On the high multiplicity traveling salesman problem

Authors:
Alexander Grigoriev;Joris Van De Klundert
Affiliations:
Department of Quantitative Economics, Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands;Department of Mathematics, Faculty of Science, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
Venue:
Discrete Optimization
Year:
2006

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Abstract

This paper considers a version of the traveling salesman problem where the cities are to be visited multiple times. Each city has its own required number of visits. We investigate how the optimal solution and its objective value change when the numbers of visits are increased by a common multiplicator. In addition, we derive lower bounds on values of the multiplicator beyond which further increase does not improve the average tour length. Moreover, we show how and when the structure of an optimal tour length can be derived from tours with smaller multiplicities.