Realistic Objective Function Research Articles

Dynamic Optimal Ground Water Remediation by Granular Activated Carbon

Objective functions to describe the operating and capital costs of granular activated carbon (GAC) treatment are incorporated into a management model for dynamic optimal pump-and-treat groundwater remediation design. The optimization approach, quasi-Newton differential dynamic programming including a constant shift in the Hessian matrix, could not reliably handle the nonconvex objective functions for GAC system. To avoid the nonconvexity, linearized iterative approximations of operating costs were used to solve the multiple management period problem, although this approach does not guarantee global optimality for the original nonconvex objective function. Repeated optimizations assuming different size absorbers were required to consider the fixed costs of the GAC system. Basing the cost function on concentrations at the beginning of each management period provided reasonable conservative cost estimates. Dynamic policies were found to be superior to steady-state policies even when capital costs of treatment were included. This work suggests that improvements in the differential dynamic programming algorithm may be needed for it to be robust technique for realistic nonconvex objective functions.

Stoichiometric model ofEscherichia coli metabolism: Incorporation of growth-rate dependent biomass composition and mechanistic energy requirements

A stoichiometric model of metabolism was developed to describe the balance of metabolic reactions during steady-state growth of Escherichia coli on glucose (or metabolic intermediates) and mineral salts. The model incorporates 153 reversible and 147 irreversible reactions and 289 metabolites from several metabolic data bases for the biosynthesis of the macromolecular precursors, coenzymes, and prosthetic groups necessary for synthesis of all cellular macromolecules. Correlations describing how the cellular composition changes with growth rate were developed from experimental data and were used to calculate the drain of precursors to macromolecules, coenzymes, and prosthetic groups from the metabolic network for the synthesis of those macromolecules at a specific growth rate. Energy requirements for macromolecular polymerization and proofreading, transport of metabolites, and maintenance of transmembrane gradients were included in the model rather than a lumped maintenance energy term. The underdetermined set of equations was solved using the Simplex algorithm, employing realistic objective functions and constraints; the drain of precursors, coenzymes, and prosthetic groups and the energy requirements for the synthesis of macromolecules served as the primary set of constraints. The model accurately predicted experimentally determined metabolic fluxes for aerobic growth on acetate or acetate plus glucose. In addition, the model predicted the genetic and metabolic regulation that must occur for growth under different conditions, such as the opening of the glyoxylate shunt during growth on acetate and the branching of the tricarboxylic acid cycle under anaerobic growth. Sensitivity analyses were performed to determine the flexibility of pathways and the effects of different rates and growth conditions on the distribution of fluxes. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 398-421, 1997.

Stoichiometric model of Escherichia coli metabolism: Incorporation of growth‐rate dependent biomass composition and mechanistic energy requirements

A stoichiometric model of metabolism was developed to describe the balance of metabolic reactions during steady-state growth of Escherichia coli on glucose (or metabolic intermediates) and mineral salts. The model incorporates 153 reversible and 147 irreversible reactions and 289 metabolites from several metabolic data bases for the biosynthesis of the macromolecular precursors, coenzymes, and prosthetic groups necessary for synthesis of all cellular macromolecules. Correlations describing how the cellular composition changes with growth rate were developed from experimental data and were used to calculate the drain of precursors to macromolecules, coenzymes, and prosthetic groups from the metabolic network for the synthesis of those macromolecules at a specific growth rate. Energy requirements for macromolecular polymerization and proofreading, transport of metabolites, and maintenance of transmembrane gradients were included in the model rather than a lumped maintenance energy term. The underdetermined set of equations was solved using the Simplex algorithm, employing realistic objective functions and constraints; the drain of precursors, coenzymes, and prosthetic groups and the energy requirements for the synthesis of macromolecules served as the primary set of constraints. The model accurately predicted experimentally determined metabolic fluxes for aerobic growth on acetate or acetate plus glucose. In addition, the model predicted the genetic and metabolic regulation that must occur for growth under different conditions, such as the opening of the glyoxylate shunt during growth on acetate and the branching of the tricarboxylic acid cycle under anaerobic growth. Sensitivity analyses were performed to determine the flexibility of pathways and the effects of different rates and growth conditions on the distribution of fluxes. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 398–421, 1997.

