Convexification of different classes of non-convex MINLP problems

Pörn, Ray; Harjunkoski, Iiro; Westerlund, Tapio

doi:10.1016/s0098-1354(98)00305-6

Cited by 75 publications

(36 citation statements)

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“…Hence, future work will focus on the development of solution methods that exploit this special structure. One alternative includes the use of convexification techniques similar to the ones presented by Westerlund et al 68,69 in search for global solutions. Our surrogate-based MINLP model includes the surrogate models of the permanent units, the reformulation of the surrogate models we just introduced for conditional units, and the algebraic equivalents of the logic constraints in (13).…”

Section: Superstructure Modeling Approachmentioning

confidence: 99%

Surrogate‐based superstructure optimization framework

2011

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in Wiley Online Library (wileyonlinelibrary.com).In principle, optimization-based ''superstructure'' methods for process synthesis can be more powerful than sequential-conceptual methods as they account for all complex interactions between design decisions. However, these methods have not been widely adopted because they lead to mixed-integer nonlinear programs that are hard to solve, especially when realistic unit operation models are used. To address this challenge, we develop a superstructure-based strategy where complex unit models are replaced with surrogate models built from data generated via commercial process simulators. In developing this strategy, we study aspects such as the systematic design of process unit surrogate models, the generation of simulation data, the selection of the surrogate's structure, and the required model fitting. We also present how these models can be reformulated and incorporated into mathematical programming superstructure formulations. Finally, we discuss the application of the proposed strategy to a number of applications.

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Section: Superstructure Modeling Approachmentioning

confidence: 99%

Surrogate‐based superstructure optimization framework

2011

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“…Noureldin and El-Halwagi (1999) studied mass integration problems for pollution prevention, proposed targets for the maximum achievable pollution, introduced an interval analysis framework for the determination of these targets, studied the pollution prevention via unit manipulation, recycle and interception, and employed the interval-based targets in a case study featuring the reduction of water usage and discharge in a tire-to-fuel plant. Pörn, Harjunkoski, and Westerlund (1999) proposed convexification schemes for classes of discrete and integer nonconvex models. They studied the exponential transformation and potential-based transformations and applied them to integer posynomial problems.…”

Section: Mixed-integer Nonlinear Optimization Minlpsmentioning

confidence: 99%

Global optimization in the 21st century: Advances and challenges

Floudas

Akrotirianakis

Caratzoulas

et al. 2005

Computers & Chemical Engineering

198

117

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This paper presents an overview of the research progress in global optimization during the last 5 years (1998)(1999)(2000)(2001)(2002)(2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixedinteger nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box/black-box/nonfactorable models, and (e) bilevel nonlinear optimization. Our research contributions part focuses on (i) improved convex underestimation approaches that include convex envelope results for multilinear functions, convex relaxation results for trigonometric functions, and a piecewise quadratic convex underestimator for twice continuously differentiable functions, and (ii) the recently proposed novel generalized ␣BB framework. Computational studies will illustrate the potential of these advances.

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“…Bodington (1992) also mentions the lack of systematic methodologies for handling nonlinear blending relations. Ramage (1998) refers to nonlinear programming (NLP, MINLP) as a necessary tool for the refineries of the 21 st century, as a result of the significant progress made in the nineties (Viswanathan and Grossmann, 1990;Pörn et al, 1999).…”

Section: Overview Of Planning and Scheduling In Oil Refineriesmentioning

confidence: 99%

Planning and scheduling for petroleum refineries using mathematical programming

Joly

Moro

Pinto

2002

Braz. J. Chem. Eng.

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-The objective of this paper is the development and solution of nonlinear and mixed-integer (MIP) optimization models for real-world planning and scheduling problems in petroleum refineries. Firstly, we present a nonlinear planning model that represents a general refinery topology and allows implementation of nonlinear process models as well as blending relations. The optimization model is able to define new operating points, thus increasing the production of the more valuable products and simultaneously satisfying all specification constraints. The second part addresses scheduling problems in oil refineries, which are formulated as MIP optimization models and rely on both continuous and discrete time representations. Three practical applications closely related to the current refinery scenario are presented. The first one addresses the problem of crude oil inventory management of a refinery that receives several types of crude oil delivered exclusively by a single oil pipeline. Subsequently, two optimization models intended to define the optimal production policy, inventory control and distribution are proposed and solved for the fuel oil and asphalt plant. Finally, the planning model of is extended in order to sequence decisions at the scheduling level in the liquefied petroleum gas (LPG) area for maximization of the production of petrochemical-grade propane and product delivery.

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Convexification of different classes of non-convex MINLP problems

Cited by 75 publications

References 0 publications

Surrogate‐based superstructure optimization framework

Surrogate‐based superstructure optimization framework

Global optimization in the 21st century: Advances and challenges

Planning and scheduling for petroleum refineries using mathematical programming

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