A penalty function approach for solving bi-level linear programs

White, D. J.; Anandalingam, G.

doi:10.1007/bf01096412

Cited by 267 publications

(89 citation statements)

References 20 publications

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“…Cutting-plane methods found in literature are essentially based on Tuy's concavity cuts (Tuy, 1964). White and Anandalingam (1993) use these cuts in a penalty function approach for solving bilevel linear programs. Marcotte et al (1993) propose a cutting-plane algorithm for solving bilevel linear programs with a guarantee of finite termination.…”

Section: Bilevel Optimization Reviewmentioning

confidence: 99%

A bilevel flow model for hazmat transportation network design

Bianco,

Caramia,

Giordani

2009

Transportation Research Part C: Emerging Technologies

182

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In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of the its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.

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Section: Bilevel Optimization Reviewmentioning

confidence: 99%

A bilevel flow model for hazmat transportation network design

Bianco,

Caramia,

Giordani

2009

Transportation Research Part C: Emerging Technologies

182

View full text Add to dashboard Cite

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“…A second branch-and-bound algorithm, which branches on binding follower constraints, was proposed by Hansen et al (1992). Besides that, also penalty function methods, which add the duality gap to the objective 2.2 Benders decomposition function, were introduced (White and Anandalingam, 1993). Saharidis and Ierapetritou (2009) proposed an algorithm based on BD (see Section 2.2) for the DCLBP.…”

Section: Bilevel Programmingmentioning

confidence: 99%

Methodological Advances and New Formulations for Bilevel Network Design Problems

Fontaine

2018

Operations Research Proceedings

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“…In the last few decades, several algorithms of this sort have been proposed for the MPEC. Among these, branch-and-bound algorithms [2,9], a penalty technique [24] and a sequential complementarity method [12] are considered to be the most efficient procedures to perform this task. A number of local methods [6-8, 10, 14, 16, 22] have also been recently developed to find stationary points for the MPEC.…”

Section: Mpecmentioning

confidence: 99%

A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

et al. 2006

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Abstract. In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

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A penalty function approach for solving bi-level linear programs

Cited by 267 publications

References 20 publications

A bilevel flow model for hazmat transportation network design

A bilevel flow model for hazmat transportation network design

Methodological Advances and New Formulations for Bilevel Network Design Problems

A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

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