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Data structures for speeding up Tabu Search when solving sparse quadratic unconstrained binary optimization problems

Author

Listed:
  • Ricardo N. Liang

    (Federal University of ABC)

  • Eduardo A. J. Anacleto

    (Federal University of ABC)

  • Cláudio N. Meneses

    (Federal University of ABC)

Abstract

The quadratic unconstrained binary optimization (QUBO) problem belongs to the NP-hard complexity class of problems and has been the subject of intense research since the 1960s. Many problems in various areas of research can be reformulated as QUBO problems, and several reformulated instances have sparse matrices. Thus, speeding up implementations of methods for solving the QUBO problem can benefit all of those problems. Among such methods, Tabu Search (TS) has been particularly successful. In this work, we propose data structures to speed up TS implementations when the instance matrix is sparse. Our main result consists in employing a compressed sparse row representation of the instance matrix, and priority queues for conducting the search over the solution space. While our literature review indicates that current TS procedures for QUBO take linear time on the number of variables to execute one iteration, our proposed structures may allow better time complexities than that, depending on the sparsity of the instance matrix. We show, by means of extensive computational experiments, that our techniques can significantly decrease the processing time of TS implementations, when solving QUBO problem instances with matrices of relatively high sparsity. To assess the quality of our results regarding more intricate procedures, we also experimented with a Path Relinking metaheuristic implemented with the TS using our techniques. This experiment showed that our techniques can allow such metaheuristics to become more competitive.

Suggested Citation

  • Ricardo N. Liang & Eduardo A. J. Anacleto & Cláudio N. Meneses, 2022. "Data structures for speeding up Tabu Search when solving sparse quadratic unconstrained binary optimization problems," Journal of Heuristics, Springer, vol. 28(4), pages 433-479, August.
    • Handle: RePEc:spr:joheur:v:28:y:2022:i:4:d:10.1007_s10732-022-09498-0
    DOI: 10.1007/s10732-022-09498-0
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    References listed on IDEAS

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    1. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    2. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    3. Gintaras Palubeckis, 2004. "Multistart Tabu Search Strategies for the Unconstrained Binary Quadratic Optimization Problem," Annals of Operations Research, Springer, vol. 131(1), pages 259-282, October.
    4. Iain Dunning & Swati Gupta & John Silberholz, 2018. "What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 608-624, August.
    5. Glover, Fred & Alidaee, Bahram & Rego, Cesar & Kochenberger, Gary, 2002. "One-pass heuristics for large-scale unconstrained binary quadratic problems," European Journal of Operational Research, Elsevier, vol. 137(2), pages 272-287, March.
    6. Fred Glover, 2014. "Exterior Path Relinking for Zero-One Optimization," International Journal of Applied Metaheuristic Computing (IJAMC), IGI Global, vol. 5(3), pages 1-8, July.
    7. Wang, Yang & Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2012. "Path relinking for unconstrained binary quadratic programming," European Journal of Operational Research, Elsevier, vol. 223(3), pages 595-604.
    8. Michele Samorani & Yang Wang & Yang Wang & Zhipeng Lv & Fred Glover, 2019. "Clustering-driven evolutionary algorithms: an application of path relinking to the quadratic unconstrained binary optimization problem," Journal of Heuristics, Springer, vol. 25(4), pages 629-642, October.
    9. Mark Lewis & John Metcalfe & Gary Kochenberger, 2019. "Robust optimisation of unconstrained binary quadratic problems," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 36(4), pages 441-454.
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