Discriminating and Clustering Ordered Permutations Using Artificial Neural Networks: A Potential Application in ANN-Guided Genetic Algorithms

Abstract

Traveling salesman, linear ordering, quadratic assignment, and flow shop scheduling are typical examples of permutation-based combinatorial optimization problems with real-life applications. These problems naturally represent solutions as an ordered permutation of objects. However, as the number of objects increases, finding optimal permutations is extremely difficult when using exact optimization methods. In those circumstances, approximate algorithms such as metaheuristics are a plausible way of finding acceptable solutions within a reasonable computational time. In this paper, we present a technique for clustering and discriminating ordered permutations with potential applications in developing neural network-guided metaheuristics to solve this class of problems. In this endeavor, we developed two different techniques to convert ordered permutations to binary-vectors and considered Adaptive Resonate Theory (ART) neural networks for clustering the resulting binary vectors. The proposed binary conversion techniques and two neural networks (ART-1 and Improved ART-1) are examined under various performance indicators. Numerical examples show that one of the binary conversion methods provides better results than the other, and Improved ART-1 is superior to ART-1. Additionally, we apply the proposed clustering and discriminating technique to develop a neural-network-guided Genetic Algorithm (GA) to solve a flow-shop scheduling problem. The investigation shows that the neural network-guided GA outperforms pure GA.