Linear Bi-level Programming Problems—A Review

Wen, Ue‐Pyng; Hsu, Shuh-Tzy

doi:10.1038/sj/jors/0420204

Cited by 31 publications

(26 citation statements)

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“…Even if the bilevel linear programming problem is generally difficult to solve and has been proved to be NP-hard [3]. The recent monographs and surveys can refer to [2,7,8,10,11,14,[17][18][19][20][21]. Many of them deal with the bilevel programming problem where the lower level is a single objective optimization problem.…”

Section: Introductionmentioning

confidence: 99%

A solution method for semivectorial bilevel programming problem via penalty method

Zheng

Wan

2010

J. Appl. Math. Comput.

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In this paper, we address a class of semivectorial bilevel programming problem in which the upper level is a scalar optimization problem and the lower level is a linear multi-objective optimization problem. Then, we present a new penalty function method, which includes two different penalty parameters, for solving such a problem. Furthermore, we give a simple algorithm. Numerical examples show that the proposed algorithm is feasible.

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Section: Introductionmentioning

confidence: 99%

A solution method for semivectorial bilevel programming problem via penalty method

Zheng

Wan

2010

J. Appl. Math. Comput.

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“…the review [16) and references therein). The mathematical formulation of a BLP problem is as follows: (10.4) (10.5) This formulation models the situation of a hierarchical system in which two levels with divergent objectives intervene in the decision making process.…”

Section: Introductionmentioning

confidence: 97%

A New Branch and Bound Method for Bilevel Linear Programs

Tụy

Ghannadan

1998

Multilevel Optimization: Algorithms and Applications

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A new branch and bound method is proposed for the Bilevel Linear Programming based on a transformation of the problem into a linear program with an additional reverse convex constraint. The method exploits the separated nonconvexity and a monotonic property of the reverse convex constraint. Computational experiments are reported which show the efficiency of the approach for problems in which the matrix A2 is substantially smaller than the total number of variables.

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“…So, many researchers have made deep contributions to this field, including the monographs, [2][3][4][5] and bibliographies about the theory, algorithm and application of bilevel programming. [6][7][8][9] The optimistic version of bilevel programming in finite dimensional space has been studied by Dempe et al [10]. Some other approaches suggested to solve BLPs in recent years include.…”

Section: Introductionmentioning

confidence: 99%

A class of integer linear fractional bilevel programming problems

2014

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The bilevel programming (BLP) problem is a leader-follower game in which two players try to maximize their own objective functions over a common feasible region. This paper discusses an integer BLP with bounded variables in which the objective function of the first level is linear fractional, the objective function of the second level is linear and the common constraint region is a polyhedron. Various cuts have been discussed, which successively rank and scan the set of feasible solutions in decreasing order of leader's objective function. By making use of these ranked solutions, we are able to solve the given BLP. An extension of BLP is also discussed in the form of constrained BLP, where in addition to the existing primary constraints, a set of secondary constraints is also introduced.

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Linear Bi-level Programming Problems—A Review

Cited by 31 publications

References 0 publications

A solution method for semivectorial bilevel programming problem via penalty method

A solution method for semivectorial bilevel programming problem via penalty method

A New Branch and Bound Method for Bilevel Linear Programs

A class of integer linear fractional bilevel programming problems

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