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A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems

Author

Listed:
  • Hongwei Jiao

    (Henan Institute of Science and Technology)

  • Binbin Li

    (Henan Institute of Science and Technology)

  • Wenqiang Yang

    (Henan Institute of Science and Technology)

Abstract

In this paper, we investigate a generalized multiplicative problem (GMP) that is known to be NP-hard even with one linear product term. We first introduce some criterion-space variables to obtain an equivalent problem of the GMP. A criterion-space branch-reduction-bound algorithm is then designed, which integrates some basic operations such as the two-level linear relaxation technique, rectangle branching rule and criterion-space region reduction technologies. The global convergence of the presented algorithm is proved by means of the subsequent solutions of a series of linear relaxation problems, and its maximum number of iterations is estimated on the basis of exhaustiveness of branching rule. Finally, numerical results demonstrate the presented algorithm can efficiently find the global optimum solutions for some test instances with the robustness.

Suggested Citation

  • Hongwei Jiao & Binbin Li & Wenqiang Yang, 2024. "A criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems," Journal of Global Optimization, Springer, vol. 89(3), pages 597-632, July.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-023-01358-w
    DOI: 10.1007/s10898-023-01358-w
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    References listed on IDEAS

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    1. Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
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    6. Jiao, Hong-Wei & Liu, San-Yang, 2015. "A practicable branch and bound algorithm for sum of linear ratios problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 723-730.
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