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A Branch-and-Cut Approach to a Traveling Salesman Problem with Side Constraints

Author

Listed:
  • M. Padberg

    (School of Business, New York University, New York, New York 10003)

  • G. Rinaldi

    (Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Roma, Italy)

Abstract

A problem posed by O. L. Deutsch (Deutsch, O. L. 1988. Artificial intelligence design challenge---Background, analysis, and relative performance of algorithms. J. Guidance, Control, and Dynamics 11 386--393.) as the Artificial Intelligence Design Challenge for the 1987 American Institute of Aeronautics and Astronautics (AIAA) Conference on Guidance, Navigation & Control (Monterey, CA, August 17--19, 1987) is formulated as a zero-one linear program. We show that the associated (relaxed) linear programming problem can be solved in polynomial time despite an exponential size of the proposed constraint system in terms of the underlying parameter n of the number of cities considered, when a nonlinear constraint of the problem is either ignored or approximated by linearization. We describe a software system AIAA/SOLVER that we have implemented to solve the problem to optimality under an apparently weak assumption about its stochastic cost structure using branch-and-cut.

Suggested Citation

  • M. Padberg & G. Rinaldi, 1989. "A Branch-and-Cut Approach to a Traveling Salesman Problem with Side Constraints," Management Science, INFORMS, vol. 35(11), pages 1393-1412, November.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:11:p:1393-1412
    DOI: 10.1287/mnsc.35.11.1393
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    Citations

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    Cited by:

    1. Robert Carr, 2004. "Separation Algorithms for Classes of STSP Inequalities Arising from a New STSP Relaxation," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 80-91, February.
    2. Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
    3. Robert Carr, 2000. "Some Results on Node Lifting of TSP Inequalities," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 395-414, December.

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