An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method...
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An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed ineffective, a trust region iteration that guarantees progress toward stationarity is invoked. To demonstrate its effectiveness, the algorithm is implemented in the Knitro [6,28] software package and is extensively tested on a wide selection of test problems.
Multiwavelength laser exposures pose unique safety challenges for both laser experts and users of laser systems. We describe two methods of optimizing optical density requirements for multiwavelength laser exposures. ...
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Multiwavelength laser exposures pose unique safety challenges for both laser experts and users of laser systems. We describe two methods of optimizing optical density requirements for multiwavelength laser exposures. The problem is first formulated and solved using standard mathematical programming techniques, and the results are compared to those from a simplified algorithm. The result is a method that can be efficiently integrated into existing laser modeling and hazard analysis software. As an example, overall visible light transmittance is maximized while maintaining eye-safe viewing conditions during a multiwavelength exposure, simultaneously minimizing the total optical density required for sufficient laser eye protection. This optimization formulation helps laser system users determine the proper laser eye protection for safe viewing in multiwavelength laser environments. (c) 2006 Laser Institute of America.
The aim of this study is to expand the application of the nonlinear softened truss model for membrane elements on beam-column joints. The softened truss model employs three equations for equilibrium, three for compati...
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The aim of this study is to expand the application of the nonlinear softened truss model for membrane elements on beam-column joints. The softened truss model employs three equations for equilibrium, three for compatibility and four equations for the constitutive laws of materials. The constitutive equations for both the concrete and steel are based on the actually observed stress-strain relationships. The model has three important attributes. The first is the nonlinear association of stress and strain. The second, and conceivably more noteworthy, is the softening of concrete in compression due to tensile strains in the perpendicular direction. The third is that the influence of the concrete tensile stresses between cracks on the average stress-strain relationship for reinforcing steel and the influence of orthogonal tensile stresses on the compression stress-strain relationship for concrete can be considered in the model. For beam-column joints, one of the most important factors influencing the behaviour is certainly the bond conditions of the beam bars. In this study, the softened truss model is expanded to take into account the influence of this important factor into account. In the revised version of the model, full strain compatibility does not exist between the steel reinforcement and the surrounding concrete and thus the factors influencing the bond-slip between concrete and reinforcement is adequately considered. The improved softened truss model is applied on 51 exterior beam-column joint tests. It is apparent from the results that the revised model gives very accurate predictions of the shear strength of joints and is an improvement on the existing version of the model proposed by Hsu. (c) 2005 Elsevier Ltd. All rights reserved.
Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the quasi-Newton method used...
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Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the quasi-Newton method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea is to use the estimated subgradient calculated from different replications and a metric matrix updated from the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to yield a quasi-Newton search direction. To avoid misjudging the minimal point, in both the line search and the quasi-Newton iterations, due to the stochastic nature, a t-test instead of a simple comparison of the mean responses is performed. It is proved that the resulting stochastic quasi-Newton algorithm is able to generate a sequence that converges to the optimal point, under certain conditions. Empirical results from a four-station queueing problem and an (s,S) inventory problem indicate that this method is able to find the optimal solutions in a statistical sense. Moreover, this method is robust with respect to the number of replications conducted at each trial point. (c) 2005 Elsevier B.V. All rights reserved.
Global convergence to first-order critical points is proved for a variant of the trust-region SQP-filter algorithm analyzed in (Fletcher, Gould, Leyffer and Toint). This variant allows the use of two types of step str...
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The availability of electric engines as primary sources of propulsion has opened the doors to new scenarios for future interplanetary missions, but has increased the complexity of trajectory design. This paper propose...
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The availability of electric engines as primary sources of propulsion has opened the doors to new scenarios for future interplanetary missions, but has increased the complexity of trajectory design. This paper proposes a novel approach to the preliminary design of interplanetary trajectories, characterized by a combination of low-thrust, propulsion and multiple gravity-assist maneuvers. Low-thrust arcs are obtained by shaping the trajectory through a set of parameterized pseudoequinoctial elements. The characterization of the solution space for a particular set of planetary encounters and a range of launch dates is then performed through a global optimization method;blending a particular evolutionary algorithm with a deterministic domain decomposition technique. The effectiveness of the proposed approach is demonstrated through a number of examples of the design of low-thrust, gravity-assist interplanetary trajectories.
