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Some new perspectives for solving 0–1 integer programming problems using Balas method

Author

Listed:
  • J. Glover

    (Ryerson University)

  • V. Quan

    (University of Toronto at Scarborough)

  • S. Zolfaghari

    (Ryerson University)

Abstract

Egon Balas’s additive algorithm, also known as implicit enumeration, is a technique that uses a branch-and-bound (B&B) approach to finding optimal solutions to 0–1 integer programming problems. Three common search strategies in B&B are depth-first search, breadth-first search and best-first search. The B&B approach generates a list of pending nodes to be evaluated and storage of these nodes becomes a memory issue for larger problems. In this paper, we propose a simple bookkeeping method that tracks the state of the problem using a single array when performing a depth-first search, dramatically reducing memory requirements. The method also provides the ability to calculate, at any point of the search, the theoretical maximum number of remaining nodes to be evaluated. We note in this paper that when using the best-first search strategy, the first candidate solution found is the optimal solution.

Suggested Citation

  • J. Glover & V. Quan & S. Zolfaghari, 2021. "Some new perspectives for solving 0–1 integer programming problems using Balas method," Computational Management Science, Springer, vol. 18(2), pages 177-193, June.
    • Handle: RePEc:spr:comgts:v:18:y:2021:i:2:d:10.1007_s10287-021-00389-6
    DOI: 10.1007/s10287-021-00389-6
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    References listed on IDEAS

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    1. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    2. Fred Glover, 1965. "A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem," Operations Research, INFORMS, vol. 13(6), pages 879-919, December.
    3. Egon Balas, 1965. "An Additive Algorithm for Solving Linear Programs with Zero-One Variables," Operations Research, INFORMS, vol. 13(4), pages 517-546, August.
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