Generalized Benders Decomposition

By Christodoulos A. Floudas. Encyclopedia of Optimization, 2009

908 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/cf9e0386c3fd2c8bb6d8f23225bd391708e979b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

In Management Science and Operations Research

Citations in the corpus

An interior-point Benders based branch-and-cut algorithm for mixed integer programs (2010, background): “…integer bi-level problems where Karush-Kuhn-Tucker optimality conditions cannot be used to transform the bi-level problem into a single level problem (Saharidis and Ierapetritou 2009) and to the generalized Benders decomposition where the subproblem is a non-linear convex program (Geoffrion 1972).”
Mixed-integer nonlinear optimization*† (2013, background): “2 Generalized Benders decomposition Generalized Benders decomposition was developed before outer approximation; see (Geoffrion, 1972).”
Models for nuclear smuggling interdiction (2007, methodology): “…nested min-max structure is not a difficulty if one can employ an outer-approximation cutting-plane algorithm such as Kelley’s cutting-plane method (Kelley, 1960), Benders’ decomposition (Benders, 1962; Geoffrion, 1972), or the L-shaped method (Van Slyke and Wets, 1969; Wollmer, 1980).”
Joint Service Caching and Task Offloading for Mobile Edge Computing in Dense Networks (2018, methodology): “While there exist various centralized techniques (such as Generalized Benders Decomposition [28]) to solve it, these methods are usually computationally prohibitive and distributed solutions are much desired.”
Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning (2016, neutral): “Another method of generating valid inequalities is through decomposition methods such as Benders’ decomposition [110,111].”
Some Efficient Optimization Methods for Solving the Security-Constrained Optimal Power Flow Problem (2014, methodology): “Additionally, a method using the generalized Benders decomposition [8] is developed in [9].”
Economic-environmental energy and reserve scheduling of smart distribution systems: A multiobjective mathematical programming approach (2014, background): “The second part, called sub-problem (or auxiliary problem), receives the values for the remaining variables, while keeping the first ones fixed, and uses these to generate cuts for the master problem [44].”
User Association in 5G Networks: A Survey and an Outlook (2015, background): “We also observe that increasing the number of transmit antennas at the macro BS improves the probability that a user is associated with the macro BS, which indicates that macro BSs having large antenna arrays are capable of carrying higher traffic loads, hence reducingthe number of small cells…”
Solving two-stage robust optimization problems using a column-and-constraint generation method (2013, methodology): “Because they are designed in the line of Benders' decomposition [6] [13] and make use of the dual information of the second-stage decision problem, we call them Benders-dual cutting plane methods or Benders-dual methods for short.”
Distribution Systems Reconfiguration Based on OPF Using Benders Decomposition (2009, methodology): “rithm [26], [27], which has already been applied to solve different problems in electric power systems [28]–[31].”
Non-convex mixed-integer nonlinear programming: A survey (2012, methodology): “Examples include generalized Benders’ decomposition [1], branch-and-bound [2], outer approximation [3], LP/NLP-based branch-and-bound [4], the extended cutting-plane method [5], branch-and-cut [6], and the hybrid methods described in [7,8].”
Robust Defense Strategy for Gas–Electric Systems Against Malicious Attacks (2016, methodology): “In general, several decomposition methods are available to solve a linear min-max-min model such as Benders decomposition [25], [27] and C&CG [18].”
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers (2011, neutral): “The general idea of dual decomposition appears to be originally due to Everett [69], and is explored in many early references [107, 84, 117, 14].”
Algorithms and Software for Convex Mixed Integer Nonlinear Programs (2012, methodology): “[91] K. G. Murty and S. N. Kabadi, Some NP-complete problems in quadratic and nonlinear programming, Mathematical Programming, 39 (1987), pp. 117– 129.”
Logic-based Benders decomposition (2003, neutral): “Benders decomposition, introduced in 1962 by Jacques Benders [2], is a popular and highly successful optimization tool.”
50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art (2010, methodology): “Geoffrion [43] produced the first important surveys on different ways to create decomposition algorithms, as well as an extension to nonlinear programs [44].”
Linear Current Flow Equations With Application to Distribution Systems Reconfiguration (2015, methodology): “The application of Benders decomposition to non-convex MINLP problems is just a heuristic since the original method, known as generalized Benders decomposition, assumes convex nonlinear functions [7] when fixing the binary variables, while the power flow equations are not convex.”
The Benders decomposition algorithm: A literature review (2017, methodology): “Many extensions have since been developed to apply the algorithm to a broader range of problems (e.g., Geoffrion, 1972; Hooker and Ottosson, 2003).”