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Floudas. A new robust optimization approach for scheduling under uncertainty: I. bounded uncertainty
 Computers & Chemical Engineering
"... The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixedinteger linear programming (MILP) problems produces “robust ” solutions which are in a sense immune against bounded uncertainty. Both the coefficients in ..."
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Cited by 18 (1 self)
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The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixedinteger linear programming (MILP) problems produces “robust ” solutions which are in a sense immune against bounded uncertainty. Both the coefficients in the objective function, the lefthandside parameters and the righthandside parameters of the inequalities are considered. Robust optimization techniques are developed for two types of uncertain data: bounded uncertainty and bounded and symmetric uncertainty. By introducing a small number of auxiliary variables and constraints, a deterministic robust counterpart problem is formulated to determine the optimal solution given the (relative) magnitude of uncertain data, feasibility tolerance, and “reliability level ” when a probabilistic measurement is applied. The robust optimization approach is then applied to the scheduling under uncertainty problem. Based on a novel and effective continuoustime shortterm scheduling model proposed by Floudas and coworkers [Ind. Eng. Chem. Res. 37 (1998a) 4341; Ind.
Global Optimization of MixedInteger Nonlinear Problems
 AIChE J
"... Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities ..."
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Cited by 14 (2 self)
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Two novel deterministic global optimization algorithms for nonconvex mixedinteger problems (MINLPs) are proposed, using the advances of the ffBB algorithm for nonconvex NLPs Adjiman et al. (1998a). The Special Structure MixedInteger ffBB algorithm (SMINffBB addresses problems with nonconvexities in the continuous variables and linear and mixedbilinear participation of the binary variables. The General Structure MixedInteger ffBB algorithm (GMINffBB), is applicable to a very general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are developed using the concepts of branchandbound, but they differ in their approach to each of the required steps. The SMINffBB algorithm is based on the convex underestimation of the continuous functions while the GMINffBB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval based variable bound updates to enhance effici...
MixedInteger Nonlinear Optimization in Process Synthesis
, 1998
"... The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the process synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw ma ..."
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Cited by 7 (0 self)
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The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the process synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process flowsheets. The mathematical modeling of the superstructure has a mixed set of binary and continuous variables and results in a mixedinteger optimization model. Due to the nonlinearity of chemical models, these problems are generally classified as MixedInteger Nonlinear Programming (MINLP) problems. A number of local optimization algorithms, developed for the solution of this class of problems, are presented in this pap...
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 2 (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...
Nonlinear and MixedInteger Optimization in Chemical Process Network Systems
"... . The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the Process Synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw ..."
Abstract
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. The use of networks allows the representation of a variety of important engineering problems. The treatment of a particular class of network applications, the Process Synthesis problem, is exposed in this paper. Process Synthesis seeks to develop systematically process flowsheets that convert raw materials into desired products. In recent years, the optimization approach to process synthesis has shown promise in tackling this challenge. It requires the development of a network of interconnected units, the process superstructure, that represents the alternative process flowsheets. The mathematical modeling of the superstructure has a mixed set of binary and continuous variables and results in a mixedinteger optimization model. Due to the nonlinearity of chemical models, these problems are generally classified as MixedInteger Nonlinear Programming (MINLP) problems. A number of local optimization algorithms for MINLP problems are outlined in this paper: Generalized Benders Decompositi...
Interaction of Design and Control: Optimization with Dynamic Models
, 1997
"... Process design is usually approached by considering the steadystate performance of the process based on an economic objective. Only after the process design is determined are the operability aspects of the process considered. This sequential treatment of the process design problem neglects the fact ..."
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Process design is usually approached by considering the steadystate performance of the process based on an economic objective. Only after the process design is determined are the operability aspects of the process considered. This sequential treatment of the process design problem neglects the fact that the dynamic controllability of the process is an inherent property of its design. This work considers a systematic approach where the interaction between the steadystate design and the dynamic controllability is analyzed by simultaneously considering both economic and controllability criteria. This method follows a process synthesis approach where a process superstructure is used to represent the set of structural alternatives. This superstructure is modeled mathematically by a set of differential and algebraic equations which contains both continuous and integer variables. Two objectives representing the steadystate design and dynamic controllability of the process are considered. T...
Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective ContinuousTime Formulation
 Ind. Engng. Chem. Res
"... this paper, we extend the formulation to address the problem of integrated design, synthesis and scheduling of multipurpose batch plants. ..."
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this paper, we extend the formulation to address the problem of integrated design, synthesis and scheduling of multipurpose batch plants.
Global Optimization with NonAnalytical Constraints
"... This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are nonanalytical (nonfactorable), defined by a computational model for which no explicit analytical representation is available. ..."
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This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are nonanalytical (nonfactorable), defined by a computational model for which no explicit analytical representation is available.