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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Online Access: | http://dx.doi.org/10.1080/21642583.2020.1805815 |
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doaj-a3b262fc1da4466e993144f04c870bff2020-12-17T14:55:58ZengTaylor & Francis GroupSystems Science & Control Engineering2164-25832020-01-018148849910.1080/21642583.2020.18058151805815A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problemsHui-Ju Chen0Department of Mathematics, National Cheng Kung UniversityWe 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).http://dx.doi.org/10.1080/21642583.2020.1805815bilevel programmingextreme point approachlinear fractional programmingquasiconvexitynonconvex programmingglobal optimization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hui-Ju Chen |
spellingShingle |
Hui-Ju Chen A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems Systems Science & Control Engineering bilevel programming extreme point approach linear fractional programming quasiconvexity nonconvex programming global optimization |
author_facet |
Hui-Ju Chen |
author_sort |
Hui-Ju Chen |
title |
A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
title_short |
A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
title_full |
A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
title_fullStr |
A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
title_full_unstemmed |
A two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
title_sort |
two-level vertex-searching global algorithm framework for bilevel linear fractional programming problems |
publisher |
Taylor & Francis Group |
series |
Systems Science & Control Engineering |
issn |
2164-2583 |
publishDate |
2020-01-01 |
description |
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). |
topic |
bilevel programming extreme point approach linear fractional programming quasiconvexity nonconvex programming global optimization |
url |
http://dx.doi.org/10.1080/21642583.2020.1805815 |
work_keys_str_mv |
AT huijuchen atwolevelvertexsearchingglobalalgorithmframeworkforbilevellinearfractionalprogrammingproblems AT huijuchen twolevelvertexsearchingglobalalgorithmframeworkforbilevellinearfractionalprogrammingproblems |
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1724379253532786688 |