Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems

  • Authors:

  • Walter H. Kohler;Kenneth Steiglitz

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA;Department of Electrical Enigneering, Princeton University, Princeton, New Jersey

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1974

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Abstract

Branch-and-bound implicit enumeration algorithms for permutation problems (discrete optimization problems where the set of feasible solutions is the permutation group Sn) are characterized in terms of a sextuple (Bp S,E,D,L,U), where (1) Bp is the branching rule for permutation problems, (2) S is the next node selection rule, (3) E is the set of node elimination rules, (4) D is the node dominance function, (5) L is the node lower-bound cost function, and (6) U is an upper-bound solution cost. A general algorithm based on this characterization is presented and the dependence of the computational requirements on the choice of algorithm parameters, S, E, D, L, and U is investigated theoretically. The results verify some intuitive notions but disprove others.