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Retrospective on Optimization
 25 TH YEAR ISSUE ON COMPUTERS AND CHEMICAL ENGINEERING
"... In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of op ..."
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Cited by 27 (1 self)
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In this paper we provide a general classification of mathematical optimization problems, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering. We then provide a review of solution methods of the major types of optimization problems for continuous and discrete variable optimization, particularly nonlinear and mixedinteger nonlinear programming. We also review their extensions to dynamic optimization and optimization under uncertainty. While these areas are still subject to significant research efforts, the emphasis in this paper is on major developments that have taken place over the last twenty five years.
Bonvin D. Dynamic optimization of batch processes: I. Characterization of the nominal solution. Comp Chem Eng
"... The optimization of batch processes has attracted attention in recent years because, in the face of growing competition, it is a natural choice for reducing production costs, improving product quality, meeting safety requirements and environmental regulations. The main bottleneck in using optimizat ..."
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Cited by 18 (9 self)
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The optimization of batch processes has attracted attention in recent years because, in the face of growing competition, it is a natural choice for reducing production costs, improving product quality, meeting safety requirements and environmental regulations. The main bottleneck in using optimization in industry is the presence of uncertainty. The most natural way to compensate for uncertainty, and thus to improve process operations, is through the use of measurements. This forms the subject of this series of two papers. In this first part, the optimal input profiles are expressed in terms of arcs and switching times, of which some push the system to the constraints of the problem while the others exploit the intrinsic compromise present in the system for the purpose of optimality. Such a characterization improves considerably the interpretability of the solution, enhances the numerical efficiency, and acts as a necessary first step towards a measurementbased optimization framework.
Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR
 Ind. Eng. Chem. Res
"... In this work we propose a scheduling and control formulation for simultaneously addressing scheduling and control problems by explicitly incorporating process dynamics in the form of system constraints that ought to be met. The formulation takes into account the interactions between such problems an ..."
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Cited by 10 (7 self)
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In this work we propose a scheduling and control formulation for simultaneously addressing scheduling and control problems by explicitly incorporating process dynamics in the form of system constraints that ought to be met. The formulation takes into account the interactions between such problems and is able to cope with nonlinearities embedded into the processing system. The simultaneous scheduling and control problems is cast as a MixedInteger Dynamic Optimization (MIDO) problem where the simultaneous approach, based on orthogonal collocation on finite elements, is used to transform it into a MixedInteger Nonlinear Programming (MINLP) problem. The proposed simultaneous scheduling and control formulation is tested using three multiproduct continuous stirred tank reactors featuring hard nonlinearities. 2 1
Optimization Strategies for Dynamic Systems
 In C. Floudas, P. Pardalos (Eds), Encyclopedia of Optimization
, 1999
"... Introduction and Problem Statement Interest in dynamic simulation and optimization of chemical processes has increased significantly during the last two decades. Common problems include control and scheduling of batch processes; startup, upset, shutdown and transient analysis; safety studies and th ..."
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Cited by 9 (2 self)
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Introduction and Problem Statement Interest in dynamic simulation and optimization of chemical processes has increased significantly during the last two decades. Common problems include control and scheduling of batch processes; startup, upset, shutdown and transient analysis; safety studies and the evaluation of control schemes. Chemical processes are modeled dynamically using differentialalgebraic equations (DAEs). The DAE formulation consists of differential equations that describe the dynamic behavior of the system, such as mass and energy balances, and algebraic equations that ensure physical and thermodynamic relations. The general dynamic optimization problem can be stated as follows: min z(t);y(t);u(t);t f ;p '(z(t f ); y(t f ); u(t<F8
A Boundary Value Problem Approach to the Optimization of Chemical Processes Described by DAE Models
, 1997
"... An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a ..."
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Cited by 6 (0 self)
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An efficient and robust technique for the optimization of dynamic chemical processes is presented. In particular, we address the solution of large, multistage optimal control and design optimization problems for processes described by DAE models of index one. Our boundary value problem approach (a simultaneous solution strategy) is based on a piecewise parametrization of the control functions and a multiple shooting discretization of the DAEs, combined with a specifically tailored SQP technique. The inherent problem structure is exploited on various levels in order to obtain an efficient overall method. In addition, the formulation lends itself well to parallel computation. Unlike other simultaneous strategies based on collocation, direct use is made of existing advanced, fully adaptive DAE solvers. An implementation of this strategy is provided by the recently developed modular optimal control package MUSCODII. Apart from a difficult DAE test problem with control and path constrain...
