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Branching From The Largest Upper Bound: Folklore And Facts

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  • Fox, B. L.
  • Lenstra, J. K.
  • Rinnooy Kan, A. H. G.
  • Schrage, L. E.

Abstract

Branch-and-bound algorithms are widely used to solve combinatorial maximization problems. At each step of such an algorithm a search strategy selects an active subset of feasible solutions for examination. In this paper we discuss the formal properties and the practical value of search strategies based on branching from the largest upper bound (BLUB strategies). We investigate conditions under which BLUB strategies are optimal in the sense that they minimize the number of subsets generated. Counterexamples show that the conditions given in the literature are not strong enough and a correct optimality condition is formulated. Finally, we argue that the practical objections raised against BLUB strategies are not necessarily convincing.

Suggested Citation

  • Fox, B. L. & Lenstra, J. K. & Rinnooy Kan, A. H. G. & Schrage, L. E., 1977. "Branching From The Largest Upper Bound: Folklore And Facts," Econometric Institute Archives 272158, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272158
    DOI: 10.22004/ag.econ.272158
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    References listed on IDEAS

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    1. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    2. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
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