Partitioning procedures for solving mixed-variables programming problems

By J. F. Benders. 2005

2,491 citations recorded by the source corpus.

Subfields: Industrial and Manufacturing Engineering

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Citations in the corpus

Learning Optimal Classification Trees: Strong Max-Flow Formulations (2020, methodology): “Due to these characteristics, formulation (1) can be naturally tackled using Benders’ decomposition, see Benders (1962).”
Economic-environmental energy and reserve scheduling of smart distribution systems: A multiobjective mathematical programming approach (2014, methodology): “In order to make the proposed model applicable for real size distribution networks with large number of consumers and overcome the difficulties related to the solution of nonlinear optimization problems with binary variables, a fast and robust optimization technique, known as Benders decomposition, ”
Ship Scheduling and Network Design for Cargo Routing in Liner Shipping (2008, methodology): “Benders decomposition (Benders (1962)) is a popular technique to solve mixed integer linear programming problems with linking constraints.”
Logic-based Benders decomposition (2003, positive): “Benders decomposition, introduced in 1962 by Jacques Benders [2], is a popular and highly successful optimization tool.”
Risk-averse two-stage stochastic programming with an application to disaster management (2012, methodology): “The L-shaped method proposed by Van Slyke and Wets [10] is a widely applied Benders-decomposition approach [11] to solve the two-stage stochastic programming problems with the expected recourse functions for the case of a finite probability space.”
Measuring and maximizing resilience of freight transportation networks (2012, methodology): “W w K k k a q q q Q w ar ap pr ar p p ar ar w k ar              , , , 0 ) ( ) ( ) ( ) (        (11)   R r A a r ar      , , 1   (12)     R r A a ar     , 1 , 0   (13)     W w K k f y w w k w k     , integer, , 1 , 0 ) (   (14) The objective function (”
Market-clearing with stochastic security-part II: case studies (2005, methodology): “In addition, as mentioned in the companion paper, the use of scenario reduction techniques [15]–[17] is promising, as are decomposition techniques based on Benders’ decomposition [18]–[21] and “branch-and-price” decomposition [22]–[24].”
The Benders decomposition algorithm: A literature review (2017, methodology): “Partial funding for this project has been provided by the Natural Sciences and Engineering Council of Canada (NSERC), through its Discovery Grant program and by the Fonds de recherche du Québec – Nature et technologie (FRQNT) through their infrastructure grants.”
Robust Linear Optimization With Recourse (2009, background): “Bender’s decomposition is typically presented for the stochastic programming problem (4) [6].”
Combinatorial Benders' Cuts for Mixed-Integer Linear Programming (2006, methodology): “Of course, we can get rid of the y variables by using Benders’ decomposition [5], but the resulting cuts are weak and still depend on the big-M values.”
Multidisciplinary design optimization: A survey of architectures (2013, methodology): “Examples of these methods include Dantzig–Wolfe decomposition [112] and Benders decomposition [113] for Problems (5) and (6), respectively.”
Monte Carlo sampling-based methods for stochastic optimization (2014, methodology): “L-shaped method in stochastic programming is commonly known as Benders’ decomposition (Benders [22]) in mixed-integer programming and Kelley’s cutting plane algorithm in convex programming (Kelley [127], HiriartUrruty and Lemaréchal [106]).”
Stochastic Multiobjective Market Clearing of Joint Energy and Reserves Auctions Ensuring Power System Security (2009, methodology): “It is noted that, in the case of bundle constraints between scenarios, decomposition techniques based on Benders’ decomposition [43], [44] can be used.”
Selected Topics in Column Generation (2002, background): “We are concerned with linking constraints, or price directive decomposition only; see, for example, Benders (1962), Lasdon (1970), and Van Roy (1983) for different points of view.”
State-of-the-art review of optimization methods for short-term scheduling of batch processes (2006, methodology): “Finally, Benders decomposition (Benders, 1962) is another technique for solving MILPs in which the problem is successively decomposed into LP subproblems for fixed 0–1 and a master problem for updating the binary variables. The major software packages for MILP are CPLEX (ILOG, 1999) and XPRESS (Dash”
Robust intermodal hub location under polyhedral demand uncertainty (2016, positive): “Next we apply the dual transformation used to linearize minmax type robust optimization problems (see, e.g., Altın et al., 2011b; Bertsimas and Sim, 2003 ).”
Stochastic dual dynamic integer programming (2018, methodology): “A well-known family of cuts used in stochastic programming is the Benders’ cut [11], where the relaxation ( R i n ) solved in the backward step is the LP relaxation of problem Therefore, the cost coefﬁcients (v in , π in ) are computed based on the optimal value of the LP relaxation and a basic…”
An interior-point Benders based branch-and-cut algorithm for mixed integer programs (2010, methodology): “Benders (1962) and McDaniel and Devine (1977) discussed the fact that every extreme point and extreme ray of the subproblem generates a valid global cut.”