A Cloud Container-Based Distributed Solving Approach to Superscale Colored Traveling Salesman Problems

Abstract The colored traveling salesman problem (CTSP) generalizes the well-known multiple traveling salesman problem (MTSP) by utilizing colors to describe the accessibility of cities to individual salesmen. Many serial algorithms have been developed to solve CTSP instances. This work presents a distributed solving method for CTSP for the first time. First, a cloud container-based distributed solving framework for CTSP is designed and implemented in a pipeline style. A superscale CTSP can be decomposed into many TSPs to solve in parallel to reduce computational complexity dramatically. Second, following the framework, we develop a distributed Delaunay-triangulation-based variable neighborhood search (DDVNS) algorithm. In DDVNS, a two-stage initialization is exploited to generate each TSP solution. Then, Delaunay-triangulation-based variable neighborhood search (DVNS) is applied to search for the local TSP optima within a neighborhood delicately. In addition, the solutions are improved further by reallocating the multicolor cities and repeating the search progress. Finally, the extensive experiments show that DDVNS outperforms the state-of-the-art serial algorithms regarding search efficiency and solution quality. Notably, We can achieve a satisfactory solution in a superscale case of 16 salesmen and 160000 cities within 15 minutes, which breaks the existing solving record of CTSPs.