Application of Convolution Neural Networks to Genetic Algorithms for Solving Constrained Optimization Problems

Abstract

Many real-world problems are formulated as an optimization problem with several constraints. Usually, a penalty function method is used for transforming a constrained problem into an unconstrained problem. On the other hand, genetic algorithms are optimization methods that mimic the mechanism of biological evolution, and a fitness evalutation for each individual is important to search for a better solution. In this research, we propose a new fitness evaluation method that incorporates the probability of satisfying constraints by using a convolution neural networks (CNN). CNN is one of deep learning methods with convolutional and pooling layers, and is very effective for extracting features from images. Based on the genetic information of individuals generated in the search process, image data are generated by using a graph convolution. Considering the probability of satisfying the constraints obtained by a CNN, we calcuate an individual’s fitness. Through a numerical example, the effectiveness of the proposed penalty method is investigated in terms of generating better solutions compared with conventional penalty function.