Simultaneous mixed-integer dynamic optimization for integrated design and control

Flores‐Tlacuahuac, Antonio; Biegler, Lorenz T.

doi:10.1016/j.compchemeng.2006.08.010

Cited by 93 publications

(79 citation statements)

References 20 publications

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“…A small subset of these applications includes portfolio optimization [21,69], block layout design in the manufacturing and service sectors [33,99], network design with queuing delay constraints [27], integrated design and control of chemical processes [54], drinking water distribution systems security [74], minimizing the environmental impact of utility plants [47], and multiperiod supply chain problems subject to probabilistic constraints [76].…”

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confidence: 99%

Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Bonami

Kılınç

Linderoth

2011

The IMA Volumes in Mathematics and Its Applications

197

181

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Abstract. This paper provides a survey of recent progress and software for solving mixed integer nonlinear programs (MINLP) wherein the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in very years. By exploiting analogies to the case of well-known techniques for solving mixed integer linear programs and incorporating these techniques into the software, significant improvements have been made in our ability to solve the problems.Key words. Mixed Integer Nonlinear Programming; Branch and Bound; AMS(MOS) subject classifications.1. Introduction. Mixed-Integer Nonlinear Programs (MINLP) are optimization problems where some of the variables are constrained to take integer values and the objective function and feasible region of the problem are described by nonlinear functions. Such optimization problems arise in many real world applications. Integer variables are often required to model logical relationships, fixed charges, piecewise linear functions, disjunctive constraints and the non-divisibility of resources. Nonlinear functions are required to accurately reflect physical properties, covariance, and economies of scale.In all its generality, MINLP forms a particularly broad class of challenging optimization problems as it combines the difficulty of optimizing over integer variables with handling of nonlinear functions. Even if we restrict our model to contain only linear functions, MINLP reduces to a Mixed-Integer Linear Program (MILP), which is an NP-Hard problem [56]. On the other hand, if we restrict our model to have no integer variable but allow for general nonlinear functions in the objective or the constraints, then MINLP reduces to a Nonlinear Program (NLP) which is also known to be NP-Hard [91]. Combining both integrality and nonlinearity can lead to examples of MINLP that are undecidable [68].

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confidence: 99%

Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Bonami

Kılınç

Linderoth

2011

The IMA Volumes in Mathematics and Its Applications

197

181

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“…Lee et al [194] Introduction to design and control Narraway et al [247] Steady state and dynamic economics Luyben and Floudas [208] Superstructure of design alt. into MINLP Mohideen et al [241] Economically optimal design and control van Schijndel and Pistikopoulos [345] Review on process design and operability Sakizlis et al [307] Review on design and control Flores-Tlacuahuac and Biegler [118] MIDO transformed to MINLP Würth et al [362] Dynamic optimization and NMPC Yuan et al [366] Review on design and control Diangelakis et al [89] Sequential design optimization and mp-MPC. Application on a residential cogeneration systems.…”

Section: Introductionmentioning

confidence: 99%

“…A branch and bound algorithm is utilized to solve the problem to global optimality. Biegler & co-workers (2007) [118] Full discretization by finite elements, and solving a large scale nonconvex MINLP. Generalized disjunctive programming are used to solve the MINLP.…”

Section: 'High Fidelity' Modelmentioning

confidence: 99%

“…This formed a prelude to the simultaneous consideration of design and control via (i) the formulation and solution of large scale optimization problems (including numerous decomposition approaches, e.g. [118]), (ii) flowsheet and graphical problem representations (e.g. [8]) and (iii) control structure selection as part of the design optimization (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Diangelakis

Pistikopoulos

2017

Computer Aided Chemical Engineering

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“…The optimization of discrete and continuous systems, herein referred as hybrid systems, has been mainly directed towards optimizing the dynamics of start-up and shut-down operations [5], grade transitions [6], [7], batch systems [8], scheduling and control systems [9], [10], simultaneous design and control [11], [12], [13], [14]. The formal optimization formulation of these problems gives rise to Mixed-Integer Dynamic Optimization (MIDO) problems whose solution can be tackled by well known numerical approaches [15].…”

Section: Introductionmentioning

confidence: 99%

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

Ruiz‐Femenia

Flores‐Tlacuahuac

Grossmann

2014

Ind. Eng. Chem. Res.

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In this work we present an extension of the Logic Outer-Approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continouos optimal control problems we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using 3 examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational load required to get the optimal solutions is modest and the solutions are relatively easy to find

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Simultaneous mixed-integer dynamic optimization for integrated design and control

Cited by 93 publications

References 20 publications

Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Algorithms and Software for Convex Mixed Integer Nonlinear Programs

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

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