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Efficient Heuristic Procedures for Integer Linear Programming with an Interior

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  • Frederick S. Hillier

    (Stanford University, Stanford, California)

Abstract

This paper presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods (after obtaining the optimal noninteger solution by the simplex method) has generally been only a small fraction of that used by the simplex method for the problems tested (which have 15 to 300 original variables). Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these methods also are outlined. A companion paper presents an optimal “bound-and-scan” algorithm that may be used in conjunction with these approximate procedures.

Suggested Citation

  • Frederick S. Hillier, 1969. "Efficient Heuristic Procedures for Integer Linear Programming with an Interior," Operations Research, INFORMS, vol. 17(4), pages 600-637, August.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:4:p:600-637
    DOI: 10.1287/opre.17.4.600
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    Cited by:

    1. Joseph, Anito & Gass, Saul I. & Bryson, Noel, 1998. "An objective hyperplane search procedure for solving the general all-integer linear programming (ILP) problem," European Journal of Operational Research, Elsevier, vol. 104(3), pages 601-614, February.
    2. Christoph Neumann & Oliver Stein & Nathan Sudermann-Merx, 2019. "A feasible rounding approach for mixed-integer optimization problems," Computational Optimization and Applications, Springer, vol. 72(2), pages 309-337, March.
    3. Robert M. Saltzman & Frederick S. Hillier, 1991. "An exact ceiling point algorithm for general integer linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 53-69, February.
    4. Sabah Bushaj & İ. Esra Büyüktahtakın, 2024. "A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack," Journal of Global Optimization, Springer, vol. 89(3), pages 655-685, July.
    5. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    6. Joseph, A. & Gass, S. I., 2002. "A framework for constructing general integer problems with well-determined duality gaps," European Journal of Operational Research, Elsevier, vol. 136(1), pages 81-94, January.
    7. Tsubakitani, Shigeru & Evans, James R., 1998. "An empirical study of a new metaheuristic for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 104(1), pages 113-128, January.
    8. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.

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