Transformations of generalized ATSP into ATSP

Authors:
D. Ben-Arieh;G. Gutin;M. Penn;A. Yeo;A. Zverovitch
Affiliations:
Department of Industrial and Manufacturing Systems Engineering, Kansas State University, USA;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK
Venue:
Operations Research Letters
Year:
2003

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Abstract

The generalized traveling salesman problem (GTSP) is stated as follows. Given a weighted complete digraph K"n^* and a partition V"1,...,V"k of its vertices, find a minimum weight cycle containing exactly one vertex from each set V"i,i=1,...,k. We study transformations from GTSP to TSP. The 'exact' Noon-Bean transformation is investigated in computational experiments. We study the 'non-exact' Fischetti-Salazar-Toth (FST) transformation and its two modifications in computational experiments and theoretically using domination analysis. One of our conclusions is that one of the modifications of the FST transformation is better than the original FST transformation in the worst case in terms of domination analysis.