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A Priori Optimization

Author

Listed:
  • Dimitris J. Bertsimas

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Patrick Jaillet

    (Ecole Nationale des Ponts et Chaussées, Noisy Le Grand, France)

  • Amedeo R. Odoni

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Consider a complete graph G = ( V , E ) in which each node is present with probability p . We are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization, under which the combinatorial optimization problem is solved optimally for every instance. We consider four problems: the traveling salesman problem (TSP), the minimum spanning tree, vehicle routing, and traveling salesman facility location. We discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance. We characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst-case guarantees. Finally, we use the TSP as an example to find practical solutions based on ideas of local optimality.

Suggested Citation

  • Dimitris J. Bertsimas & Patrick Jaillet & Amedeo R. Odoni, 1990. "A Priori Optimization," Operations Research, INFORMS, vol. 38(6), pages 1019-1033, December.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:6:p:1019-1033
    DOI: 10.1287/opre.38.6.1019
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