Branch-and-cut for linear programs with overlapping SOS1 constraints
@article{Fischer2018BranchandcutFL, title={Branch-and-cut for linear programs with overlapping SOS1 constraints}, author={Tobias Fischer and Marc E. Pfetsch}, journal={Mathematical Programming Computation}, year={2018}, volume={10}, pages={33-68} }
SOS1 constraints require that at most one of a given set of variables is nonzero. In this article, we investigate a branch-and-cut algorithm to solve linear programs with SOS1 constraints. We focus on the case in which the SOS1 constraints overlap. The corresponding conflict graph can algorithmically be exploited, for instance, for improved branching rules, preprocessing, primal heuristics, and cutting planes. In an extensive computational study, we evaluate the components of our implementation…
10 Citations
Relaxations and Cutting Planes for Linear Programs with Complementarity Constraints
- Mathematics
- 2022
We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying…
On the structure of linear programs with overlapping cardinality constraints
- Computer ScienceDiscret. Appl. Math.
- 2020
New Classes of Facets for Complementarity Knapsack Problems
- MathematicsISCO
- 2022
. The complementarity knapsack problem (CKP) is a knapsack problem with real-valued variables and complementarity conditions between pairs of its variables. We extend the polyhedral studies of De…
Monoidal Cut Strengthening and Generalized Mixed-Integer Rounding for Disjunctive Programs
- Mathematics
- 2016
This article investigates cutting planes for mixed-integer disjunctive programs. In the early 1980s, Balas and Jeroslow presented monoidal disjunctive cuts exploiting the integrality of variables.…
Monoidal cut strengthening and generalized mixed-integer rounding for disjunctions and complementarity constraints
- MathematicsOper. Res. Lett.
- 2017
An enhanced logical benders approach for linear programs with complementarity constraints
- Computer ScienceJ. Glob. Optim.
- 2020
This work develops a novel interpretation of the logical Benders method as a reversed branch-and-bound search, where the whole exploration procedure starts from the leaf nodes in an enumeration tree, and presents an optimization-based sparsification process which makes the cut generation more efficient.
The SCIP Optimization Suite 3.2
- Computer Science
- 2016
This paper highlights the new features of version 3.2 of the SCIP Optimization Suite and presents new and improved extensions of SCIP, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs.
Cardinality Minimization, Constraints, and Regularization: A Survey
- Computer ScienceArXiv
- 2021
It is highlighted that modern mixed-integer programming can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings.
Solving linear programs with complementarity constraints using branch-and-cut
- Computer ScienceMathematical Programming Computation
- 2018
A branch-and-cut algorithm to find a global optimum for this class of optimization problems, where the branches branch directly on complementarities, and the computational results show that the approach is a strong alternative to constructing an integer programming formulation using big-M terms to represent bounds for variables.
References
SHOWING 1-10 OF 53 REFERENCES
Branch-and-cut for complementarity-constrained optimization
- Computer ScienceMath. Program. Comput.
- 2014
The results on the use of complementarity cuts within a major commercial optimization solver show that they are of critical importance to tackling difficult CCOP instances, typically reducing the computational time required to solve them tremendously.
On the structure of linear programs with overlapping cardinality constraints
- Computer ScienceDiscret. Appl. Math.
- 2020
New Branch-and-Cut Algorithm for Bilevel Linear Programming
- Computer Science
- 2004
The proposed algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems and also proposes also a set of algorithmic tests and procedures to improve the method.
Branch-and-cut for combinatorial optimization problems without auxiliary binary variables
- MathematicsThe Knowledge Engineering Review
- 2001
This work presents a branch-and-cut approach that considers the combinatorial constraints without the introduction of binary variables and shows how strong constraints can be derived using ideas from polyhedral combinatorics.
A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints
- Computer ScienceJ. Glob. Optim.
- 2006
In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates…
On linear programs with linear complementarity constraints
- Computer ScienceJ. Glob. Optim.
- 2012
Several approaches for the global resolution of the LPCC are described, including a logical Benders approach that can be applied to problems that may be infeasible or unbounded.
On the Global Solution of Linear Programs with Linear Complementarity Constraints
- Computer ScienceSIAM J. Optim.
- 2008
A parameter-free integer-programming-based algorithm for the global resolution of a linear program with linear complementarity constraints (LPCCs), which establishes that the algorithm can handle infeasible, unbounded, and solvable LPCCs effectively.
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph
- MathematicsDiscret. Optim.
- 2016
Heuristics for convex mixed integer nonlinear programs
- BusinessComput. Optim. Appl.
- 2012
Diving heuristics, the Feasibility Pump, and Relaxation Induced Neighborhood Search can be adapted in the context of mixed integer nonlinear programming to help find feasible solutions faster and reduce the total solution time of the branch-and-bound algorithm.
A polyhedral study of the cardinality constrained knapsack problem
- MathematicsMath. Program.
- 2003
Computational results are reported that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0-1 variables over the traditional MIP approach for this class of problems.