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A Genetic Algorithm for the Multiple-Choice Integer Program

Author

Listed:
  • Atidel Ben Hadj-Alouane

    (University of Michigan, Ann Arbor, Michigan)

  • James C. Bean

    (University of Michigan, Ann Arbor, Michigan)

Abstract

We present a genetic algorithm for the multiple-choice integer program that finds an optimal solution with probability one (though it is typically used as a heuristic). General constraints are relaxed by a nonlinear penalty function for which the corresponding dual problem has weak and strong duality. The relaxed problem is attacked by a genetic algorithm with solution representation special to the multiple-choice structure. Nontraditional reproduction, crossover and mutation operations are employed. Extensive computational tests for dual degenerate problem instances show that suboptimal solutions can be obtained with the genetic algorithm within running times that are shorter than those of the OSL optimization routine.

Suggested Citation

  • Atidel Ben Hadj-Alouane & James C. Bean, 1997. "A Genetic Algorithm for the Multiple-Choice Integer Program," Operations Research, INFORMS, vol. 45(1), pages 92-101, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:92-101
    DOI: 10.1287/opre.45.1.92
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    Citations

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    Cited by:

    1. Alexouda, Georgia & Paparrizos, Konstantinos, 2001. "A genetic algorithm approach to the product line design problem using the seller's return criterion: An extensive comparative computational study," European Journal of Operational Research, Elsevier, vol. 134(1), pages 165-178, October.
    2. Jeffrey W. Ohlmann & James C. Bean & Shane G. Henderson, 2004. "Convergence in Probability of Compressed Annealing," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 837-860, November.
    3. Zhihua Chen & Xuchen Xu & Hongbo Liu, 2023. "Improved Dual-Population Genetic Algorithm: A Straightforward Optimizer Applied to Engineering Optimization," Sustainability, MDPI, vol. 15(20), pages 1-32, October.
    4. Zong-Zhi Lin & James C. Bean & Chelsea C. White, 2004. "A Hybrid Genetic/Optimization Algorithm for Finite-Horizon, Partially Observed Markov Decision Processes," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 27-38, February.
    5. Jeffrey W. Ohlmann & Barrett W. Thomas, 2007. "A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 80-90, February.
    6. Lee, Yusin & Cheng, Juey-Fu, 2001. "A model for calculating optimal vertical alignments of interchanges," Transportation Research Part B: Methodological, Elsevier, vol. 35(5), pages 423-445, June.
    7. Miettinen, Kaisa & Makela, Marko M., 2006. "Synchronous approach in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 170(3), pages 909-922, May.
    8. Kurt DeMaagd & Johannes M. Bauer, 2011. "Modeling the dynamic interactions of agents in the provision of network infrastructure," Information Systems Frontiers, Springer, vol. 13(5), pages 669-680, November.
    9. Martin Schlüter & Matthias Gerdts, 2010. "The oracle penalty method," Journal of Global Optimization, Springer, vol. 47(2), pages 293-325, June.
    10. Zhihua Chen & Xuchen Xu & Hongbo Liu, 2023. "The Successive Approximation Genetic Algorithm (SAGA) for Optimization Problems with Single Constraint," Mathematics, MDPI, vol. 11(8), pages 1-26, April.
    11. Jacob R. Fooks & Kent D. Messer & Maik Kecinski, 2018. "A Cautionary Note on the Use of Benefit Metrics for Cost-Effective Conservation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(4), pages 985-999, December.
    12. Alice E. Smith, 2023. "Note from the Editor," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 711-712, July.

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