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Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms

Author

Listed:
  • Vladyslav Sokol

    (School of Computing Science, Simon Fraser University, Surrey, British Columbia V3T 0A3, Canada)

  • Ante Ćustić

    (Department of Mathematics, Simon Fraser University, Surrey, British Columbia V3T 0A3, Canada)

  • Abraham P. Punnen

    (School of Management, Northwestern Polytechnical University, 710072 Xi’an, China; Department of Mathematics, Simon Fraser University, Surrey, British Columbia V3T 0A3, Canada)

  • Binay Bhattacharya

    (School of Computing Science, Simon Fraser University, Surrey, British Columbia V3T 0A3, Canada)

Abstract

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem . In this paper, we study the problem from the computational analysis point of view. Several classes of neighborhood structures are introduced for the problem along with some theoretical analysis. These neighborhoods are then explored within a local search and variable neighborhood search frameworks with multistart to generate robust heuristic algorithms. In addition, we present several very fast construction heuristics. Our systematic experimental analysis disclosed some interesting properties of the BAP, different from those of comparable models. We have also introduced benchmark test instances that can be used for future experiments on exact and heuristic algorithms for the problem.

Suggested Citation

  • Vladyslav Sokol & Ante Ćustić & Abraham P. Punnen & Binay Bhattacharya, 2020. "Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 730-746, July.
    • Handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:730-746
    DOI: 10.1287/ijoc.2019.0893
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    References listed on IDEAS

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    1. Punnen, Abraham P. & Wang, Yang, 2016. "The bipartite quadratic assignment problem and extensions," European Journal of Operational Research, Elsevier, vol. 250(3), pages 715-725.
    2. Glover, Fred & Ye, Tao & Punnen, Abraham P. & Kochenberger, Gary, 2015. "Integrating tabu search and VLSN search to develop enhanced algorithms: A case study using bipartite boolean quadratic programs," European Journal of Operational Research, Elsevier, vol. 241(3), pages 697-707.
    3. William P. Pierskalla, 1968. "Letter to the Editor—The Multidimensional Assignment Problem," Operations Research, INFORMS, vol. 16(2), pages 422-431, April.
    4. Torki, Abdolhamid & Yajima, Yatsutoshi & Enkawa, Takao, 1996. "A low-rank bilinear programming approach for sub-optimal solution of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 384-391, October.
    5. Frieze, A. M., 1983. "Complexity of a 3-dimensional assignment problem," European Journal of Operational Research, Elsevier, vol. 13(2), pages 161-164, June.
    6. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
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