In this work, we first discuss recent advances towards the integration of process design, process control and process operability from the open literature and then we focus on techniques towards this endeavor that wer...
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In this work, we first discuss recent advances towards the integration of process design, process control and process operability from the open literature and then we focus on techniques towards this endeavor that were developed within our group at Imperial College. While most of the approaches employ controllability measures to achieve this goal, our developments can be classified as a simultaneous process and control design methodology. Based on novel mixed integer dynamic optimization algorithms, our strategy features high fidelity process dynamic models, conventional PI control schemes, explicit consideration of structural process and control design aspects (such as number of trays, pairing of manipulated and controlled variables) through the introduction of 0-1 variables, and explicit consideration of time-varying disturbances and time-invariant uncertainties. The application of this strategy to a typical distillation system is discussed. In the second part of this chapter we present an extension of the process and control design framework that incorporates advanced model-based predictive controllers. parametric programming is used for the controller derivation giving rise to a closed-form controller structure and removing the need for solving an optimization problem on-line. The resulting parametric controller is readily incorporated in the design optimization framework bringing about significant economic and operability benefits. The key features and advantages of this approach are highlighted via a simple binary distillation example. (C) 2004 Elsevier Ltd. All rights reserved.
The global optimization of the sum of linear fractional functions has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are nonconvex, various sp...
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The global optimization of the sum of linear fractional functions has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are nonconvex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms may be difficult to implement and are usually relatively inaccessible. In this article, we show that, by using suitable transformations, a number of potential and known methods for globally solving these problems become available. These methods are often more accessible and use more standard tools than the customized algorithms proposed to date. They include, for example, parametric convex programming and concave minimization methods.
The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, a...
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The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, and Karush-Kuhn-Tucker (KKT)-methods are applied to obtain equivalent problems or relaxations of a simpler structure. The relaxations are viewed as a perturbation P-tau of the original problem P, depending on a perturbation parameter tau > 0, and are analyzed by using parametric programming techniques. We give convergence results and results on the rate of convergence for the minimal values and the optimal solutions of P-tau when tau tends toward 0. We review earlier studies and present new ones.
Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex). (C) 2003 Published by Elsevier B.V.
Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex). (C) 2003 Published by Elsevier B.V.
Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex). (C) 2003 Published by Elsevier B.V.
Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex). (C) 2003 Published by Elsevier B.V.
In Fuzzy Optimization is desirable that fuzzy solutions can be really attained because then the decision maker will be able of making a decision "a posteriori" according to the current decision environment. ...
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ISBN:
(纸本)0780385667
In Fuzzy Optimization is desirable that fuzzy solutions can be really attained because then the decision maker will be able of making a decision "a posteriori" according to the current decision environment. In this way, no more runs of the optimization technique are needed when decision environment changes or when decisor requires check out several decisions in order to stablish the more appropriates. In this sense, Multi-objective optimization is similar to Fuzzy optimization, since it's also desirable to capture the Pareto front composing the solution. Multi-objective Evolutionary Algorithms have been shown in the last few years as powerfull techniques to solve multi-objective optimization problems because they can search for multiple Pareto solutions in a single run of the algorithm. In this contribution we first introduce a multi-objective approach for nonlinear constrained optimization problems with fuzzy costs, and then all "ad hoc" multi-objective evolutionary algorithm to solve the former problem. A case-study of a fuzzy optimization problem arising in some import-export companies in the south of Spain is analised and the proposed solutions from the evolutionary algorithm here considered are shown.
Although work has been carried out on parametric programming on CNC centres, there have been few papers which focus on error compensation. parametric programming for error compensation is presented in this paper on th...
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Although work has been carried out on parametric programming on CNC centres, there have been few papers which focus on error compensation. parametric programming for error compensation is presented in this paper on the basis of a simple model of machining system deflections induced by the radial cutting force in CNC turning operations. The resulting errors are introduced as compensation values to the conventional tool movements along the programmed tool path. This can result in a complex tool path. parametric programming is applied to handle this complexity for error compensation.
Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: th...
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Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programining formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations.
This work proposes a novel methodology to solve scheduling problems under uncertainty using parametric programming. Uncertainty, such as in processing times and equipment availabilities, is incorporated into schedulin...
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This work proposes a novel methodology to solve scheduling problems under uncertainty using parametric programming. Uncertainty, such as in processing times and equipment availabilities, is incorporated into scheduling models, which are then transformed into multi-parametric mixed integer linear programming (mp-MILP) problems. A solution procedure based upon recently proposed mp-MILP algorithms is then discussed. The key advantage of the proposed methodology is that the complete map of optimal schedules can be obtained as a function of varying parameters; rescheduling can thus be performed via simple function evaluations without any further optimization. Numerical examples are presented to illustrate the significance of the proposed methodology.
In this paper an algorithm is presented for the derivation of the explicit optimal control policy for linear dynamic systems that also involve (i) discrete decisions and (ii) constraints on process inputs and outputs....
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In this paper an algorithm is presented for the derivation of the explicit optimal control policy for linear dynamic systems that also involve (i) discrete decisions and (ii) constraints on process inputs and outputs. The control actions are usually computed by solving regularly an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in this paper derives the optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.
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