GSOA: Growing Self-Organizing Array - Unsupervised learning for the Close-Enough Traveling Salesman Problem and other routing problems

This paper presents a novel unsupervised learning procedure called the Growing Self-Organizing Array (GSOA) that is inspired by principles of the self-organizing maps for the Traveling Salesman Problem (TSP). The proposed procedure is a consolidation of principles deployed in solution of several variants of the generalized TSP with Neighborhoods (TSPN) for which the main ideas of the proposed unsupervised learning already demonstrates a wide range of applicability. The herein presented learning procedure is a conceptually simple algorithm which outperforms previous self-organizing map based approaches for the TSP in terms of the solution quality and required computational time. The main benefit of the proposed learning procedure is in solving routing problems that combine a combinatorial solution of some variant of the TSP with the continuous optimization, i.e., problems where it is needed to determine a sequence of visits to the given sets with determination of the particular waypoint location from each (possibly infinite) set. Low computational requirements of the proposed method are demonstrated in a solution of the Close-Enough Traveling Salesman Problem (CETSP), which is a special case of the TSPN with the disk-shaped neighborhoods. The results indicate the proposed procedure provides competitive solutions to the existing heuristics while it is about one order of magnitude faster and at least about two orders of magnitude faster than a heuristic solution of the discretized variant of the CETSP considered as the Generalized TSP.