Presolving in linear programming

Andersen, Erling D.; Andersen, Knud D.

doi:10.1007/bf01586000

Cited by 158 publications

(114 citation statements)

References 22 publications

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“…We will address all of these implementation topics and provide detailed information of our implementation. As we will compare arc-search method and Mehrotra's method, to make a meaningful and fair comparison, we will implement everything discussed in this section the same way for both methods, so that the only differences of the two algorithms in our implementations are in Steps 4 and 5, where the arc-search method uses formulae (23) and (24) and Mehrotra's method uses (25) and (26). But the difference of the computational cost is very small because these computations are all analytic.…”

Section: Implementation Detailsmentioning

confidence: 99%

“…Many literatures have been focused on this topic, for example, [1,7,25,26,27]. As we will test all linear programming problems in standard form in Netlib, we focus on the strategies only for the standard linear programming problems in the form of (1) and solved in normal equations 2 .…”

Section: Pre-processmentioning

confidence: 99%

“…The first part f obj at the beginning is zero and is updated all the time as we reduce the problem (remove some c k from c); the terms in the summation in the second part are continuously reduced and c k are updated as necessary when we reduce the problem. The first 6 pre-process methods presented below were reported in various literatures, such as [1,17,25,26,27]; the rest of them, to the best of our knowledge, are not reported anywhere. …”

Section: Pre-processmentioning

confidence: 99%

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CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the proposed arc-search infeasible interior-point algorithm is a more efficient algorithm than Mehrotra's algorithm.

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Section: Implementation Detailsmentioning

confidence: 99%

Section: Pre-processmentioning

confidence: 99%

Section: Pre-processmentioning

confidence: 99%

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CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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“…Its origins can be traced to [6]; it is known not to achieve bound consistency [7] (apart from some special cases [8]), a desirable property for Constraint Satisfaction Problems (CSP): a CSP is bound consistent if every projection of its feasible region on each range X i is X i itself [5]. The FBBT was employed as a range reduction technique for Mixed Integer Linear Programs (MILP) in [9,10] and then for MINLPs in [11]. Within the context of GO, the FBBT was discussed in [12] and recently improved in [13] by considering its effect on common subexpressions of g(x).…”

Section: Introductionmentioning

confidence: 99%

Feasibility-Based Bounds Tightening via Fixed Points

Belotti¹,

Cafieri²,

Lee³

et al. 2010

Combinatorial Optimization and Applications

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Abstract. The search tree size of the spatial Branch-and-Bound algorithm for Mixed-Integer Nonlinear Programming depends on many factors, one of which is the width of the variable ranges at every tree node. A range reduction technique often employed is called Feasibility Based Bounds Tightening, which is known to be practically fast, and is thus deployed at every node of the search tree. From time to time, however, this technique fails to converge to its limit point in finite time, thereby slowing the whole Branch-and-Bound search considerably. In this paper we propose a polynomial time method, based on solving a linear program, for computing the limit point of the Feasibility Based Bounds Tightening algorithm applied to linear equality and inequality constraints.

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“…In fact, there is a wide literature on the detection and elimination of redundant constraints in LP models [1][2][3][4][5][6][7][8][9][10][11]. Heuristic approach [13] is using an intercept matrix to identify redundant constraints prior to the start of the solution process.…”

Section: Introductionmentioning

confidence: 99%