Achieving MILP feasibility quickly using general disjunctions

Achieving MILP feasibility quickly using general disjunctions

Branch and bound algorithms for Mixed-Integer Linear Programming (MILP) almost universally branch on a single variable to create disjunctions. General linear expressions involving multiple variables are another option for branching disjunctions, but are not used for two main reasons: (i) descendent LPs tend to solve more slowly because of the added constraints, so the overall solution time is i...

Experiments 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, ...

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...

Improved 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...

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