A genetic algorithm for the close-enough traveling salesman problem with application to solar panels diagnostic reconnaissance

Abstract

This paper addresses a variant of the classical Traveling Salesman Problem known as Close-Enough Traveling Salesman Problem . In this problem, there is a set of nodes (customers, targets), each of them associated with a region, denoted as neighborhood, that contains it. The goal is to determine the shortest tour that visits all the nodes, where a node is visited when the tour traverses or reaches the region associated with the node. We propose a genetic algorithm (GA), which uses several strategies to optimize the tour, such as 2opt, second-order cone programming, and a bisection algorithm. The proposed approach is tested on 62 benchmark instances. The results show that GA produces better or similar solutions compared to the ones produced by state-of-the-art algorithms in a reasonable computing time. Besides, GA found 32 new best solutions out of 62 instances. Furthermore, we propose different metrics to classify problem instances with the goal of detecting which problem characteristics have a larger impact on the difficulty of solving the problem. We also revised the already proposed metric, called Overlap Ratio, and correct its calculation done in previous contributions. Finally, we present a case study related to the diagnostic reconnaissance of solar panels. The case study is related to a research project developed at the University of Molise in collaboration with private IT companies. We show that the problem under study is properly modeled as a Close-Enough Traveling Salesman Problem and apply the GA to solve it, focusing on the benefits obtained by applying this solution approach.