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Advances in Operations Research
Volume 2014, Article ID 397025, 8 pages
Research Article

On One Approach to TSP Structural Stability

Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, S. Kovalevskoi 16, Ekaterinburg 620990, Russia

Received 19 January 2014; Revised 15 April 2014; Accepted 5 May 2014; Published 26 June 2014

Academic Editor: Walter J. Gutjahr

Copyright © 2014 Evgeny Ivanko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we study an inverse approach to the traveling salesman reoptimization problem. Namely, we consider the case of the addition of a new vertex to the initial TSP data and fix the simple “adaptation” algorithm: the new vertex is inserted into an edge of the optimal tour. In the paper we consider the conditions describing the vertexes that can be inserted by this algorithm without loss of optimality, study the properties of stability areas, and address several model applications.