Adaptive repair method for constraint handling in multi-objective optimization based on constraint-variable relation

Evolutionary algorithms are popular tools for optimization of both theoretical and real-world problems due to their ability to perform global search and to deal with non-convex, multi-objective problems. Handling the constraints is a major concern in optimization that can prolong the search or prevent the algorithm from convergence. Common approaches for constraint handling usually discard or devalue infeasible solutions, losing the valuable information they carry. Alternatively, common repair methods for constraint handling are limited to specific problem types. This study focuses on the development of a repair method for constraint handling in multi-objective optimization. A generic approach is proposed for improving the constraint handling. The method identifies infeasible solutions with high-quality objective values or small constraint violations. These solutions are modified to make them feasible while preserving their good position in the objective space. The repair is performed based on the relationship between constraints and variables in the problem. Variables causing infeasibility are replaced with values from other solutions. The number of repaired solutions varies during optimization. The remaining part of the solution set is created by usual operators to preserve the diversity and normal procedure of the algorithm. The proposed repair method is applied to NSGA-II as one of the most commonly used multi-objective algorithms. The algorithm is tested on an optimization benchmark test case and an engineering optimization problem involving the structural design of a product tanker. The performance of the proposed approach is compared to the original algorithm and a few other constraint handling methods. Also, a competitive evolutionary algorithm, MOEA/D, is used for validation of the results. The proposed method showed faster convergence to the Pareto frontier and better diversity, covering the highly constrained regions of the design space. Additionally, the proposed algorithm was successful in reaching feasible solutions much faster, which is important in the case of computationally expensive problems, a common situation in engineering.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat