带层次目标函数的旅行商问题

T. Dam, D. T. Nguyen, Q. Bui, T. Do
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引用次数: 1

摘要

我们解决了著名的旅行推销员问题(TSP)的一个新变体,称为带层次目标的旅行推销员问题(TSPHO)。在这个问题中,客户被分成几个优先级递减的组,即第一组比第二组重要,第二组比第三组重要,以此类推。TSPHO与经典TSP的区别在于目标函数。分层目标不是最小化总旅行成本,而是最小化第一组的完成时间,然后最小化第二组的完成时间,以此类推。首先提出了将TSPHO转换为等效的非对称TSP,从而可以使用协和式或lin - kernighan - helsgaon (LKH)等有效的TSP求解器来求解问题。遗传算法也是一种替代的解决方案。计算结果表明了方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Traveling Salesman Problem with Hierarchical Objective Function
We address a novel variant of the wellknown Traveling Salesman Problem (TSP) called the Traveling Salesman Problem with Hierarchical Objective (TSPHO). In this problem, the customers are divided in to several groups with decreasing priority levels, i.e., the first group is more important than the second one and the second one is more important than the third one, and so on. The difference between TSPHO and the classical TSP lies in the objective function. The Hierarchical Objective does not minimize the total travel cost, but aims to minimize the completion time of the first group then the completion time of the second group, etc. A transformation of the TSPHO into an equivalent Asymmetric TSP is first proposed from which one can use efficient TSP solvers such as Concorde or Lin-Kernighan-Helsgaun (LKH) to solve the problem. A genetic algorithm is also developed as an alternative solution. Computational results show the performance of our methods.
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