Neural network-enabled discovery of mapping between variables and constraints for autonomous repair-based constraint handling in multi-objective structural optimization

Abstract

Repairing infeasible solutions is a seldomly used constraint handling technique (CHT) in optimization because, with this technique, users must define ways to prevent constraint violation, which is difficult or impossible in many situations. To overcome this challenge, in this paper we propose an approach based on artificial neural networks to automatically discover variable-constraint mapping that specifies which variables must be modified if a constraint is violated. We embed this procedure into a recent repair-based CHT that uses members of the current population, either feasible or infeasible, to determine the new value for the repaired variables. Here, the CHT is modified to repair each constraint separately using a different solution that does not violate the same constraint. The entire technique is fully autonomous, meaning that a user does not provide any insights into the problem. The modified CHT is implemented in the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and compared with four other multi-objective optimization algorithms and a few CHTs. Four test problems are considered: a mathematical benchmark problem, two truss problems and structural optimization of a chemical tanker. The tanker case is a real-world optimization problem with 94 variables and 376 nonlinear constraints. A minimum of 30 independent runs are performed with each algorithm, and various statistical results are shown. With the proposed automated mapping, the modified repair-assisted NSGA-II obtains significantly better results than NSGA-II with other CHTs on all test problems while outperforming all other algorithms and CHTs for the tanker.