The Reformulation-Optimization Software Engine

Liberti, Leo; Cafieri, Sonia; Savourey, David

doi:10.1007/978-3-642-15582-6_50

Cited by 16 publications

(28 citation statements)

References 21 publications

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“…Secondly, we ran the FBBT on the linear constraintsĝ(x) ≤Ĝ 0 , with a termination condition set at |X k △X k−1 | ≤ 10 −6 on slow progress at iteration k. We then computed the fixed point by solving the LP (14)- (34) applied toĝ(x) ≤Ĝ 0 . The FBBT, as well as the automatic construction of the LP (14)- (34), were implemented in ROSE [31,32]. LPs were solved using CPLEX 11 [33].…”

Section: Computational Resultsmentioning

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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Section: Computational Resultsmentioning

confidence: 99%

Feasibility-Based Bounds Tightening via Fixed Points

Belotti¹,

Cafieri²,

Lee³

et al. 2010

Combinatorial Optimization and Applications

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“…We also use a new solver/reformulator called ROSE (Reformulation Optimization Software Engine, see [28,27]), of which we exploit the following features:…”

Section: Computational Settingmentioning

confidence: 99%

A storm of feasibility pumps for nonconvex MINLP

et al. 2012

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One of the foremost difficulties in solving Mixed-Integer Nonlinear Programs, either with exact or heuristic methods, is to find a feasible point. We address this issue with a new feasibility pump algorithm tailored for nonconvex Mixed-Integer Nonlinear Programs. Feasibility pumps are algorithms that iterate between solving a continuous relaxation and a mixed-integer relaxation of the original problems. Such approaches currently exist in the literature for Mixed-Integer Linear Programs and convex Mixed-Integer Nonlinear Programs: both cases exhibit the distinctive property that the continuous relaxation can be solved in polynomial time. In nonconvex Mixed-Integer Nonlinear Programming such a property does not hold, and therefore special care has to be exercised in order to allow feasibility pump algorithms to rely only on local optima of the continuous relaxation. Based on a new, high level view of feasibility pump algorithms as a special case of the well-known successive projection method, we show that many possible different variants of the approach can be developed, depending on how several different (orthogonal) implementation choices are taken. A remarkable twist of feasibility pump algorithms is that, unlike most previous successive projection methods from the literature, projection is "naturally" taken in two different norms in the two different subproblems. To cope with this issue while retaining the local convergence properties of standard successive projection methods we propose the introduction of appropriate norm constraints in the subproblems; these actually seem to significantly improve the practical performance of the approach. We present extensive computational results on the MINLPLib, showing the effectiveness and efficiency of our algorithm.

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“…The orbital-shrinking relaxation is constructed automatically using a mixture of bash scripting, GAP gap4 (2007), AMPL Fourer and Gay (2002), and ROSE Liberti et al (2010).…”

Section: Automatic Generation Of the Whole Symmetry Groupmentioning

confidence: 99%

Orbital shrinking: Theory and applications

Fischetti

Liberti

Salvagnin

et al. 2017

Discrete Applied Mathematics

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We present a method, based on formulation symmetry, for generating MixedInteger Linear Programming (MILP) relaxations with fewer variables than the original symmetric MILP. Our technique also extends to convex MINLP, and some nonconvex MINLP with a special structure. We consider an appropriate subgroup of the formulation group, and replace each orbit with a single variable. By means of the orbit barycenter, we are able to prove that the new MILP formulation is a relaxation of the original one. We showcase the effectiveness of our relaxation both on a library of symmetric MILP, and as part of a decomposition method applied to two important applications (multi-activity shift scheduling and multiple knapsack problem), showing that it can improve CPU times by several orders of magnitude compared to pure MIP or CP approaches.

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The Reformulation-Optimization Software Engine

Cited by 16 publications

References 21 publications

Feasibility-Based Bounds Tightening via Fixed Points

Feasibility-Based Bounds Tightening via Fixed Points

A storm of feasibility pumps for nonconvex MINLP

Orbital shrinking: Theory and applications

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