Introducing Generative adversarial networks on Estimation of distribution algorithm to solve permutation-based problems

Abstract

As a subclass of evolutionary algorithms, estimation of distribution algorithms (EDAs) have found widespread use in a variety of optimization problems with impressive performance. In each generation, they build a probabilistic model representing the promising individuals, and the next generation constructs by sampling this model. Constructing and sampling the probabilistic model is a real challenge in developing such algorithms. Generative adversarial networks (GANs) are a popular kind of generative model that has been widely adopted due to their ability to generate new samples that closely match the distribution of training data. However, research on how GANs handle permutation spaces is lacking. We suggest a novel Estimation of Distribution Algorithm (EDA) that uses GANs as a probabilistic model estimator to advance this subject. in order to preserve the information captured from the selected individuals, those promising individuals were represented by a one-hot matrix, then used to train GANs. The proposed algorithm is tested to solve two permutation problems: The Travelling Salesman Problem (TSP) and Permutation Flowshop Scheduling Problem (PFSP). The Experimental results show that the proposed algorithm can obtain the optimal solution in some instances and a near-optimal in others.