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A robust optimization approach with probe-able uncertainty

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  • Lee, Chungmok

Abstract

We consider optimization problems whose objective functions have uncertain coefficients. We assumed that, initially, the uncertain data are given as ranges, and probing of the true values of data is possible. The complete probing of all uncertain data will yield the true optimal solution. However, probing all uncertain data is undesirable because each probing may require cost or time depending on the methods of probing. We are interested in finding a solution, which we call Γ-optimal, that is guaranteed to remain the best solution even after additional Γ probings of uncertain data. An iterative algorithm to find the Γ-optimal solution is developed with theoretical probability bounds of the Γ-optimal solution being true optimal. Special algorithms are also developed for the problems on networks. The extensive computational study shows that the proposed approach could find the true optimal solutions at very high percentages, even with small numbers of probings.

Suggested Citation

  • Lee, Chungmok, 2022. "A robust optimization approach with probe-able uncertainty," European Journal of Operational Research, Elsevier, vol. 296(1), pages 218-239.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:1:p:218-239
    DOI: 10.1016/j.ejor.2021.06.064
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    Cited by:

    1. Goerigk, Marc & Lendl, Stefan & Wulf, Lasse, 2022. "Two-Stage robust optimization problems with two-stage uncertainty," European Journal of Operational Research, Elsevier, vol. 302(1), pages 62-78.

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