A general class of n-dimensional direct (derivative-free) optimization procedures is introduced for solving multiextremal mathematical programming problems. For the case of minimizing a Lipschitz-continuous objective ...
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作者：
TAVAKOLI, MSHOUSER, DRM. S. Tavakoli
D. R. Houser Gear Dynamics and Gear Noise Research Laboratory The Ohio State University 206 W. 18th Avenue Columbus Ohio 43210
A procedure for computing static transmission errors and tooth load sharing was developed for low and high contact ratio internal and external spur gears. A suitable optimization algorithm was used to minimize any com...
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A procedure for computing static transmission errors and tooth load sharing was developed for low and high contact ratio internal and external spur gears. A suitable optimization algorithm was used to minimize any combination of the harmonics of gear mesh frequency components of the static transmission error. Different combinations of tip and root relief may be used to achieve optimization. These include varying the starting point of relief and varying the magnitude of relief, and selecting the gear and/or the pinion teeth to be tip and/or root-relieved. Also, there exists an option for using either linear or parabolic relief. In addition to the presentation of optimal profile modifications, the effects of off-design loads, nonoptimum modifications, and random spacing errors are presented.
The orthogonal collocation approach is now well known to solve, effectively, the state constrained optimal control problems. Mathematical programming technique was also used as an effective tool to construct the optim...
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The orthogonal collocation approach is now well known to solve, effectively, the state constrained optimal control problems. Mathematical programming technique was also used as an effective tool to construct the optim...
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The orthogonal collocation approach is now well known to solve, effectively, the state constrained optimal control problems. Mathematical programming technique was also used as an effective tool to construct the optimal trajectories. In this paper, a study is done on the efficiency and accuracy requirements of the combined orthogonal collocation and mathematical programming approach, as regarding the employed optimization algorithm, and the number of orthogonal collocation points. It is shown, by experimentation with numerical examples that Fletcher-Powell optimization algorithm is much more faster to produce convergence than Fletcher-Reeves algorithm. The efficiency can be a ratio of six-to-one. The results are compared with an alternative approach to solve the same problem. It is shown that the present algorithm is less costly than the alternative approach, although requiring more computation time. The choice is then a compromise one. As the number of orthogonal points increases, the resulting solutions are more accurate, but the convergence speed decreases. Experimentation with N, shows a save of five-to-one in computing time can be achieved with almost the same cost function. Finally, it is shown, by a numerical example, that uniformly distributed collocation points result in non-optimal solutions, which also violate the problem constraints. It is a numerical proof of the superiority of the orthogonal collocation approach.
This paper presents three general schemes for extending differentiable optimization algorithms to nondifferentiable problems. It is shown that the Armijo gradient method, phase-I–phase-II methods of feasible directio...
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This paper presents three general schemes for extending differentiable optimization algorithms to nondifferentiable problems. It is shown that the Armijo gradient method, phase-I–phase-II methods of feasible directions and exact penalty function methods have conceptual analogs for problems with locally Lipschitz functions and implementable analogs for problems with semismooth functions. The exact penalty method has required the development of a new optimality condition.
The problem of choosing buffer allocation strategies occurs in the design of any store-and-forward computer network. A good buffer allocation strategy can reduce message blocking; and hence provide more efficient use ...
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The problem of choosing buffer allocation strategies occurs in the design of any store-and-forward computer network. A good buffer allocation strategy can reduce message blocking; and hence provide more efficient use of network storage resources. We first summarize five buffer allocation strategies and then provide algorithms for determining the minimum buffer sizes required by these strategies given that each outgoing channel must satisfy certain blocking requirements. After that, we compare them under different network conditions such as heavy or light input traffic rate, uniform or non-uniform server utilization and different blocking requirements. Guidelines on which strategy to use under different conditions are also given.
This paper describes an optimization algorithm which uses up torth-order derivatives to find the optimum of anr-times continuously differentiable function of many variables. The algorithm, developed by Kalaba and Tish...
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This paper describes an optimization algorithm which uses up torth-order derivatives to find the optimum of anr-times continuously differentiable function of many variables. The algorithm, developed by Kalaba and Tishler (Ref. 1), obtains the exact values of the derivatives required for the optimization from the table algorithm presented in Kalabaet al. (Ref. 2) and Kalaba and Tishler (Ref. 3). The optimization algorithm described here reduces to the well-known Newton-Raphson algorithm when only first-order and second-order derivatives are used.
Whether in storm or normal seas, the ideal offshore cable-stayed compliant tower moves in harmony with the wind and waves. A properly tuned cable configuration is the key to controlled dynamic response. Formulated her...
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Whether in storm or normal seas, the ideal offshore cable-stayed compliant tower moves in harmony with the wind and waves. A properly tuned cable configuration is the key to controlled dynamic response. Formulated here are a nonlinear dynamic model involving wind, wave, current, tower, and cable interactions and a cable optimization algorithm. The objective function, the rms tower rotation, is minimized subject to appropriate constraints involving compatible system geometries and loads, as well as bounds on the platform level accelerations needed for human comfort. Tower motion is limited to a plane.
In this paper we describe an extension of an existing optimization technique to the tolerance design of a printer actuator mechanism. We provide the designer with a method for selecting optimal nominal design values f...
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In this paper we describe an extension of an existing optimization technique to the tolerance design of a printer actuator mechanism. We provide the designer with a method for selecting optimal nominal design values for the parameters of a generalized system which allows maximum tolerance excursions away from the nominal design values and yet still maintains performance standards. The method uses an interactive linear-programming based design optimization algorithm to select optimal nominal parameter values and their associated maximal tolerances. We illustrate the method with a simple two-dimensional example. Finally we show the results from the tolerance optimization of a printer actuator which demonstrates the applicability of the theory to a real design problem.
This paper presents a general optimization algorithm using first-order torth order derivatives to find the optimum of anr-continuously differentiable function of many variables. This algorithm collapses to the Newton-...
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This paper presents a general optimization algorithm using first-order torth order derivatives to find the optimum of anr-continuously differentiable function of many variables. This algorithm collapses to the Newton-Raphson algorithm when only first- and second-order derivatives are used. The computation of the required higher-order derivatives are readily available through thetable algorithm. The generalized CES production function is used as an example.
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