Journal ArticleDOI
Preprocessing and Probing Techniques for Mixed Integer Programming Problems
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TLDR
This work presents a framework for describing basic techniques to improve the representation of a mixed integer programming problem, and discusses recent extensions to these basic techniques.Abstract:
In the first part of the paper, we present a framework for describing basic techniques to improve the representation of a mixed integer programming problem. We elaborate on identification of infeasibility and redundancy, improvement of bounds and coefficients, and fixing of binary variables. In the second part of the paper, we discuss recent extensions to these basic techniques and elaborate on the investigation and possible uses of logical consequences. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.read more
Citations
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Journal ArticleDOI
SCIP: solving constraint integer programs
TL;DR: An overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs is given and experimental results show that the approach outperforms current state-of-the-art techniques for proving the validity of properties on circuits containing arithmetic.
Integer and Combinatorial Optimization
Karla Hoffman,Ted K. Ralphs +1 more
TL;DR: In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.
Optimization Toolbox User's Guide
TL;DR: The software described in this document is furnished under a license agreement and the rights of the Government regarding its use, reproduction and disclosure are as set forth in Clause 52.227-19(c)(2) of the FAR.
Journal ArticleDOI
Branching and bounds tighteningtechniques for non-convex MINLP
TL;DR: An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver.
Journal ArticleDOI
Mixed-integer nonlinear optimization
TL;DR: An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.
References
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Journal ArticleDOI
Solving Large-Scale Zero-One Linear Programming Problems
TL;DR: The results indicate that cutting-planes related to the facets of the underlying polytope are an indispensable tool for the exact solution of this class of problem.
Journal ArticleDOI
Analysis of mathematical programming problems prior to applying the simplex algorithm
TL;DR: An algorithm to detect structure is described and this algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized.
MINTO, a mixed integer optimizer
TL;DR: MINTO as mentioned in this paper is a software system that solves mixed-integer linear programs by a branch-and-bound algorithm with linear programming relaxations, and provides automatic constraint classification, preprocessing, primal heuristics and constraint generation.
Journal ArticleDOI
Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut
Karla Hoffman,Manfred Padberg +1 more
TL;DR: Various techniques for automatically improving the LP-representation of general zero-one linear programming problems are presented, including detection of redundant rows and blatant infeasibilities, coefficient reduction using the Euclidean algorithm, optimality fixing and variable elimination.
Book ChapterDOI
LP-Based Combinatorial Problem Solving
Karla Hoffman,Manfred Padberg +1 more
TL;DR: A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given in this article, where the design aspects of a combinatory problem solver are discussed in general terms.