A Linearization Procedure for Quadratic and Cubic Mixed-Integer Problems

Oral, Muhittin; Kettani, Ossama

doi:10.1287/opre.40.1.s109

Cited by 87 publications

(46 citation statements)

References 12 publications

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“…These linearizations are some of the oldest MIP formulation techniques [58,7,100,133,59,162,60,70,8,117,72,135] and continue to be a very active area of research [5,3,71,64,65,4]. They are an important tool for nonconvex mixed integer nonlinear programming [29] and have been extensively studied in the context of mathematical programming reformulations [109,108].…”

Section: Linearization Of Productsmentioning

confidence: 99%

Mixed Integer Linear Programming Formulation Techniques

Vielma¹

2015

SIAM Rev.

258

143

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1. Introduction. Throughout more than 50 years of existence, mixed integer linear programming (MIP) theory and practice have been significantly developed, and it is now an indispensable tool in business and engineering [68,94,104]. Two reasons for the success of MIP are linear programming (LP) based solvers and the modeling flexibility of MIP. We now have several extremely effective state-of-the-art solvers [82,69, 52,171] that incorporate many advanced techniques [1,2,25,23,92,112,24] and, since its early stages, MIP has been used to model a wide range of applications [44,45].While in many cases constructing valid MIP formulations is relatively straightforward, some care should be taken in this construction as certain formulation attributes can significantly reduce the effectiveness of LP-based solvers. Fortunately, constructing formulations that behave well with state-of-the-art solvers can usually be achieved by following simple guidelines described in standard textbooks. However, more advanced techniques can often perform significantly better than textbook formulations and are sometimes a necessity. The main objective of this survey is to summarize the state of the art of such formulation techniques for a wide range of problems. To keep the length of this survey under control, we concentrate on formulations for sets of a mixed integer nature that require both integer constrained and continuous variables. We hence purposefully place less emphasis on some related areas such as combinatorial optimization, quadratic and polynomial 0/1 optimization, and polyhedral approximations of convex sets. These topics are certainly areas of important and active research, so we cover them succinctly in section 12.

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Section: Linearization Of Productsmentioning

confidence: 99%

Mixed Integer Linear Programming Formulation Techniques

Vielma¹

2015

SIAM Rev.

258

143

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“…Hahn et al (2010) and Hahn et al (2012) used the reformulation-linearization technique to solve QAP. Additional methods have been proposed by Glover and Woolsey (1974), Armour and Buffa (1963), Foulds (1983), Adams and Sherali (1986), and Oral and Kettani (1992). Heragu and Kusiak (1991) present two linearizations for the facility layout problem.…”

Section: Related Literaturementioning

confidence: 99%

A hierarchical facility layout planning approach for large and complex hospitals

et al. 2015

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The transportation processes for patients, personnel, and material in large and complex maximum-care hospitals with many departments can consume significant resources and thus induce substantial logistics costs. These costs are largely determined by the allocation of the different departments and wards in possibly multiple connected hospital buildings. We develop a hierarchical layout planning approach based on an analysis of organizational and operational data from the Hannover Medical School, a large and complex university hospital in Hannover, Germany.The purpose of this approach is to propose locations for departments and wards for a given system of buildings such that the consumption of resources due to those transportation processes is minimized. We apply the approach to this real-world organizational and operational dataset as well as to a fictitious hospital building and analyze the algorithmic behavior and resulting layout.

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“…The technique known as radix-based discretization described by Kolodziej [14] and Castro [25] is used to discretize the bilinear term. The product y = f · x can be represented exactly with the following constraints and disjunction:…”

Section: Radix-based Discretizationmentioning

confidence: 99%

A global optimization approach for a class of MINLP problems with applications to crude oil scheduling problem

Duan¹,

Yang²,

Xu³

et al. 2015

J. Nonlinear Sci. Appl.

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A global optimization algorithm is proposed to solve the crude oil schedule problem. We first developed a lower and upper bounding model by using a multiparametric disaggregation method. Secondly, the lower and the upper bounding models combined with finite state method (FSM) are incorporated to solve the bilinear programing problem jointly. The advantage of using FSM is that we can generate promising substructure and partial solution. Furthermore, the FSM can guarantee that the entire solution space is uniformly covered. Therefore, the algorithm has better global performance than some existing algorithms. Finally, a real-life crude oil scheduling problem from the literature is used for conducting simulation. The experimental results validate that the proposed method outperforms commercial solvers. c ⃝2015 All rights reserved.

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A Linearization Procedure for Quadratic and Cubic Mixed-Integer Problems

Cited by 87 publications

References 12 publications

Mixed Integer Linear Programming Formulation Techniques

Mixed Integer Linear Programming Formulation Techniques

A hierarchical facility layout planning approach for large and complex hospitals

A global optimization approach for a class of MINLP problems with applications to crude oil scheduling problem

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