A cloud computing approach to superscale colored traveling salesman problems

The colored traveling salesman problem (CTSP) generalizes the well-known multiple traveling salesman problem by utilizing colors to describe the accessibility of cities to individual salesmen. Many centralized algorithms have been developed to solve CTSP instances. This work presents a distributed solving framework and method for CTSP for the first time. The framework consists of multiple container-based computing nodes that rely on specific cloud infrastructures to perform distributed optimization in a pipeline style. In the framework, we develop a distributed Delaunay-triangulation-based variable neighborhood search (DDVNS) algorithm for solving a CTSP case decomposed into many traveling salesman problems. DDVNS exploits a two-stage initialization to generate an initial solution for all TSPs. After that, Delaunay-triangulation-based variable neighborhood search (DVNS) is employed to find local optima. Furthermore, the obtained solutions are improved by reallocating multicolor cities and iterating the search progress, ultimately leading to a group of CTSP solutions. Finally, extensive experiments show that DDVNS outperforms the state-of-the-art centralized VNS algorithms in terms of search efficiency and solution quality. Notably, we can achieve the best solution in a superscale case with 16 salesmen and 160,000 cities within 15 minutes, breaking the best record of CTSPs.