Adaptive repair method for constraint handling in multi-objective genetic algorithm based on relationship between constraints and variables

Abstract

While evolutionary algorithms are known among the best methods for solving both theoretical and real-world optimization problems, constraint handling is still one of the major concerns. Common constraint handling methods reject or devalue infeasible solutions depending on their distance from the feasible space, even if they dominate feasible solutions. Alternatively, repair methods aim to overcome infeasibility, but they are currently limited to specific types of problems. In this paper, we propose a more generic repair approach to improve efficiency of constraint handling in non-dominance based genetic algorithm. We start by identifying variables which influence each constraint. This information is used to replace variable values that caused constraint violation, using other solutions in the current generation. Repairing is carried out on the solutions that dominate all feasible members of the population, or have the smallest constraint violation. The repair approach is implemented into NSGA-II and tested on one optimization test case and an engineering optimization problem. The latter focuses on structural design of a ship hull girder, involving two conflicting objectives, 94 decision variables and 376 nonlinear constraints. The proposed repairing approach reduces drastically the number of function evaluations needed to find the feasible space, and it leads to faster convergence and better spread of the non-dominated front. Starting from different random populations, the new algorithm finds feasible solutions within one generation, while the original algorithm takes between 7 and 72 generations. Effectiveness of the optimization is analyzed in terms of the hypervolume performance metric. The repairing algorithm obtains significantly better hypervolume values throughout the optimization run. The highest improvements are achieved in the initial phase of the optimization, which is important for the practical design. The new algorithm performs better than two constraint handling approaches from the literature. It also outperforms MOEA/D algorithm in the engineering problem.