Model-Based Evolutionary Algorithms and Generative Deep Learning Models for Permutation-Based Problems

Abstract

Estimation of Distribution Algorithms (EDAs) are a type of evolutionary algorithm that are good at solving optimization problems. EDAs work by building a model of the best solutions found so far and then using this model to generate new solutions. The main challenge with EDAs is building a good model. This is especially hard for permutation problems. We introduce a novel Estimation of Distribution Algorithm (EDA), the Position-Guided Sampling EDA (PGS-EDA), tailored for permutation problems. PGS-EDA focuses on the po- sitions of elements in the solution rather than the elements themselves. This makes PGS-EDA better at solving permutation problems. We tested PGS-EDA on the Permutation Flow-Shop Scheduling Problem (PFSP). Our results showed that PGS-EDA is good at solving the PFSP, es- pecially for small and medium-sized problems. PGS-EDA outperformed other EDAs designed for permutation problems on the PFSP, achieving the lowest Average Relative Percentage De- viation (ARPD). We also explored the use of Generative Adversarial Networks (GANs) in EDAs. GANs are good at generating samples that look like the training data. However, they have not been well- studied for permutation problems. To address this gap, we proposed a new EDA that uses GANs to estimate the probabilistic model. We represent candidate solutions with one-hot matrices to preserve important information during GAN training. We tested our proposed algorithm on two permutation problems: the Traveling Salesman Problem (TSP) and the PFSP. Our results showed that the algorithm can find the best solution in some cases and near-best solutions in others