Graph convolutional neural networks in genetic algorithms for constrained optimization

Abstract For constrained optimization, penalty function methods take constraint violations into account when evaluating solutions and are one of the most popular constraint handling techniques. However, the disadvantage of the penalty function is that it requires adjustment of some parameters, such as the penalty factor. To alleviate this burden of adjustment, this study proposes a self-adaptive penalty function using a graph convolutional neural network. The proposed idea considers the probability that a solution does not meet or violates constraints and is applied to suitability assessment to find solutions by genetic algorithms. Through simulation and comparison of several benchmark problems, we show that the proposed method shows good performance in that it stably finds a good solution even with a small number of function evaluations.