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Two-Stage robust optimization problems with two-stage uncertainty
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DOI：10.1016/j.ejor.2021.12.046.png)
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摘要
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We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty set. Afterwards, the decision maker can react to this scenario by completing the partial first-stage solution to a full solution. We extend this classic setting by adding another adversary stage after the second decision-maker stage, which results in min-max-min-max problems, thus pushing two-stage settings further towards more general multi-stage problems. We focus on budgeted uncertainty sets and consider both the continuous and discrete case. For the former, we show that a wide range of robust combinatorial optimization problems can be decomposed into polynomially many subproblems, which can be solved in polynomial time for example in the case of ( REPRESENTATIVE ) SELECTION . For the latter, we prove NP-hardness for a wide range of problems, but note that the special case where first-and second-stage adversarial costs are equal can remain solvable in polynomial time.(c) 2022 Elsevier B.V. All rights reserved.
Keyword:
Robustness and sensitivity analysis
Robust optimization
Combinatorial optimization
Budgeted uncertainty
Multistage optimization
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6
论文数:
2.2W
被引数:
6.4W
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