An additive bounding procedure for the asymmetric travelling salesman problem

In this paper, new lower bounds for the asymmetric travelling salesman problem are presented, based on spanning arborescences. The new bounds are combined in an additive procedure whose theoretical performance is compared with that of the Balas and Christofides procedure (1981). Both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems.

[1]  M. Fischetti,et al.  AN ADDITIVE APPROACH FOR THE OPTIMAL SOLUTION OF THE PRIZE-COLLECTING TRAVELLING SALESMAN PROBLEM. VEHICLE ROUTING: METHODS AND STUDIES. STUDIES IN MANAGEMENT SCIENCE AND SYSTEMS - VOLUME 16 , 1988 .

[2]  Matteo Fischetti,et al.  An Additive Bounding Procedure for Combinatorial Optimization Problems , 1989, Oper. Res..

[3]  Mandell Bellmore,et al.  Pathology of Traveling-Salesman Subtour-Elimination Algorithms , 1971, Oper. Res..

[4]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[5]  Robert E. Tarjan,et al.  Finding optimum branchings , 1977, Networks.

[6]  Nicos Christofides,et al.  Technical Note - Bounds for the Travelling-Salesman Problem , 1972, Oper. Res..

[7]  D. R. Fulkerson,et al.  Packing rooted directed cuts in a weighted directed graph , 1974, Math. Program..

[8]  T. H. C. Smith,et al.  A Lifo Implicit Enumeration Search Algorithm for the Symmetric Traveling Salesman Problem Using Held and Karp's 1-Tree Relaxation , 1977 .

[9]  Matteo Fischetti,et al.  New lower bounds for the Symmetric Travelling Salesman Problem , 1989, Math. Program..

[10]  Matteo Fischetti,et al.  A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem , 2001 .

[11]  Egon Balas,et al.  A restricted Lagrangean approach to the traveling salesman problem , 1981, Math. Program..

[12]  Paolo Toth,et al.  Algorithms and codes for the assignment problem , 1988 .

[13]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[14]  E. Lawler,et al.  Erratum: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1986 .

[15]  A. Volgenant,et al.  On dual solutions of the linear assignment problem , 1985 .

[16]  Gerald L. Thompson,et al.  Computational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems. , 1977 .

[17]  Patrick D. Krolak,et al.  A man-machine approach toward solving the traveling salesman problem , 1970, DAC '70.

[18]  P. Toth,et al.  Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem , 1980 .

[19]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[20]  Francesco Maffioli,et al.  A note on finding optimum branchings , 1979, Networks.

[21]  Francesco Maffioli,et al.  The k best spanning arborescences of a network , 1980, Networks.