An Improved Gradient-Based Repair Method for Constrained Numerical Optimization

Recently, gradient-based repair methods have been commonly introduced into constraint-handling techniques to handle linear and non-linear constraints. These gradient-based repair methods are only designed to reduce constraint violations, and they do not act on the objective function in the repairing process. Nevertheless, the gradient descent optimization method is originally proposed to optimize the objective function without constraints. Motivated by this consideration, this study develops an improved gradient-based repair method that incorporates the objective function to handle the constraints and optimize the objective function simultaneously. The proposed repair method is integrated into a multiobjective differential evolution framework to investigate its effectiveness. Experiments have been conducted on 57 real-world constrained benchmark test functions. The empirical result shows that, compared to the selected state-of-the-art algorithms, our proposed gradient-based repair method can assist the adopted constrained optimization approach to obtain high-quality feasible solutions.