Nonlinear Programming Problem (nonlinear + programming_problem)

Distribution by Scientific Domains

Selected Abstracts

Application and comparison of metaheuristic techniques to reactive power planning problem

Mehdi Eghbal Non-Member
Abstract This paper presents the application and comparison of metaheuristic techniques to reactive power planning (RPP) problem which involves optimal allocation and combination of to-be-installed VAr sources to satisfy voltage constraints during normal and contingency states for multiple load levels. The main objective of the proposed RPP problem is to minimize the investment cost through balanced installation of SCs and SVCs while keeping a specified security level and minimizing the amount of load shedding. The problem is formulated as a large scale mixed integer nonlinear programming problem, which is a nonsmooth and nondifferentiable optimization problem using conventional optimization techniques and induces lots of local minima. Among the metaheuristic techniques, genetic algorithm (GA), particle swarm optimization (PSO) and evolutionary particle swarm optimization (EPSO) are applied to solve the RPP problem. To investigate the effectiveness of the metaheuristic techniques, the proposed approaches have been successfully tested on IEEE-14 buses, as well as IEEE-57 buses test system. The results obtained are compared and the effectiveness of each technique has been illustrated. Copyright © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

Designing globally optimal delta,sigma modulator topologies via signomial programming

Yuen-Hong Alvin Ho
Abstract We present a design methodology for globally optimizing the topologies of delta,sigma modulators (DSMs). Previous work cast the design task into a general non-convex, nonlinear programming problem, whereas we propose to recast it as a signomial programming problem. Convexification strategies are presented for transforming the signomial programming problem into its equivalent convex counterpart, thereby enabling the solution of globally optimal design parameters. It is also possible to include circuit non-ideal effects that affect the transfer function of the modulator into the formulation without affecting the computational efficiency. The proposed framework has been applied to topology synthesis problems of single-loop and multi-loop low-pass DSMs based on discrete-time circuitry. Numerical results confirm the effectiveness of the proposed approach over conventional nonlinear programming techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A multi-objective optimization approach to polygeneration energy systems design

AICHE JOURNAL, Issue 5 2010
Pei Liu
Abstract Polygeneration, typically involving co-production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large-scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity polygeneration plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non-convex mixed-integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

Optimal capacity in a coordinated supply chain

Xiuli Chao
Abstract We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source]

Direct optimization of dynamic systems described by differential-algebraic equations

Brian C. Fabien
Abstract This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the DAE are approximated using a Rosenbrock,Wanner (ROW) method. In this way the infinite-dimensional optimal control problem is transformed into a finite-dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming (QP) technique that minimizes the L, exact penalty function, using only strictly convex QP subproblems. This paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem and (ii) an efficient technique for evaluating the function, constraints and gradients associated with the NLP problem. This paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Reinsurance control in a model with liabilities of the fractional Brownian motion type

N. E. Frangos
Abstract We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Cell Population Modeling and Parameter Estimation for Continuous Cultures of Saccharomyces cerevisiae

Prashant Mhaskar
Saccharomyces cerevisiae is known to exhibit sustained oscillations in chemostats operated under aerobic and glucose-limited growth conditions. The oscillations are reflected both in intracellular and extracellular measurements. Our recent work has shown that unstructured cell population balance models are capable of generating sustained oscillations over an experimentally meaningful range of dilution rates. A disadvantage of such unstructured models is that they lack variables that can be compared directly to easily measured extracellular variables. Thus far, most of our work in model development has been aimed at achieving qualitative agreement with experimental data. In this paper, a segregated model with a simple structured description of the extracellular environment is developed and evaluated. The model accounts for the three most important metabolic pathways involved in cell growth with glucose substrate. As compared to completely unstructured models, the major advantage of the proposed model is that predictions of extracellular variables can be compared directly to experimental data. Consequently, the model structure is well suited for the application of estimation techniques aimed at determining unknown model parameters from available extracellular measurements. A steady-state parameter selection method developed in our group is extended to oscillatory dynamics to determine the parameters that can be estimated most reliably. The chosen parameters are estimated by solving a nonlinear programming problem formulated to minimize the difference between predictions and measurements of the extracellular variables. The efficiency of the parameter estimation scheme is demonstrated using simulated and experimental data. [source]

Nonlinear Predictive Control of Fed-Batch Cultures of Escherichia coli

S. Tebbani
Abstract A strategy for controlling a fed-batch Escherichia coli culture is described to maintain the culture at the boundary between oxidative and oxido-fermentative regimes. A nonlinear predictive controller is designed to regulate the acetate concentration, constraining the feed rate to follow an optimal reference profile which maximizes the biomass growth. For the sake of simplicity and efficiency, the original problem is converted into an unconstrained nonlinear programming problem, solved by control vector parameterization techniques. The robustness of the structure is further improved by explicitly including the difference between system and model prediction. A robustness study based on a Monte Carlo approach is used to evaluate the performance of the proposed controller. This control law is finally compared to the generic model control strategy. [source]

An algorithm for the use of surrogate models in modular flowsheet optimization

AICHE JOURNAL, Issue 10 2008
Josť A. Caballero
Abstract In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular process simulators in which the derivatives are not available and some unit operations introduce noise preventing the calculation of accurate derivatives. The black box modules are substituted by metamodels based on a kriging interpolation that assumes that the errors are not independent but a function of the independent variables. A Kriging metamodel uses non-Euclidean measure of distance to avoid sensitivity to the units of measure. It includes adjustable parameters that weigh the importance of each variable for obtaining a good model representation, and it allows calculating errors that can be used to establish stopping criteria and provide a solid base to deal with "possible infeasibility" due to inaccuracies in the metamodel representation of objective function and constraints. The algorithm continues with a refining stage and successive bound contraction in the domain of independent variables with or without kriging recalibration until an acceptable accuracy in the metamodel is obtained. The procedure is illustrated with several examples. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source]