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Esposito, William R.; Floudas, Christodoulos A.

doi:10.1023/a:1026578104213

Cited by 133 publications

(18 citation statements)

References 43 publications

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“…In chemical engineering dynamic processes arise in many applications and often an optimal trajectory is sought. For example we need the control path for optimal resource consumption in changes of product grade on polymer plants, estimating dynamic states for process control as well as in model building applications (Esposito and Floudas, 2000b;, design of batch systems in chemical engineering, including dynamic rectors and a system with a reactor, heat exchanger, separator and distillation column (Bhatia and Biegler, 1996), simultaneous dynamic optimisation for the calculation of optimal transient trajectories for a polymerisation process (Flores-Tlacuahuac et al, 2005), dynamic optimisation of distillation columns with particular focus on equilibrium constraints (Raghunathan et al, 2004), computation of optimal time trajectories for the control of the different flows in a simulated moving-bed process (Kloppenburg and Gilles, 1999), and a logic-based solution approach applied to a multistage batch distillation process of a ternary mixture (Oldenburg et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, their algorithms rigorously find all global optima within bounds or are at least able to provide a theoretical guarantee that the global optima have been found. A branch and bound framework was used with the αBB method (Adjiman et al, 1996) in a sequential approach and applied to four different optimal control problems including the optimal control of batch and semi-batch processes (Esposito and Floudas, 2000b), and to parameter estimation problems to determine reaction kinetic constants from time series data (Esposito and Floudas, 2000a). In principle the method of (Esposito and Floudas, 2000a,b) provides a guaranteed global optimum.…”

Section: Introductionmentioning

confidence: 99%

“…However, the set or relaxation used is merely a representation of the true solution set and when operations with overestimated values are propagated (in an integration algorithm for example) the result can be extremely overconservative. Esposito and Floudas (2000b) 7 1 Esposito and Floudas (2000a) 3 5 Papamichail and Adjiman (2002) 2 3…”

Section: Introductionmentioning

confidence: 99%

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Global optimisation for dynamic systems using interval analysis

Pérez-Galván

Bogle

2017

Computers & Chemical Engineering

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Engineers seek optimal solutions when designing dynamic systems but a crucial element is to ensure bounded performance over time. Finding a globally optimal bounded trajectory requires the solution of the ordinary differential equation (ODE) systems in a verified way. To date these methods are only able to address low dimensional problems and for larger systems are unable to prevent gross overestimation of the bounds. In this paper we show how interval contractors can be used to obtain tightly bounded optima. A verified solver constructs tight upper and lower bounds on the dynamic variables using contractors for initial value problems (IVP) for ODEs within a global optimisation method. The solver provides guaranteed bound on the objective function and on the first order sensitivity equations in a branch and bound framework. The method is compared with three previously published methods on three examples from process engineering.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global optimisation for dynamic systems using interval analysis

Pérez-Galván

Bogle

2017

Computers & Chemical Engineering

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“…Hence, in addition to the solution itself, these methods provide as output a rigorous interval within which the best possible solution (i.e., global optimum) must fall. Despite recent advances in deterministic global optimization methods [5,6], their application to parameter estimation has been quite scarce. Two main deterministic GO methods exist: spatial branch-and-bound (sBB) [2,5-7], and outer approximation [8].…”

Section: Introductionmentioning

confidence: 99%

“…This reformulated NLP was then solved by means of a sBB method. To this end, they constructed a convex relaxation of the reformulated problem following the α BB approach previously proposed by the authors [5-7]. Despite being valid for twice continuous differentiable functions, these relaxations may provide weak bounds in some particular cases and therefore lead to large CPU times when used in the context of a spatial branch and bound framework [9].…”

Section: Introductionmentioning

confidence: 99%

Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems

et al. 2012

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BackgroundThe estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens.ResultsThis work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied.ConclusionThe capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

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Research challenges, opportunities and synergism in systems engineering and computational biology

Floudas

2005

AIChE Journal

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Introduction During the last three decades, the research area of systems engineering has emerged as a domain of fundamental importance and major impact within chemical engineering, as well as a cornerstone area in interdisciplinary research initiatives with computer science, operations research, applied mathematics, materials and life sciences. This is attributed to the unique characteristics of systems engineering which are the combination of analysis and synthesis for the design, optimization, and operation of processes and products. The product and process discovery research efforts are founded on fundamental advances in mathematical modeling, optimization theory and algorithms, and insights derived either from existing operations and/or from biology, chemistry, and physics. The fundamental advances are epitomized through new theoretical, algorithmic, and modeling frameworks for (a) mixed-integer linear and nonlinear optimization, (b) deterministic global optimization, and (c) dynamic simulation and optimization. The proposed modeling and optimization approaches have multiscale applications ranging from macroscopic to mesoscopic to microscopic systems, and which provide a natural and fundamental link between systems engineering, computational chemistry, computational biology and systems biology. Approaches based on mixed-integer linear and nonlinear optimization which were typically identified with process synthesis, scheduling and planning applications, have entered the domains of gene regulatory networks, metabolic networks, signal transduction networks, beta-sheet topology prediction in proteins, de novo peptide and protein design, DNA recombination, phase problem in X-ray crystallography, side chain optimization in protein prediction, peptide identification via tandem mass spectroscopy. Approaches based on deterministic global optimization associated with process design, synthesis, scheduling, and pooling/blending applications, are now in the main stream of product design, structure prediction in protein folding, dynamics of protein folding, NMR protein structure refinement, and de novo protein design. Approaches based on dynamic models and large scale optimization which were identified with process models and their applications, are suited for metabolic and signal transduction networks. As a result, a synergism between systems engineering, computational biology, and systems biology has evolved gradually, opened new research avenues and has reached the stage where fascinating research contributions address important questions in computational biology with methods and tools from systems engineering which combine mathematical rigor with key biological insights.This article provides a perspective on the challenges and opportunities that emerge from the fundamental developments in the research fields of systems engineering and computational biology. The advances in the areas of deterministic global optimization and process scheduling are introduced first, followed by their respective research opportunities. Th...

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Cited by 133 publications

References 43 publications

Global optimisation for dynamic systems using interval analysis

Global optimisation for dynamic systems using interval analysis

Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems

Research challenges, opportunities and synergism in systems engineering and computational biology

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