This paper proposes an optimized dispatch control strategy for active and reactive powers delivered by a doubly fed induction generator in a wind park. In this control approach, wind turbines are supposed to operate o...
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This paper proposes an optimized dispatch control strategy for active and reactive powers delivered by a doubly fed induction generator in a wind park. In this control approach, wind turbines are supposed to operate over a deloaded maximum power extraction curve and with respond to a supervisory wind farm control after a request from a system operator for adjusting the outputs of the wind park. The definition of the active and reactive powers operating points, for each wind turbine, is defined from an optimization algorithm that uses the primal-dual predictor corrector interior point method. The control strategy used at the wind generator level exploits a combination of pitch control and control of the static converters to adjust the rotor speed for the required operation points. A small wind park is used to illustrate the effectiveness of the developed approach.
nonlinear equality and inequality constrained optimization problems with uncertain parameters can be addressed by a robust worst-case formulation that is, however, difficult to treat computationally. In this paper we ...
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nonlinear equality and inequality constrained optimization problems with uncertain parameters can be addressed by a robust worst-case formulation that is, however, difficult to treat computationally. In this paper we propose and investigate an approximate robust formulation that employs a linearization of the uncertainty set. In case of any norm bounded parameter uncertainty, this formulation leads to penalty terms employing the respective dual norm of first order derivatives of the constraints. The main advance of the paper is to present two sparsity preserving ways for efficient computation of these derivatives in the case of large scale problems, one similar to the forward mode, the other similar to the reverse mode of automatic differentiation. We show how to generalize the techniques to optimal control problems, and discuss how even infinite dimensional uncertainties can be treated efficiently. Finally, we present optimization results for an example from process engineering, a batch distillation.
The optimal design of multiple tuned mass dampers (multiple TMD's) to suppress multi-mode structural response of beams and floor structures was investigated. A new method using a numerical optimizer, which can eff...
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The optimal design of multiple tuned mass dampers (multiple TMD's) to suppress multi-mode structural response of beams and floor structures was investigated. A new method using a numerical optimizer, which can effectively handle a large number of design variables, was employed to search for both optimal placement and tuning of TMD's for these structures under wide-band loading. The first design problem considered was vibration control of a simple beam using 10 TMD's. The results confirmed that for structures with widely-spaced natural frequencies, multiple TMD's can be adequately designed by treating each structural vibration mode as an equivalent SDOF system. Next, the control of a beam structure with two closely-spaced natural frequencies was investigated. The results showed that the most effective multiple TMD's have their natural frequencies distributed over a range covering the two controlled structural frequencies and have low damping ratios. Moreover, a single TMD can also be made effective in controlling two modes with closely spaced frequencies by a newly identified control mechanism, but the effectiveness can be greatly impaired when the loading position changes. Finally, a realistic problem of a large floor structure with 5 closely spaced frequencies was presented. The acceleration responses at 5 positions on the floor excited by 3) wide-band forces were simultaneously suppressed using 10 TMD's. The obtained multiple TMD's were shown to be very effective and robust.
A new optimal reactive power flow (ORPF) model in rectangular form is proposed in this paper. In this model, the load tap changing (LTC) transformer branch is represented by an ideal transformer and its series impedan...
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A new optimal reactive power flow (ORPF) model in rectangular form is proposed in this paper. In this model, the load tap changing (LTC) transformer branch is represented by an ideal transformer and its series impedance with a dummy node located between them. The voltages of the two sides of the ideal transformer are then used to replace the turn ratio of the LTC so that the ORPF model becomes quadratic. The Hessian matrices in this model are constants and need to be calculated only once in the entire optimal process, which speed up the calculation greatly. The solution of the ORPF problem by the predictor corrector primal dual interior point method is described in this paper. Two separate prototypes for the new and the conventional methods are developed in MATLAB in order to compare the performances. The results obtained from the implemented seven test systems ranging from 14 to 1338 buses indicate that the proposed method achieves a superior performance than the conventional rectangular coordinate-based ORPF.
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