A class of algorithms for mixed-integer bilevel min–max optimization

Tang, Yen Zhi; Richard, Jean‐Philippe P.; Smith, J. Cole

doi:10.1007/s10898-015-0274-7

Cited by 54 publications

(54 citation statements)

References 32 publications

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“…• A very extensive computational study is reported-different classes of test problems from the literature are considered, including those proposed by DeNegre and Ralphs (2009), Xu and Wang (2014), Tang et al (2015) and Fischetti et al (2016b). Our analysis shows that the new approach outperforms by a large margin alternative state-of-the-art methods from the literature-including the most recent ones, namely those proposed in (Xu andWang 2014, Tang et al 2015) and Fischetti et al (2016b).…”

Section: Introductionmentioning

confidence: 82%

“…For the special family of zero-sum bilevel problems, i.e., when the leader and the follower share the same objective but with the opposite signs, three generic solution algorithms have recently been proposed by Tang et al (2015). Their algorithms require leader variables to be binary, whereas the follower can be a general MILP.…”

Section: Literature Overview On Miblpmentioning

confidence: 99%

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A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs

Fischetti

Ljubić

Monaci

et al. 2017

Operations Research

138

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Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, optimal expansion of gas networks, critical infrastructure defense, and machine learning. In this paper, we present a new general purpose branch-and-cut framework for the exact solution of mixed-integer bilevel linear programs (MIBLP), which constitute a very significant subfamily of bilevel optimization problems. Our framework introduces several new classes of valid inequalities to speed-up the solver, along with a very effective bilevel-specific preprocessing procedure. A very extensive computational study is presented, where we evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature-this is by far the most extensive computational analysis ever performed for exact MIBLP solvers. Our new algorithm consistently outperforms (often by a large margin) all alternative state-of-the-art methods from the literature, including methods which exploit problem specific information for special instance classes. In particular, it allows to solve to optimality more than 300 instances previously unsolved instances from literature.

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Section: Introductionmentioning

confidence: 82%

Section: Literature Overview On Miblpmentioning

confidence: 99%

A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs

Fischetti

Ljubić

Monaci

et al. 2017

Operations Research

138

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“…Algorithms have also been proposed for solving other types of relevant programs, including min-max programs [33,34,9], semi-infinite programs [35][36][37], and generalized semi-infinite programs [38][39][40]. However, there is no direct relationship between the proposed algorithm and these algorithms.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The unit production cost (w(i)) equals the summation of p(i) and a random parameter uniformly generated on 0.1 [ 2,2] U × − . The upper bound for capacity (cu(i)) is uniformly distributed on 50 [2,9]…”

Section: Examplementioning

confidence: 99%

“…Bilevel programs [4], including MIBLPs, are frequently utilized to model Stackelberg games in game theory [5,6]. MIBLPs are intrinsically challenging to solve, and the use of mixed-integer linear programming (MILP) algorithms for solving MIBLPs is not straightforward [7][8][9]. Although MIBLPs can be solved using some general-purpose mixed-integer bilevel nonlinear program (MIBNLP) algorithms, most of them only have small-scale applications reported in the literature [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs

et al. 2018

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We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper-and lower-level problems. In particular, we consider MIBLPs with upper-level constraints that involve lower-level variables. We assume that the inducible region is nonempty and all variables are bounded. By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm. The solution procedure is enhanced by a projection strategy that does not require the relatively complete response property. To ensure its performance, we prove that our new method converges to the global optimal solution in a finite number of iterations. A large-scale computational study on random instances and instances of hierarchical supply chain planning are presented to demonstrate the effectiveness of the algorithm.

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Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Dempe

2020

Springer Optimization and Its Applications

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A class of algorithms for mixed-integer bilevel min–max optimization

Cited by 54 publications

References 32 publications

A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs

A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs

A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs

Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

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