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Cooperative multiobjective optimization with bounds on objective functions

Author

Listed:
  • I. Kaliszewski

    (Systems Research Institute, Polish Academy of Sciences
    Warsaw School of Information Technology)

  • J. Miroforidis

    (Systems Research Institute, Polish Academy of Sciences)

Abstract

When solving large-scale multiobjective optimization problems, solvers can get stuck because of memory and/or time limitations. In such cases, one is left with no information on the distance to the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information. To this aim we make use of the concept of lower shells and upper shells, developed in our earlier works. No specific assumptions about the problems to be solved are made. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from single-objective multidimensional knapsack problems in the Beasley OR Library. We address cases when a top-class commercial mixed-integer linear solver fails to provide Pareto optimal solutions attempted to be derived by scalarization.

Suggested Citation

  • I. Kaliszewski & J. Miroforidis, 2021. "Cooperative multiobjective optimization with bounds on objective functions," Journal of Global Optimization, Springer, vol. 79(2), pages 369-385, February.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:2:d:10.1007_s10898-020-00946-4
    DOI: 10.1007/s10898-020-00946-4
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    References listed on IDEAS

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    1. Ignacy Kaliszewski, 2006. "Soft Computing For Complex Multiple Criteria Decision Making," International Series in Operations Research and Management Science, Springer, number 978-0-387-30177-8, March.
    2. Kaliszewski, Ignacy & Miroforidis, Janusz & Podkopaev, Dmitry, 2012. "Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy," European Journal of Operational Research, Elsevier, vol. 216(1), pages 188-199.
    3. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    4. I. Kaliszewski & J. Miroforidis, 2014. "Two-Sided Pareto Front Approximations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 845-855, September.
    5. Ignacy Kaliszewski & Janusz Miroforidis & Dmitry Podkopaev, 2016. "Multiple Criteria Decision Making by Multiobjective Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-32756-3, March.
    6. I. Kaliszewski & J. Miroforidis, 2018. "On upper approximations of Pareto fronts," Journal of Global Optimization, Springer, vol. 72(3), pages 475-490, November.
    7. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    8. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
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    1. I. Kaliszewski & J. Miroforidis, 2022. "Probing the Pareto front of a large-scale multiobjective problem with a MIP solver," Operational Research, Springer, vol. 22(5), pages 5617-5673, November.

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