Open Problems on Benders Decomposition Algorithm

The Benders decomposition method is based on the idea of exploiting the structure of an optimization problem so that its solution can be obtained as the solution of several smaller subproblems. We review here the fundamental method proposed by Jacobus F. Benders and present several open problems related to its application.

[1]  Georgios K. D. Saharidis,et al.  Initialization of the Benders master problem using valid inequalities applied to fixed-charge network problems , 2011, Expert Syst. Appl..

[2]  Marianthi G. Ierapetritou,et al.  Speed-up Benders decomposition using maximum density cut (MDC) generation , 2013, Ann. Oper. Res..

[3]  István Maros.  Jacques F. Benders is 80 , 2005, Comput. Manag. Sci..

[4]  Leon S. Lasdon,et al.  A scenario-based stochastic programming model for water supplies from the highland lakes , 2000 .

[5]  Georgios K. D. Saharidis,et al.  Latest Advances on Benders Decomposition , 2019, Advanced Methodologies and Technologies in Business Operations and Management.

[6]  Michel Gendreau,et al.  The Benders decomposition algorithm: A literature review , 2017, Eur. J. Oper. Res..

[7]  Z.A. Vale,et al.  Notice of Violation of IEEE Publication PrinciplesA Benders Decomposition and Fuzzy Multicriteria Approach for Distribution Networks Remuneration Considering DG , 2009, IEEE Transactions on Power Systems.

[8]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[9]  N. Kagan,et al.  A Benders' decomposition approach to the multi-objective distribution planning problem , 1993 .

[10]  Jean-Baptiste Hiriart-Urruty,et al.  Potpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization , 2007, SIAM Rev..

[11]  Georgios K. D. Saharidis,et al.  Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach , 2013, Ann. Oper. Res..

[12]  Steven A. Gabriel,et al.  A Benders Decomposition Method for Solving Stochastic Complementarity Problems with an Application in Energy , 2010 .

[13]  Thomas M. Liebling,et al.  Analysis of Backtrack Algorithms for Listing All Vertices and All Faces of a Convex Polyhedron , 1997, Comput. Geom..

[14]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[15]  Marianthi G. Ierapetritou,et al.  Improving benders decomposition using maximum feasible subsystem (MFS) cut generation strategy , 2010, Comput. Chem. Eng..

[16]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[17]  Marianthi G. Ierapetritou,et al.  Accelerating Benders method using covering cut bundle generation , 2010, Int. Trans. Oper. Res..

[18]  Matteo Fischetti,et al.  A note on the selection of Benders’ cuts , 2010, Math. Program..