Information-based branching schemes for binary linear mixed integer problems

Karzan, Fatma Kılınç; Nemhauser, George L.; Savelsbergh, Martin W. P.

doi:10.1007/s12532-009-0009-1

Cited by 46 publications

(17 citation statements)

References 28 publications

(27 reference statements)

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“…Further strategies based on the same criteria can be found in [9,4,7,10,11,12]. Recent research efforts on different criteria for variable-based branching rules include, e.g., [13,14,15,16,17,18].…”

Section: Related Workmentioning

confidence: 99%

Branching on Multi-aggregated Variables

Gamrath

Melchiori

Berthold

et al. 2015

Integration of AI and OR Techniques in Constraint Programming

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Abstract. In mixed-integer programming, the branching rule is a key component to a fast convergence of the branch-and-bound algorithm. The most common strategy is to branch on simple disjunctions that split the domain of a single integer variable into two disjoint intervals. Multi-aggregation is a presolving step that replaces variables by an affine linear sum of other variables, thereby reducing the problem size. While this simplification typically improves the performance of MIP solvers, it also restricts the degree of freedom in variable-based branching rules. We present a novel branching scheme that tries to overcome the above drawback by considering general disjunctions defined by multi-aggregated variables in addition to the standard disjunctions based on single variables. This natural idea results in a hybrid between variable-and constraint-based branching rules. Our implementation within the constraint integer programming framework SCIP incorporates this into a full strong branching rule and reduces the number of branch-and-bound nodes on a general test set of publicly available benchmark instances. For a specific class of problems, we show that the solving time decreases significantly.

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Section: Related Workmentioning

confidence: 99%

Branching on Multi-aggregated Variables

Gamrath

Melchiori

Berthold

et al. 2015

Integration of AI and OR Techniques in Constraint Programming

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“…No-good cuts were originally introduced in [1], and have been used by the Constraint Programming community and in several other contexts (see e.g. [9,10,18]). In general, a no-good cut forx takes the form NG(x) = x −x ≥ , where the norm is typically the 1-norm, but is not restricted to be so.…”

Section: Main Algorithmic Ideasmentioning

confidence: 99%

Rounding-based heuristics for nonconvex MINLPs

Nannicini

Belotti

2011

Math. Prog. Comp.

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We propose two primal heuristics for nonconvex mixed-integer nonlinear programs. Both are based on the idea of rounding the solution of a continuous nonlinear program subject to linear constraints. Each rounding step is accomplished through the solution of a mixed-integer linear program. Our heuristics use the same algorithmic scheme, but they differ in the choice of the point to be rounded (which is feasible for nonlinear constraints but possibly fractional) and in the linear constraints. We propose a feasibility heuristic, that aims at finding an initial feasible solution, and an improvement heuristic, whose purpose is to search for an improved solution within the neighborhood of a given point. The neighborhood is defined through local branching cuts or box constraints. Computational results show the effectiveness in practice of these simple ideas, implemented within an open-source solver for nonconvex mixedinteger nonlinear programs. Mathematics Subject Classification (2000)

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“…Much of the success of modern SAT solvers stems from their ability to quickly learn new constraints from infeasible search states via conflict-directed clause learning (CDCL). Conflict analysis has also been applied in the context of mixed-integer programming (MIP) [1,17] and constraint programming (CP) [15,21,24] as "nogood" learning. In the context of constraint programming, nogood learning techniques have been proposed for specific combinatorial structures that arise from global constraints.…”

Section: Introductionmentioning

confidence: 99%

BDD-Guided Clause Generation

Kell

Sabharwal

Hoeve

2015

Integration of AI and OR Techniques in Constraint Programming

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Abstract. Nogood learning is a critical component of Boolean satisfiability (SAT) solvers, and increasingly popular in the context of integer programming and constraint programming. We present a generic method to learn valid clauses from exact or approximate binary decision diagrams (BDDs) and resolution in the context of SAT solving. We show that any clause learned from SAT conflict analysis can also be generated using our method, while, in addition, we can generate stronger clauses that cannot be derived from one application of conflict analysis. Importantly, since SAT instances are often too large for an exact BDD representation, we focus on BDD relaxations of polynomial size and show how they can still be used to generated useful clauses. Our experimental results show that when this method is used as a preprocessing step and the generated clauses are appended to the original instance, the size of the search tree for a SAT solver can be significantly reduced.

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Information-based branching schemes for binary linear mixed integer problems

Cited by 46 publications

References 28 publications

Branching on Multi-aggregated Variables

Branching on Multi-aggregated Variables

Rounding-based heuristics for nonconvex MINLPs

BDD-Guided Clause Generation

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