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APPROXIMATION GUARANTEES FOR MIN-MAX-MIN ROBUST OPTIMIZATION AND k -ADAPTABILITY UNDER OBJECTIVE UNCERTAINTY.
- Source :
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SIAM Journal on Optimization . 2024, Vol. 34 Issue 2, p2121-2149. 29p. - Publication Year :
- 2024
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Abstract
- In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It is known that the min-max-min robust problem can be solved efficiently if k is at least the dimension of the problem, while it is theoretically and computationally hard if k is small. However, nothing is known about the intermediate case, i.e., k lies between one and the dimension of the problem. We approach this open question and present an approximation algorithm which achieves good problem-specific approximation guarantees for the cases where k is close to or a fraction of the dimension. The derived bounds can be used to show that the min-max-min robust problem is solvable in oracle-polynomial time under certain conditions even if k is smaller than the dimension. We extend the previous results to the robust k-adaptability problem. As a consequence we can provide bounds on the number of necessary second-stage policies to approximate the exact two-stage robust problem. We derive an approximation algorithm for the k-adaptability problem which has similar guarantees as for the min-max-min problem. Finally, we test both algorithms on knapsack and shortest path problems. The experiments show that both algorithms calculate solutions with relatively small optimality gap in seconds. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ROBUST optimization
*APPROXIMATION algorithms
*OPEN-ended questions
*BACKPACKS
Subjects
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 34
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 178370499
- Full Text :
- https://doi.org/10.1137/23M1595084