A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems

We propose a new two-level vertex-searching algorithm framework that finds a global optimal solution to the continuous bilevel linear fractional programming problem over a compact polyhedron, in which both the upper and the lower objectives are linear fractional. Our solution method adopts the verte...

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Vydáno v:Systems science & control engineering Ročník 8; číslo 1; s. 488 - 499
Hlavní autor: Chen, Hui-Ju
Médium: Journal Article
Jazyk:angličtina
Vydáno: Macclesfield Taylor & Francis 01.01.2020
Taylor & Francis Ltd
Taylor & Francis Group
Témata:
Algorithms
Bilevel programming
extreme point approach
global optimization
linear fractional programming
Mathematical programming
nonconvex programming
Optimization
Polyhedra
quasiconvexity
Search algorithms
Upper bounds
ISSN:2164-2583, 2164-2583
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Shrnutí:We propose a new two-level vertex-searching algorithm framework that finds a global optimal solution to the continuous bilevel linear fractional programming problem over a compact polyhedron, in which both the upper and the lower objectives are linear fractional. Our solution method adopts the vertex-searching approach on the polyhedron, and the search space is determined by the set of candidates of optimal base to the lower level problem. In order to search base, a modified enumerative scheme, that is a new upper bound filter scheme inserted into the classical enumerative scheme, is proposed. The main solution procedure is designed on solving a sequence of upper and lower level mathematical programs; instead of a single-level problem reformulation approach, which is popularly and widely used in literature. An extension on general upper level objective functions such as quasiconvex/quasiconcave for the proposed vertex-searching approach is discussed. Numerical experiments show that our algorithm leads us to a global optimum. We conclude that our proposed algorithm framework has the simplest solution procedure and has potential efficiency advantages, which may reduce the complexity of enumerative schemes for medium or large-scale problems, while comparing with existing global algorithms such as the Kth-best algorithm (a two-level vertex-searching algorithm) and the single-level duality-based reformulation algorithm (a single-level vertex-searching algorithm).
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ISSN:2164-2583
2164-2583
DOI:10.1080/21642583.2020.1805815