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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.
Collocation software for boundary value differentialalgebraic equations
 SIAM J. Sci. Comput
, 1994
"... We describe the methods and implementation of a generalpurpose code, COLDAE. This code can solve boundary value problems for nonlinear systems of semiexplicit differentialalgebraic equations (DAEs) of index at most 2. Fully implicit index1 boundary value DAE problems can be handled as well. The ..."
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Cited by 24 (3 self)
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We describe the methods and implementation of a generalpurpose code, COLDAE. This code can solve boundary value problems for nonlinear systems of semiexplicit differentialalgebraic equations (DAEs) of index at most 2. Fully implicit index1 boundary value DAE problems can be handled as well. The code COLDAE is an extension of the package COLNEW (COLSYS) for solving boundary value ODEs. The implemented method is piecewise polynomial collocation at Gaussian points, extended as needed by the projection method of AscherPetzold. For general semiexplicit index2 problems, as well as for fully implicit index1 problems, we define a selective projected collocation method, and demonstrate its use. The mesh selection procedure of COLSYS is modified for the case of index2 constraints. We also discuss shooting for initial guesses. The power and generality of the code are demonstrated by examples.
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 21 (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.
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...
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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Cited by 2 (0 self)
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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.
Dynamic Optimization with Path Constraints
, 1998
"... Dynamic optimization problems, also called constrained optimal control problems, are of interest in many areas of engineering. However, numerical solution of such problems is difficult and thus the application of dynamic optimization in process engineering has been limited. The dynamic optimization ..."
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Dynamic optimization problems, also called constrained optimal control problems, are of interest in many areas of engineering. However, numerical solution of such problems is difficult and thus the application of dynamic optimization in process engineering has been limited. The dynamic optimization problems of interest in process engineering typically consist of large systems of differential and algebraic equations (DAEs), and often contain path equality or inequality constraints on the state variables. The objective of this thesis was to improve the efficiency with which largescale dynamic optimization problems may be solved and to develop improved methods for including path constraints. The most efficient method for numerical solution of large dynamic optimization problems is the control parameterization method. The cost of solving the dynamic optimization problem is typically dominated by the cost of solving the sensitivity system. The efficiency with which the sensitivity system can be solved is significantly improved with the staggered corrector sensitivity algorithm which was developed and implemented during the course of this thesis.
A Novel Approach to Dynamic Optimization of ODE and DAE Systems as HighIndex Problems
, 1995
"... Solution of many problems in plant operations requires determination of optimal control profiles subject to state constraints for systems modeled by ordinary differential equations (ODEs) or differentialalgebraic equations (DAEs). For example, optimal temperature and/or feed rate profiles are im ..."
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Solution of many problems in plant operations requires determination of optimal control profiles subject to state constraints for systems modeled by ordinary differential equations (ODEs) or differentialalgebraic equations (DAEs). For example, optimal temperature and/or feed rate profiles are important for the operation of many batch reactions. Similar observations apply to reflux policies for batch distillation, and feedstock changeover in oil refineries. Currently there are two different classes of methods for determining optimal control profiles for DAEs. Control parameterization techniques rely on the discretization of the control variables to reduce the optimal control problem to an NLP. These methods require repeated integration of the DAEs and some variational equations, which effectively discretizes the state variables within the numerical integrator. Path constraints are typically handled by the master NLP solver, and can force the NLP solver to call for a large nu...
Global Optimization of Hybrid Systems
, 2006
"... Systems that exhibit both discrete state and continuous state dynamics are called hybrid systems. In most nontrivial cases, these two aspects of system behavior interact to such a significant extent that they cannot be decoupled effectively by any kind of abstraction and must be analyzed simultaneo ..."
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Systems that exhibit both discrete state and continuous state dynamics are called hybrid systems. In most nontrivial cases, these two aspects of system behavior interact to such a significant extent that they cannot be decoupled effectively by any kind of abstraction and must be analyzed simultaneously. Hybrid system models are important in many areas of science and engineering, including flipflops and latching relays, manufacturing systems, airtraffic management systems, controller synthesis, switched systems, chemical process systems, signaling and decision making mechanisms in (biological) cells, robotic systems, safety interlock systems, and embedded systems. The primary focus of this thesis is to explore deterministic methods for the global optimization of hybrid systems. While the areas of modeling, simulation and sensitivity analysis of hybrid systems have received much attention, there are many challenging difficulties associated with the optimization of such systems. The contents of this thesis represent the first steps toward deterministic global optimization of