The proposed algorithm evolves one population by the constraint relaxation technique to preserve promising infeasible solutions and the other population by both objective and constraint relaxation techniques to preserve promising infeasible dominated solutions. In this way, our method can overcome the drawback of existing CHTs. Besides, an archive update strategy is designed to maintain encountered feasible solutions by the two populations to approximate the CPF. Experiments on challenging benchmark problems and real-world problems have demonstrated the superiority or at least competitiveness of our proposed CMOEA. Moreover, to verify the generality of the objective relaxation technique, we embed it into two existing CMOEA frameworks and the results show that it can significantly improve the performance in handling challenging problems.