Optimization Framework for the Synthesis of Chemical Reactor Networks
, 1998
"... The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks ..."
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Cited by 3 (1 self)
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The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...
Dynamic Optimization Of Bioprocesses: Deterministic And Stochastic Strategies
, 1998
"... The general problem of dynamic optimization of bioprocesses with unspecified final time is considered. Several solution strategies, both deterministic and stochastic, are compared based on their results for three bioprocess case studies. A hybrid (stochasticdeterministic) method is also presented a ..."
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Cited by 3 (1 self)
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The general problem of dynamic optimization of bioprocesses with unspecified final time is considered. Several solution strategies, both deterministic and stochastic, are compared based on their results for three bioprocess case studies. A hybrid (stochasticdeterministic) method is also presented and evaluated, showing significant advantages in terms of robustness and computational effort. INTRODUCTION In recent years, many efforts have been devoted to the optimization and control of bioprocesses. An example of a problem that has received major attention is the dynamic optimization (open loop optimal control) of fedbatch bioreactors (e.g. van Impe, 1996; Roubos et al, 1997; Banga et al., 1997; Tholudur and Ramirez, 1997). Most bioprocesses have highly nonlinear dynamics, and constraints are also frequently present on both the state and the control variables. Thus, efficient and robust dynamic optimization methods are needed in order to successfully obtain their optimal operating po...
Advantages of a Nonlinear Programming Based Methodologies for Inequality Path Constrained Optimal Control Problems  A Numerical Study
 SIAM J. Scientific Computing
, 2008
"... In this work, we address some advantages of Nonlinear Programming (NLP) based methods for inequality path constrained optimal control problems. The analysis is carried out on the Partial Dierential Equation (PDE) constrained optimization problem presented in [3]. This problem possesses the essential ..."
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Cited by 2 (1 self)
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In this work, we address some advantages of Nonlinear Programming (NLP) based methods for inequality path constrained optimal control problems. The analysis is carried out on the Partial Dierential Equation (PDE) constrained optimization problem presented in [3]. This problem possesses the essential characteristics of a typical inequality path constrained optimal control problem. The PDEconstrained problem can be converted to a Dierential Algebraic Equation (DAE) constrained optimization problem by spatial discretization. In a DAEconstrained optimization setting, the index of the path constraint can be arbitrarily increased ( ner spatial grids), and this facilitates the study of the eect of the index of a path constraint on the solution obtained using an NLP based methodology. We show that the Direct Transcription approach leads to a problem that does not satisfy Linear Independence Constraint Qualication (LICQ), but satises the weaker MangasarianFromowitz Constraint Quali cation (MFCQ). Interior Point methods have convergence results for NLPs satisfying MFCQ. The Direct Transcription approach leads to a convex QP with the result that the control obtained is the unique global minimizer. Also, with the Indirect Approach we show that it is dicult to numerically integrate the ODEs over the constrained arc because of stability and error control reasons. These observations explain some of the results of [3]. We believe that NLP based methodologies have additional
exibility with respect to constraint quali cations, and this can be put to use in the case of inequality path constrained optimal control problems to obtain meaningful solutions. 1 1
Optimal Operation of Alternating Activated Sludge Processes
"... The study presents dynamic optimisation of a small size single basin wastewater treatment plant. The objectives are to determine an optimal sequence of aeration/nonaeration times so that for a typical diurnal pattern of disturbances, the e#uent constraints are respected, the plant remains in peri ..."
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The study presents dynamic optimisation of a small size single basin wastewater treatment plant. The objectives are to determine an optimal sequence of aeration/nonaeration times so that for a typical diurnal pattern of disturbances, the e#uent constraints are respected, the plant remains in periodical steady state, and energy consumption is minimised.
State of the Art of Research in Flexibility, Operability & Dynamics
, 1998
"... this paper and need to be defined. Flexibility commonly refers to the range of operating conditions, normally steady state conditions, which a particular process design can achieve. Switchability refers to the ability of a plant to move from alternative steady state conditions. Controllability refer ..."
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this paper and need to be defined. Flexibility commonly refers to the range of operating conditions, normally steady state conditions, which a particular process design can achieve. Switchability refers to the ability of a plant to move from alternative steady state conditions. Controllability refers to the ability of a particular design, usually including TWG3/D Bogle/R&D SoA Review/Rev P/19980112 3 the control system, to maintain safe and stable operating conditions following disturbances.