Branching and bounds tighteningtechniques for non-convex MINLP

Belotti, Pietro; Lee, Jon; Liberti, Leo; Margot, François; Wächter, Andreas

doi:10.1080/10556780903087124

Cited by 496 publications

(462 citation statements)

References 71 publications

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“…The expression representation for functions is well known in computer science [15], engineering [16,17] and GO [18][19][20] where it is used for two substeps of the sBB algorithm: lower bound computation and FBBT. More formal constructions of E can be found in [21], Sect.…”

Section: Expression Graphsmentioning

confidence: 99%

“…Some are based on the factorability of the functions in g(x) [25][26][27], whilst others are based on a symbolic reformulation of (1) based on the problem DAG D [18][19][20]. We employ the latter approach: each non-leaf node z in the vertex set of D is replaced by an added variable w z and a corresponding constraint (4) is adjoined to to the formulation (usually, two variables w v , w u corresponding to identical defining constraints are replaced by one single added variable).…”

Section: Linear Relaxation Of the Minlpmentioning

confidence: 99%

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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: Expression Graphsmentioning

confidence: 99%

Section: Linear Relaxation Of the Minlpmentioning

confidence: 99%

Feasibility-Based Bounds Tightening via Fixed Points

Belotti¹,

Cafieri²,

Lee³

et al. 2010

Combinatorial Optimization and Applications

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“…This BQP can either be solved directly using standard BB-based solvers [1,11,7] or reformulated exactly (see [8] for a formal definition of reformulation) to a MILP, by means of the PRODBIN reformulation [9,5] prior to solving is with standard MILP solvers. A few preliminary experiments showed that the MILP reformulation yielded longer solution times compared to solving the BQP directly.…”

Section: Setsmentioning

confidence: 99%

Optimal Technological Architecture Evolutions of Information Systems

Giakoumakis

Krob

Liberti

et al. 2010

Complex Systems Design &Amp; Management

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We discuss a problem arising in the strategic management of IT enterprises: that of replacing some existing services with new services without impairing operations. We formalize the problem by means of a Mathematical Programming formulation of the Mixed-Integer Nonlinear Programming class and show it can be solved to a satisfactory optimality approximation guarantee by means of existing off-the-shelf software tools.

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“…We have chosen Couenne [4] (version 0.5.6), a free global solver for nonconvex MINLP based on branch-and-bound and convex envelopes, and SCIP [5] (version 3.2.1), a commercial open-source framework for Constraint Integer Programming, to solve the following instances.…”

Section: Benchmarks and Resultsmentioning

confidence: 99%

Gearbox Design via Mixed-Integer Programming

Dörig¹,

Ederer²,

Pelz³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Gearboxes are mechanical transmission systems that consist of multiple gear wheels and shafts. The transmission ratios of the gears are determined by the size and interconnection of these components. Gearboxes have to adhere to very strict requirements regarding weight, production costs, and available space. Moreover, the load cases as a result of motor-vehiclepairings are often not clear a priori. Therefore, automobile manufacturers are confronted with a multicriteria design problem under uncertainty.In this work, we present an approach on how to formulate the gearbox design problem as a mixed-integer nonlinear program. This enables us to compute provably globally optimal gearbox designs. We show how different degrees of freedom, input parameters and the numerical accuracy influence the computation time and the quality of solutions.Acknowledgement.

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Branching and bounds tighteningtechniques for non-convex MINLP

Cited by 496 publications

References 71 publications

Feasibility-Based Bounds Tightening via Fixed Points

Feasibility-Based Bounds Tightening via Fixed Points

Optimal Technological Architecture Evolutions of Information Systems

Gearbox Design via Mixed-Integer Programming

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