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Optimized Crossover for the Independent Set Problem

Author

Listed:
  • Charu C. Aggarwal

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Ray P. Tai

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We propose a knowledge-based crossover mechanism for genetic algorithms that exploits the structure of the solution rather than its coding. More generally, we suggest broad guidelines for constructing the knowledge-based crossover mechanisms. This technique uses an optimized crossover mechanism, in which the one of the two children is constructed in such a way as to have the best objective function value from the feasible set of children, while the other is constructed so as to maintain the diversity of the search space. We implement our approach on a classical combinatorial problem, called the independent set problem. The resulting genetic algorithm dominates all other genetic algorithms for the problem and yields one of the best heuristics for the independent set problem in terms of robustness and time performance. The primary purpose of this paper is to demonstrate the power of knowledge based mechanisms in genetic algorithms.

Suggested Citation

  • Charu C. Aggarwal & James B. Orlin & Ray P. Tai, 1997. "Optimized Crossover for the Independent Set Problem," Operations Research, INFORMS, vol. 45(2), pages 226-234, April.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:2:p:226-234
    DOI: 10.1287/opre.45.2.226
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    Citations

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    Cited by:

    1. Hui-Chin Tang & Chiang Kao, 2004. "Searching for Good Multiple Recursive Random Number Generators via a Genetic Algorithm," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 284-290, August.
    2. Helena R. Lourenço & José P. Paixão & Rita Portugal, 2001. "Multiobjective Metaheuristics for the Bus Driver Scheduling Problem," Transportation Science, INFORMS, vol. 35(3), pages 331-343, August.
    3. Jordi Pereira & Igor Averbakh, 2013. "The Robust Set Covering Problem with interval data," Annals of Operations Research, Springer, vol. 207(1), pages 217-235, August.
    4. Bergey, Paul K. & Ragsdale, Cliff, 2005. "Modified differential evolution: a greedy random strategy for genetic recombination," Omega, Elsevier, vol. 33(3), pages 255-265, June.
    5. Chu, Chao-Hsien & Premkumar, G. & Chou, Hsinghua, 2000. "Digital data networks design using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 127(1), pages 140-158, November.
    6. Trick, Michael A. & Yildiz, Hakan, 2012. "Locally Optimized Crossover for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 216(2), pages 286-292.
    7. Michelle Dunbar & Simon Belieres & Nagesh Shukla & Mehrdad Amirghasemi & Pascal Perez & Nishikant Mishra, 2020. "A genetic column generation algorithm for sustainable spare part delivery: application to the Sydney DropPoint network," Annals of Operations Research, Springer, vol. 290(1), pages 923-941, July.

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