An Improved Oracle Adaption for Bilevel Programs

Bilevel programs with nonconvex lower levels occur in many applications in engineering but are notoriously challenging: A global optimization problem must be solved even to check the feasibility of a given candidate solution point. We present an adaption of the approach of Tsoukalas et al. [J. Glob....

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Bibliographic Details
Published inComputer Aided Chemical Engineering Vol. 53; pp. 3301 - 3306
Main Authors Jungen, Daniel, Mitsos, Alexander
Format Book Chapter
LanguageEnglish
Published 2024
Subjects
benchmark
bilevel programming
oracle
bilevel programming
benchmark
oracle
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ISBN9780443288241
0443288240
ISSN1570-7946
DOI10.1016/B978-0-443-28824-1.50551-2

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Summary:Bilevel programs with nonconvex lower levels occur in many applications in engineering but are notoriously challenging: A global optimization problem must be solved even to check the feasibility of a given candidate solution point. We present an adaption of the approach of Tsoukalas et al. [J. Glob. Optim. 44, 235-250 (2009)]. Our algorithm adaption changes the oracle to minimize directly the lower-level objective, with the target objective value inscribed into its constraints. With this formulation, we aim to obtain lower-level-optimal solution points to the oracle, and thus faster generation of good upper bounds. We implement and compare our approach to the original approach and the state-of-the-art solvers of Mitsos et al. [J. Glob. Optim. 42, 475-513 (2008)] and Djelassi et al. [J. Glob. Optim. 75, 341-392 (2019)] using a comprehensive benchmark test set comprising more than 160 problem instances. Our approach outperforms the original oracle algorithm and the solver of Mitsos et al. but not the one of Djelassie et al.
ISBN:9780443288241
0443288240
ISSN:1570-7946
DOI:10.1016/B978-0-443-28824-1.50551-2