Branching rules revisited

Achterberg, Tobias; Koch, Thorsten; Martín, Alexander

doi:10.1016/j.orl.2004.04.002

Cited by 373 publications

(294 citation statements)

References 6 publications

(8 reference statements)

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“…Interesting branching strategies suitable for MIQCQP include simple heuristic strategies for determining the variable with the greatest associated error [6,7,18], strong branching [2], violation transfer [133,134], and reliability branching [2,27]. GloMIQO uses reliability branching, a technique that integrates strong branching with a pseudocost heuristic to predict the best branching variable [2,27].…”

Section: Literature Reviewmentioning

confidence: 99%

GloMIQO: Global mixed-integer quadratic optimizer

2012

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This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2,

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Section: Literature Reviewmentioning

confidence: 99%

GloMIQO: Global mixed-integer quadratic optimizer

2012

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“…As previously mentioned, experiments by Linderoth and Savelsbergh [1999] and Achterberg et al [2005] provided empirical evidence that selecting variable disjunctions on the basis of estimated increase in the lower bound after such a branching could result in a reduction in the number of subproblems solved. Therefore, we base our first criteria for choosing branching disjunctions on the same principle.…”

Section: Branching To Maximize Lower Boundmentioning

confidence: 87%

“…Pseudo-cost branching consists of estimating the change on the basis of the actual change that occurred when the candidate disjunction was previously imposed (in some other subproblem). Recently, Achterberg et al [2005] showed empirically that using a hybrid approach, called reliability branching, yields better results in practice than either of above two approaches used alone.…”

Section: Previous Workmentioning

confidence: 99%

Experiments with Branching using General Disjunctions

Mahajan

Ralphs

2009

Operations Research and Cyber-Infrastructure

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Branching is an important component of the branch-and-cut algorithm for solving mixed integer linear programs. Most solvers branch by imposing a disjunction of the form"x i ≤ k ∨ x i ≥ k + 1" for some integer k and some integer-constrained variable x i . A generalization of this branching scheme is to branch by imposing a more general disjunction of the form "πx ≤ π 0 ∨ πx ≥ π 0 + 1." In this paper, we discuss the formulation of two optimization models for selecting such a branching disjunction and then describe methods of solution using a standard MILP solver. We report on computational experiments carried out to study the effects of branching on such disjunctions.

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“…As we have just described, an important advantage of our algorithm over its predecessor from Moore and , is the fact that we are not forced to branch after producing an infeasible integer solution and are therefore free to employ the well-developed branching strategies used in algorithms for traditional ILP, such as strong branching, pseudocost branching, or the recently introduced reliability branching [Achterberg et al, 2005].…”

Section: Branchingmentioning

confidence: 99%

A Branch-and-cut Algorithm for Integer Bilevel Linear Programs

DeNegre

Ralphs

2009

Operations Research and Cyber-Infrastructure

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We describe a rudimentary branch-and-cut algorithm for solving integer bilevel linear programs that extends existing techniques for standard integer linear programs to this very challenging computational setting. The algorithm improves on the branch-and-bound algorithm of Moore and Bard in that it uses cutting plane techniques to produce improved bounds, does not require specialized branching strategies, and can be implemented in a straightforward way using only linear solvers. An implementation built using software components available in the COIN-OR software repository is described and preliminary computational results presented.

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Branching rules revisited

Cited by 373 publications

References 6 publications

GloMIQO: Global mixed-integer quadratic optimizer

GloMIQO: Global mixed-integer quadratic optimizer

Experiments with Branching using General Disjunctions

A Branch-and-cut Algorithm for Integer Bilevel Linear Programs

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