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A Multilevel Search Algorithm for the Maximization of Submodular Functions

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  • Goldengorin, Boris
  • Ghosh, Diptesh

    (Groningen University)

Abstract

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective function is convex. This result is also stated in terms of random variables. Next, we present a class of convex approximations of the objective function, which are obtained by perturbing the distributions of the right-hand side parameters. We derive a uniform bound on the absolute error of the approximation. Finally, we give a representation of convex simple integer recourse problems as continuous simple recourse problems, so that they can be solved by existing special purpose algorithms

Suggested Citation

  • Goldengorin, Boris & Ghosh, Diptesh, 2004. "A Multilevel Search Algorithm for the Maximization of Submodular Functions," Research Report 04A20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:04a20
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    File URL: http://irs.ub.rug.nl/ppn/288251229
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    References listed on IDEAS

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    1. Boris Goldengorin & Gerard Sierksma & Gert A. Tijssen & Michael Tso, 1999. "The Data-Correcting Algorithm for the Minimization of Supermodular Functions," Management Science, INFORMS, vol. 45(11), pages 1539-1551, November.
    2. 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.
    3. Stefano Benati, 2003. "An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 43-58, September.
    4. Goldengorin, Boris & Ghosh, Diptesh & Sierksma Gerard, 2004. "Data Correcting Algorithms in Combinatorial Optimization," IIMA Working Papers WP2004-04-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
    6. Beasley, J. E., 1993. "Lagrangean heuristics for location problems," European Journal of Operational Research, Elsevier, vol. 65(3), pages 383-399, March.
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    Cited by:

    1. Yijing Wang & Dachuan Xu & Yishui Wang & Dongmei Zhang, 2020. "Non-submodular maximization on massive data streams," Journal of Global Optimization, Springer, vol. 76(4), pages 729-743, April.

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