The Black and White Traveling Salesman Problem

Authors:
Gianpaolo Ghiani;Gilbert Laporte;Frdric Semet
Affiliations:
Centre de recherche sur les transports, Universit de Montral, C.P. 6128, Succursale Centre-ville, Montral, Quebec, Canada H3C 3J7 and Dipartimento di Ingegneria dellInnovazione, Universit di Lecce ...;Centre de recherche sur les transports, Universit de Montral, C.P. 6128, Succursale Centre-ville, Montral, Quebec, Canada H3C 3J7 and HEC Montral, 3000 chemin de la Cte-Sainte-Catherine, Montral, ...;LAMIH, Universit de Valenciennes et du Hainaut-Cambrsis, Le Mont-Houy, 59311 Valenciennes Cedex 9, France
Venue:
Operations Research
Year:
2006

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Abstract

The black and white traveling salesman problem (BWTSP) is defined on a graph G whose vertex set is partitioned into black and white vertices. The aim is to design a shortest Hamiltonian tour on G subject to cardinality and length constraints: both the number of white vertices as well as the length of the tour between two consecutive black vertices are bounded above. The BWTSP has applications in airline scheduling and in telecommunications. This paper proposes an integer linear formulation for the undirected BWTSP, as well as several classes of valid inequalities. An exact branch-and-cut algorithm is then developed. Extensive tests show that it can solve exactly instances involving up to 100 vertices. The algorithm can also be applied directly to solve unit demand vehicle routing problems of similar sizes.