求解多旅行商问题的一种有效的迭代两阶段启发式算法
An Effective Iterated Two-stage Heuristic Algorithm for the Multiple Traveling Salesmen Problem
摘要：
多个旅行商问题（mTSP）是著名的NP-hard旅行商问题（TSP）的一般推广，即有m（m > 1）个推销员访问城市。在本文中，我们解决的mTSP与minsum目标和minmax目标，其目的是最小化的总长度的$m$旅游和最长的旅游的长度，在所有的m个旅游，分别。我们提出了一个迭代的两阶段启发式算法称为ITSHA的mTSP。ITSHA的每次迭代都包括初始化阶段和改进阶段。初始化阶段旨在生成高质量和多样化的初始解决方案。改进阶段主要应用可变邻域搜索（VNS）的方法，我们提出了有效的局部搜索邻域的基础上，以优化初始解。此外，一些局部最优逃逸的方法，以提高算法的搜索能力。广泛的公共基准实例上的广泛的实验结果表明，ITSHA显着优于国家的最先进的启发式算法在解决mTSP的两个目标。
英文摘要：
The multiple Traveling Salesmen Problem (mTSP) is a general extension of the famous NP-hard Traveling Salesmen Problem (TSP), that there are m (m > 1) salesmen to visit the cities. In this paper, we address the mTSP with both the minsum objective and minmax objective, which aims at minimizing the total length of the $m$ tours and the length of the longest tour among all the m tours, respectively. We propose an iterated two-stage heuristic algorithm called ITSHA for the mTSP. Each iteration of ITSHA consists of an initialization stage and an improvement stage. The initialization stage aims to generate high-quality and diverse initial solutions. The improvement stage mainly applies the variable neighborhood search (VNS) approach based on our proposed effective local search neighborhoods to optimize the initial solution. Moreover, some local optima escaping approaches are employed to enhance the search ability of the algorithm. Extensive experimental results on a wide range of public benchmark instances show that ITSHA significantly outperforms the state-of-the-art heuristic algorithms in solving the mTSP on both the objectives.
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