Note on the Inverse Metric Traveling Salesman Problem Against the Minimum Spanning Tree Algorithm

• Published in: Management science & financial engineering Vol. 20; no. 1; pp. 17 - 19
• Main Author: Chung, Yerim
• Format: Journal Article
• Language: English
• Published: Seoul 한국경영과학회 01.05.2014; KORMS
• Subjects: 경영학; Combinatorial Optimization; TSP; Minimum Spanning Tree Algorithm; Inverse Optimization
• ISSN: 2287-2043; 2287-2361
• DOI: 10.7737/MSFE.2014.20.1.017

In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an in-stance (G, w) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle HC0. The task is then to adjust the edge cost vector w to w' so that the new cost vector w' satisfies the triangle inequality condition and HC0 can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w'. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the L1-norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem. KCI Citation Count: 1