A multi-commodity flow formulation for the generalized pooling problem

Alfaki, Mohammed; Haugland, Dag

doi:10.1007/s10898-012-9890-7

Cited by 25 publications

(35 citation statements)

References 55 publications

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“…51,52 But we want to automatically translate every pooling problem into just one formulation (here, the proposed canonical PQ-formulation) and save implementation time by specializing methodologies such as cutting planes to just one formulation.…”

Section: Canonical Representation For the Pq-formulationmentioning

confidence: 99%

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Using functional programming to recognize named structure in an optimization problem: Application to pooling

2016

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in Wiley Online Library (wileyonlinelibrary.com) Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems.

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Section: Canonical Representation For the Pq-formulationmentioning

confidence: 99%

“…1, 43,44,[50][51][52] The recognition algorithm simultaneously converts the MINLP to canonical pooling form and recognizes network structure. The article describes the algorithm implementation; the online supplementary material justifies why the algorithm is implemented in F#.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Using functional programming to recognize named structure in an optimization problem: Application to pooling

2016

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“…Furthermore, let x I ia denote the flow in y a , a ∈ A, that comes from input i ∈ I . The formulation was first proposed for standard pooling problems by Ben-Tal et al [16] and has been extended to generalized pooling problems by Alfaki and Haugland [8]. It can be stated as follows:…”

Section: Input Commodities: Mcf-i-(p)q-formulationmentioning

confidence: 99%

“…Inspired by the ideas of the Reformulation-Linearization Technique (RLT) [46], the MCF-I-PQformulation adds valid (but redundant) constraints to the MCF-I-Q-formulation. The formulation was first proposed for standard pooling problems by Tawarmalani and Sahinidis [48] and has been extended to generalized pooling problems by Alfaki and Haugland [8].…”

Section: Input Commodities: Mcf-i-(p)q-formulationmentioning

confidence: 99%

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New multi-commodity flow formulations for the pooling problem

2016

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The pooling problem is a nonconvex nonlinear programming problem with numerous applications. The nonlinearities of the problem arise from bilinear constraints that capture the blending of raw materials. Bilinear constraints are well-studied and significant progress has been made in solving large instances of the pooling problem to global optimality. This is due in no small part to reformulations of the problem. Recently, Alfaki and Haugland proposed a multi-commodity flow formulation of the pooling problem based on input commodities. The authors proved that the new formulation has a stronger linear relaxation than previously known formulations. They also provided computational results which show that the new formulation outperforms previously known formulations when used in a global optimization solver. In this paper, we generalize their ideas and propose new multi-commodity flow formulations based on output, input and output and (input, output)-commodities. We prove the equivalence of formulations, and we study the partial order of formulations with respect to the strength of their LP relaxations. In an extensive computational study, we evaluate the performance of the new formulations. We study the trade-off between disaggregating commodities and therefore increasing the size of formulations versus strengthening the relaxed linear programs and improving the computational performance of the nonlinear programs. We provide computational results which show that output commodities often outperform input commodities, and that disaggregating commodities further only marginally strengthens the linear relaxations. In fact, smaller formulations often show a significantly better performance when used in a global optimization solver.

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A cost minimization heuristic for the pooling problem

Alfaki

Haugland

2013

Ann Oper Res

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A multi-commodity flow formulation for the generalized pooling problem

Cited by 25 publications

References 55 publications

Using functional programming to recognize named structure in an optimization problem: Application to pooling

Using functional programming to recognize named structure in an optimization problem: Application to pooling

New multi-commodity flow formulations for the pooling problem

A cost minimization heuristic for the pooling problem

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