Using machine learning in combinatorial optimization: Extraction of graph features for travelling salesman problem

Abstract

Machine learning has emerged as a paradigmatic approach for addressing complex problems across various scientific disciplines, including combinatorial optimization. This article specifically explores the application of machine learning to the Travelling Salesman Problem (TSP) as a technique for evaluating and classifying graph edges. The methodology involves extracting a set of graph features and statistical measures for each edge in the graph. Subsequently, a machine learning model is constructed using the training data, and this model is employed to classify edges in a TSP instance, determining whether they are part of the optimal solution or not. This article contributes to existing knowledge in these key aspects: (a) enhancement of statistical measures, (b) introduction of a novel graph feature, and (c) preparation of training data to simulate real-world problem scenarios. Rigorous experimentation on benchmark instances from the well-established TSP library demonstrates a noteworthy increase in classification accuracy compared to the original approach without the improvements; various popular machine learning techniques are employed and evaluated. Furthermore, the characteristics and effects of the novel approaches are assessed and discussed, including their application to a basic heuristic algorithm. This research finds practical applications in problem reduction, involving the elimination of decision variables, or as a support for heuristic or metaheuristic algorithms in finding solutions.