Oracle-based algorithms for binary two-stage robust optimization

In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the determ...

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Vydané v:Computational optimization and applications Ročník 77; číslo 2; s. 539 - 569
Hlavní autori: Kämmerling, Nicolas, Kurtz, Jannis
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY Springer US 01.11.2020
Springer Nature B.V
Predmet:
Algorithms
Branch and bound algorithm
Capital budgeting
Convex and Discrete Geometry
Lower bounds
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Non-linear binary optimization
Operations Research
Operations Research/Decision Theory
Optimization
Parameter uncertainty
Robustness
Site selection
Statistics
Two-stage robust optimization
Non-linear binary optimization
Branch and bound algorithm
Two-stage robust optimization
ISSN:1573-2894, 0926-6003, 1573-2894
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Shrnutí:In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-020-00207-w