Shift-and-Propagate

Berthold, Timo; Hendel, Gregor

doi:10.1007/s10732-014-9271-0

Cited by 10 publications

(13 citation statements)

References 30 publications

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“…Moreover, let z − Mw ≥ 0 be a variable lower bound constraint of z with w ∈ {0, 1}. Applying (9) and (10) leads to…”

Section: Example 3 Letmentioning

confidence: 99%

“…In this paper, we mostly follow the concepts and the notation of [2]. Followup publications suggested methods to use conflict information for variable selection in branching [3,34], to tentatively generate conflicts before branching [6,8,11], and to analyze infeasibility detected in primal heuristics [9,10,51]. Besides, instead of simply analyzing infeasibility that is derived more or less coincidentally, methods were introduced to generate additional conflict information explicitly [21,51].…”

Section: Introductionmentioning

confidence: 99%

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Computational aspects of infeasibility analysis in mixed integer programming

Witzig

Berthold²,

Stefan³

2021

Math. Prog. Comp.

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The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems: conflict graph analysis and dual proof analysis. While conflict graph analysis detects sets of contradicting variable bounds in an implication graph, dual proof analysis derives valid linear constraints from the proof of the dual LP’s unboundedness. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide a comprehensive computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first combined approach that uses both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set Miplib 2017; the presented algorithms have been implemented within the non-commercial MIP solver and the commercial MIP solver .

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“…Moreover, let z − Mw ≥ 0 be a variable lower bound constraint of z with w ∈ {0, 1}. Applying (9) and (10) leads to…”

Section: Example 3 Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational aspects of infeasibility analysis in mixed integer programming

Witzig

Berthold²,

Stefan³

2021

Math. Prog. Comp.

Self Cite

View full text Add to dashboard Cite

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“…Shift-and-propagate [7] is a pre-root heuristic which aims at constructing a feasible solution even before the initial root LP is solved. The heuristic starts with a trivial solution that fulfills variable bounds but potentially violates some constraints.…”

Section: Shift-and-propagatementioning

confidence: 99%

Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming

sci¹

2019

JCM

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The modeling flexibility and the optimality guarantees provided by mixed-integer programming greatly aid the design of robust and future-proof decision support systems. The complexity of industrial-scale supply chain optimization, however, often poses limits to the application of general mixed-integer programming solvers. In this paper we describe algorithmic innovations that help to ensure that MIP solver performance matches the complexity of the large supply chain problems and tight time limits encountered in practice. Our computational evaluation is based on a diverse set, modeling real-world scenarios supplied by our industry partner SAP.

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“…This process is iterated until all discrete variables in the used global structure were fixed. It can be interpreted as a dive in the tree with a domain propagation call after each fixing instead of solving a linear program, which is similar to the shift-and-propagate heuristic [10]. If domain propagation detects an infeasibility for the current assignment of variables, we backtrack one level, i.e., we undo the last fixing as well as the domain reductions deduced from it.…”

Section: Structure-based Primal Heuristicsmentioning

confidence: 99%

“…They repeatedly fix variables and perform domain propagation to consider the direct consequences of these fixings on the domains of other variables. While this is a known approach in MIP heuristics (see, e.g., the shift-and-propagate heuristic [10]), our new heuristics take a step further and make domain propagation their driving force. They use the global structures to predict the effects of domain propagation in the fixing phase and by this determine the fixing order and fixing values for the variables.…”

Section: Introductionmentioning

confidence: 99%

Structure-Based Primal Heuristics for Mixed Integer Programming

Gamrath

Berthold

Stefan

et al. 2015

Optimization in the Real World

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Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.

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Shift-and-Propagate

Cited by 10 publications

References 30 publications

Computational aspects of infeasibility analysis in mixed integer programming

Computational aspects of infeasibility analysis in mixed integer programming

Tackling Industrial-Scale Supply Chain Problems by Mixed-Integer Programming

Structure-Based Primal Heuristics for Mixed Integer Programming

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