Efficient algorithm for virtual topology design in multihop lightwave networks

One of the major challenges in the virtual topology design of a WDM star based system, is to incorporate in the optimization process both realistic objective functions and real system behavior. The authors present an efficient discrete optimization algorithm that meets these goals while incorporating the prevailing traffic conditions. They simulate the real system and then approximate the objective function by a short term simulation. The optimization process is based on an ordinal optimization approach, i.e., is insensitive to the approximation of the objective function obtained by short term simulation. Another crucial issue in virtual topology design is how to evaluate the quality of the solution obtained by the algorithm. They propose a new metric to evaluate the solution quality, the so called suboptimal quality, obtained by deriving the solution's relative position in the state space according to the performance order. The experiments presented in the paper attest to the quality (efficiency and robustness) of the optimization algorithm and its suitability to solve the wavelength assignment problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An approach to structure/control simultaneous optimization for largeflexible spacecraft

This paper presents an approach to the simultaneous optimal design of a structure and control system for large flexible spacecrafts based on realistic objective function and constraints. The weight or total cost of structure and control system is minimized subject to constraints on the magnitude of response to a given disturbance involving both rigid-body and elastic modes. A nested optimization technique is developed to solve the combined problem. As an example, simple beam-like spacecraft under a steady-state white-noise disturbance force is investigated and some results of optimization are presented. In the numerical examples, the stiffness distribution, location of controller, and control gains are optimized. Direct feedback control and linear quadratic optimal controls laws are used with both inertial and noninertial disturbing force. It is shown that the total cost is sensitive to the overall structural stiffness, so that simultaneous optimization of the structure and control system is indeed useful.

Politically realistic objective functions and trade policy PROFs and tariffs

This paper demonstrates a mathematical correspondence between the deus ex machina tariff formation approach and political economy approach. The correspondence implies that the tariff chosen by lobbying-influenced policy makers will be equivalent to a tariff chosen by a deus ex machina government that gives ‘too much’ weight to profits. This result allows many political economy issues to be addressed in the simple framework of a deus ex machina government which faces a politically realistic objective function (PROF).

Failure Diagnosis Using Quadratic Programming

This paper discusses the problem of determining which of a large set of possible but improbable malfunctions gave rise to a given set of measurements. The classes of systems under consideration generally lead to underdetermined sets of equations. Three methods of formulating and solving this class of problems are presented: 1) the pseudoinverse method: this leads to an easily-solved computational problem but it is not physically realistic and it tends to give poor results; 2) a pattern recognition approach based on a more realistic problem formulation: unfortunately, the computational problems associated with this formulation may be formoidable; and 3) a quadratic programming approack: this is based on minimization of a physically realistic objective function. A bmaosdification to eliminate discontinuities in the objetive function and a quasilinearization transform the original problem to an inequality-constrained quadratic minimization problem, which is readily solved by Lemke's complementary pivoting method. A sequence of successive quasilinearizations and estimations is defilned which is proved to converge to a minimum of the original objective function. In tests this convergence occurred very fast. Examples are given; very general classes of problems are discussed which can be handled in this way.

Legal Constraints on Urban Water Systems

Strategic level decisions regarding urban water management are largely political, whereas tactical level water decisions are mostly administrative. Both are subject to legal constraints. In a systems study, it is desirable to find ways to improve a water system such that the level of performance of the system is improved. Legal constraints which inhibit such improvement are classified and their effect on a typical regional water system, Denver, Colo., is considered briefly. It is shown that a clear statement of goals is necessary in order to formulate a realistic objective function. To speak of optimizing such a function in a general urban sense is overly ambitious at this time because of the severity of the constraints on the system. To consider the general issues in a systems framework is useful, however, because it focuses on the important problem areas so that fruitful debate can occur.