منابع مشابه
Branching on general disjunctions
This paper considers a modification of the branch-and-cut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploits the relation between branching disjunctions and intersection cuts. In this work, we focus on di...
متن کاملImproved Strategies for Branching on General Disjunctions
where c ∈ R, b ∈ R, A ∈ R and NI ⊂ N = {1, . . . , n}. The LP relaxation of (1) is the linear program obtained by dropping the integrality constraints, and is denoted by P̄ . The Branch-and-Bound algorithm makes an implicit use of the concept of disjunctions [1]: whenever the solution of the current relaxation is fractional, we divide the current problem P into two subproblems P1 and P2 such tha...
متن کاملExperiments with Branching using General Disjunctions
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“xi ≤ k ∨ xi ≥ k + 1” for some integer k and some integer-constrained variable xi. A generalization of this branching scheme is to branch by imposing a more general disjunction of the form “πx ≤ π0 ∨ πx ≥ π0 + 1.” In this paper, ...
متن کاملBranching on Split Disjunctions
Branch-and-Cut is the most commonly used algorithm for solving Integer and Mixed-Integer Linear Programs. In order to reduce the number of nodes that have to be enumerated before optimality of a solution can be proven, branching on general disjunctions (i.e. split disjunctions involving more than one variable, as opposed to branching on simple disjunctions defined on one variable only) was show...
متن کاملOn the Complexity of Selecting Branching Disjunctions in Integer Programming
Branching is an important component of branch-and-bound algorithms for solving mixed integer linear programs. We consider the problem of selecting, at each iteration of the branchand-bound algorithm, a general branching disjunction of the form “πx ≤ π0∨πx ≥ π0+1”, where π, π0 are integral. We show that the problem of selecting an optimal such disjunction, according to specific criteria describe...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2009
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-009-0332-3