An Evolutionary Computation Framework for Predicting the Effect of Constraint Relaxation on Optimal Solutions in Multi-Constrained Optimization Problems

Abstract

Many optimization problems in industrial applications involve multiple constraints, forming multi-constrained optimization problems. In such problems, the quality of the optimal solution can vary significantly depending on how the constraints are defined. This study proposes a method for predicting how the optimal solution changes when constraints are relaxed. Specifically, we propose a framework that combines an evolutionary algorithm as the optimization method with Gaussian process regression as a predictive model. The effectiveness of the proposed method is demonstrated using the knapsack problem, a representative benchmark for constrained combinatorial optimization. The experimental results reveal that while the proposed method achieves good approximation with a limited number of sample points, it may suffer from sampling bias.