Local search for the Traveling Salesman Problem: A comparative study

Yuezhong Wu, T. Weise, R. Chiong
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引用次数: 21

Abstract

The Traveling Salesman Problem (TSP) is one of the most well-studied combinatorial optimization problems. Best heuristics for solving the TSP known today are Lin-Kernighan (LK) local search methods. Recently, Multi-Neighborhood Search (MNS) has been proposed and was demonstrated to outperform Variable Neighborhood Search based methods on the TSP. While LK performs a variable k-opt based search operation, MNS is able to carry out multiple 2-, 3-, or 4-opt moves at once, which are discovered by a highly efficient scan of the current solution. Apart from LK and MNS, many other modern heuristics for TSPs can be found in the relevant literature. However, existing studies rarely use robust statistics for the heuristic algorithms in comparison, let alone investigate their progress over time. This leads to flawed comparisons of simple end-of-run statistics and inappropriate or even incorrect conclusions. In this paper, we thoroughly compare LK and MNS as well as their hybrid versions with Evolutionary Algorithms (EAs) and Population-based Ant Colony Optimization (PACO). This work, to the best of our knowledge, is the first statistically sound comparison of the two efficient heuristics as well as their hybrids with EAs and PACO over time based on a large-scale experimental study. We not only show that hybrid PACO-MNS and PACO-LK are both very efficient, but also find that the full runtime behavior comparison provides deeper and clearer insights whereas a focus of final results could indeed have led to a deceitful conclusion.
旅行商问题的本地搜索:比较研究
旅行商问题(TSP)是研究最多的组合优化问题之一。目前已知的解决TSP的最佳启发式方法是Lin-Kernighan (LK)局部搜索方法。最近,多邻域搜索(MNS)被提出,并被证明在TSP上优于基于可变邻域搜索的方法。当LK执行基于变量k-opt的搜索操作时,MNS能够一次执行多个2-,3-或4-opt移动,这些移动是通过对当前解决方案的高效扫描发现的。除了LK和MNS之外,在相关文献中还可以找到许多其他关于tsp的现代启发式方法。然而,现有的研究很少对启发式算法使用稳健的统计数据进行比较,更不用说调查它们随时间的进展。这导致了简单的运行结束统计数据的有缺陷的比较,以及不适当甚至不正确的结论。在本文中,我们将LK和MNS及其混合版本与进化算法(EAs)和基于种群的蚁群优化(PACO)进行了全面比较。据我们所知,这项工作是基于大规模实验研究,首次在统计上对两种有效的启发式方法以及它们与ea和PACO的混合方法进行比较。我们不仅证明了混合的PACO-MNS和PACO-LK都非常高效,而且还发现,完整的运行时行为比较提供了更深入、更清晰的见解,而对最终结果的关注确实可能导致欺骗性的结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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