The Benders decomposition algorithm: A literature review

Rahmaniani, Ragheb; Crainic, Teodor Gabriel; Gendreau, Michel; Rei, Walter

doi:10.1016/j.ejor.2016.12.005

Cited by 575 publications

(239 citation statements)

References 143 publications

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“…For detailed descriptions and comprehensive surveys on the Benders decomposition and the BBC algorithm, see, for example, Costa (), Rahmaniani et al. (), and Moreno et al. ().…”

Section: A Branch‐and‐benders‐cut Algorithmmentioning

confidence: 99%

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Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

Martin

Birgin

Lobato

et al. 2019

Int Trans Operational Res

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In this paper, we address the constrained two‐dimensional rectangular guillotine single large placement problem (2D_R_CG_SLOPP). This problem involves cutting a rectangular object to produce smaller rectangular items from orthogonal guillotine cuts. In addition, there is an upper limit on the number of copies that can be produced of each item type. To model this problem, we propose a new pseudopolynomial integer nonlinear programming (INLP) formulation and obtain an equivalent integer linear programming (ILP) formulation from it. Additionally, we developed a procedure to reduce the numbers of variables and constraints of the integer linear programming (ILP) formulation, without loss of optimality. From the ILP formulation, we derive two new pseudopolynomial models for particular cases of the 2D_R_CG_SLOPP, which consider only two‐staged or one‐group patterns. Finally, as a specific solution method for the 2D_R_CG_SLOPP, we apply Benders decomposition to the proposed ILP formulation and develop a branch‐and‐Benders‐cut algorithm. All proposed approaches are evaluated through computational experiments using benchmark instances and compared with other formulations available in the literature. The results show that the new formulations are appropriate in scenarios characterized by few item types that are large with respect to the object's dimensions.

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“…For detailed descriptions and comprehensive surveys on the Benders decomposition and the BBC algorithm, see, for example, Costa (), Rahmaniani et al. (), and Moreno et al. ().…”

Section: A Branch‐and‐benders‐cut Algorithmmentioning

confidence: 99%

“…Our solution method is a BBC according to the nomenclature presented in Rahmaniani et al. (); the algorithm can also be seen as a branch‐and‐cut method with no‐good cuts. In our method, we use the Benders decomposition to reformulate Model (9), as follows: …”

Section: A Branch‐and‐benders‐cut Algorithmmentioning

confidence: 99%

Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

Martin

Birgin

Lobato

et al. 2019

Int Trans Operational Res

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“…Benders decomposition algorithm [37][38][39] is adopted to transform model (36) into a two-stage RTEP model. Accordingly, we first rewrite (36) as follows.…”

Section: Two-stage Rtep Methods With Benders Decomposition Algorithmmentioning

confidence: 99%

“…Furthermore, the objective function value of the original problem is equal to that of the dual problem at the optimal point. After solving the dual problem, we introduce an auxiliary variable η to return the valid Benders cut information in (39) to the first-stage master investment problem of (38), as follows:…”

Section: Two-stage Rtep Methods With Benders Decomposition Algorithmmentioning

confidence: 99%

An Extreme Scenario Method for Robust Transmission Expansion Planning with Wind Power Uncertainty

et al. 2018

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Abstract:The rapid incorporation of wind power resources in electrical power networks has significantly increased the volatility of transmission systems due to the inherent uncertainty associated with wind power. This paper addresses this issue by proposing a transmission network expansion planning (TEP) model that integrates wind power resources, and that seeks to minimize the sum of investment costs and operation costs while accounting for the costs associated with the pollution emissions of generator infrastructure. Auxiliary relaxation variables are introduced to transform the established model into a mixed integer linear programming problem. Furthermore, the novel concept of extreme wind power scenarios is defined, theoretically justified, and then employed to establish a two-stage robust TEP method. The decision-making variables of prospective transmission lines are determined in the first stage, so as to ensure that the operating variables in the second stage can adapt to wind power fluctuations. A Benders' decomposition algorithm is developed to solve the proposed two-stage model. Finally, extensive numerical studies are conducted with Garver's 6-bus system, a modified IEEE RTS79 system and IEEE 118-bus system, and the computational results demonstrate the effectiveness and practicability of the proposed method.

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“…The structure of large-scale two-stage optimization problems like the UC formulations in Definitions 1-3 in general lends itself very naturally to solution by decomposition algorithms such as Benders decomposition (see, Rahmaniani et al, 2017), and column-and-constraint generation (see, Zeng and Zhao, 2013). Both approaches seek to derive a solution by considering a smaller optimization problem which is solved repeatedly.…”

Section: Benders Decomposition Algorithmmentioning

confidence: 99%

Hybrid Robust/Stochastic Unit Commitment With Iterative Partitions of the Continuous Uncertainty Set

2018

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The Benders decomposition algorithm: A literature review

Cited by 575 publications

References 143 publications

Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

Models for the two‐dimensional rectangular single large placement problem with guillotine cuts and constrained pattern

An Extreme Scenario Method for Robust Transmission Expansion Planning with Wind Power Uncertainty

Hybrid Robust/Stochastic Unit Commitment With Iterative Partitions of the Continuous Uncertainty Set

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