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

Zhicheng Lin, Jun Li, Yongcui Li
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Abstract

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.
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一种基于云容器的超大规模有色旅行商问题分布式求解方法
彩色旅行商问题(CTSP)是对著名的多重旅行商问题(MTSP)的推广,利用颜色来描述城市对单个推销员的可达性。为了求解CTSP实例,已经开发了许多串行算法。本文首次提出了CTSP的分布式求解方法。首先,以管道方式设计并实现了基于云容器的CTSP分布式求解框架。超大尺度CTSP可以分解成多个tsp并行求解,大大降低了计算复杂度。其次,根据该框架,我们开发了一种基于分布式delaunay三角剖分的变量邻域搜索(DDVNS)算法。在DDVNS中,利用两阶段初始化来生成每个TSP解决方案。然后,采用基于delaunay三角剖分的变量邻域搜索(DVNS),在邻域内精细搜索局部TSP最优。此外,通过重新分配多色城市和重复搜索过程,进一步改进了解决方案。最后,大量的实验表明,DDVNS在搜索效率和解质量方面优于最先进的串行算法。值得注意的是,我们可以在15分钟内完成16个销售人员,16万个城市的超大规模案例的满意解决,打破了现有ctsp的解决记录。
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