Direct Search Technique Research Articles

Optimum design of thin-walled closed cross-sections: a numerical approach

In this paper, the problem of optimum design of a thin-walled closed cross-section is presented. The problem consists in minimizing the material area of a thin-walled closed cross-section symmetrical with respect to both x and y centroidal axes, and subjected to flexural and torsional rigidity constraints and strength constraints. The unknown function is the middle line of the thin-walled closed cross-section while its thickness is t prescribed. The solution approach is numerical and the minimizing procedure is based on an improved simulated annealing method, a simple but robust direct search technique that works well on fast PCs.

Controller Design via Nonsmooth Multi-Directional Search

We propose an algorithm which combines multi-directional search (MDS) with nonsmooth techniques such as bundling to solve several difficult synthesis problems in automatic control. Applications include static and fixed-order output feedback controller design, simultaneous stabilization, H2/H∞ synthesis to cite just a few. We show in which way direct search techniques may be safeguarded by nonsmooth oracles in order to maintain convergence certificates in the presence of nonsmoothness. Our numerical testing includes numerous benchmark examples. For instance, our algorithm needs 0.41 seconds to compute a static output feedback stabilizing controller for the Boeing 767 flutter benchmark problem (E.J. Davison, 1990), a system with 55 states.

Global optimisation-based control algorithms applied to boundary layer transition problems

Turbulent flow has a significantly higher drag than the corresponding laminar flow at the same flow conditions. The presence of turbulent flow over a large part of an aircraft therefore incurs a significant penalty of increased fuel consumption due to the extra thrust required. One possible way of decreasing the drag is to apply surface suction to delay the transition from laminar to turbulent flow. However, in order for the gain from the reduction in drag to outweigh the extra costs associated with the suction system, the suction must be distributed in an optimum, or near optimum, manner. In this paper two practical cases are considered. In the first of these a flat plate with panels whose positions are adjustable but do not overlap is treated. Since the cost function in this case is multi-modal, non-smooth and non-convex, methods for solving the optimisation problems necessary to design multi-panel suction systems based on direct search techniques are developed. In the second case considered the problem is that of linear distributed suction over the front part of an aerofoil. For this case, the computational load increases so significantly that in some cases it is not really feasible to continue the investigation using a single processor code. To overcome this, three parallel global optimisation algorithms are developed for the design of multi-panel suction systems on an aerofoil and it is shown that good solutions can be found efficiently.

Procedure for Optimum Design of a Two-Stage Spur Gear System

In this paper, an optimum design of a two-stage spur gear system is performed. The optimization is based on a multicriterion technique consisting of a Min-Max method combined with a direct search technique. The optimum design includes the minimization of seven objective functions. They are the volume of gears, the center distance and five dynamic factors in the input shaft, first-teeth meshing, intermediate shaft, second meshing and the output shaft. The dynamic factors are estimated using a dynamic model of twelve degrees of freedom. The objective functions are governed by eleven design variables, chosen to be the number of teeth and face width of the pinion of each stage, stiffness of the input, intermediate, and output shafts and the inertia of the four gears of the mechanism. The developed optimum design is found to give compact-gear system with quiet running (minimum dynamic factors) compared with the classical design. The angle between the power transmitting directions is found to have an important role on the objective functions and the optimum design. A value of 180° for this angle is found to be the optimal for all functions.

Optimum Design of Squeeze Film Dampers Supporting Multiple-Mode Rotors

In this paper a study of the optimum design of squeeze film dampers for multimode rotors is presented. The optimum design program obtains the best possible damper parameters for a given rotor to satisfy the minimization requirements for the objective function. The objectives are to minimize the amplitude response of the rotor at the critical speed, minimize the force transmitted to the support at the operating speed, or maximize the power dissipated by the damper. A combination of these objectives can also be used, with weighting factors to weigh the importance of each of these objectives. These are the possible objectives for the design of squeeze film dampers for aircraft engine applications. The basis of the optimum design program is an extremely fast algorithm which is able to quickly calculate the unbalance response of a rotor, for circular centered orbits of the journal in the damper. A commercial routine is used for the optimization, and is based on a complex direct search technique. The variation of the optimum clearance, length, and retainer spring stiffness are plotted against various rotor parameters. Recommendations for the design of squeeze film dampers are made. Applications to an aircraft engine illustrate the power of the developed algorithm.

An optimisation study of a hydraulic breaking system

This paper describes a computer-aided optimisation study of a hydraulic breaking system capable of withstanding 2000 kN of breaking forces. A mathematical model for the breaking system was formulated and good agreement was obtained between the predicted and measured results. The mathematical model is linked with an optimisation algorithm to search for combinations of design variables that produce the optimum system performance and the study used a multi-variable constrained direct-search optimisation technique. The case in question consists of some 48 free variables that are geometrically related and are highly constrained in a search domain of a 49 dimensional hyperspace. Results reconfirm the value of computer-aided optimisation in engineering design application.

Robust optimization of total joint replacements incorporating environmental variables.

Direct search techniques for the optimal design of biomechanical devices are computationally intensive requiring many iterations before converging to a global solution. This, along with the incorporation of environmental variables such as multiple loading conditions and bone properties, makes direct search techniques infeasible. In this study, we introduced new methods that are based on the statistical design and analysis of computer experiments to account efficiently for environmental variables. Using data collected at a relatively small set of training sites, the method employs a computationally inexpensive predictor of the structural response that is statistically motivated. By using this predictor in place of the simulator (e.g., finite element model), a sufficient number of iterations can be performed to facilitate the optimization of the complex system. The applicability of these methods was demonstrated through the design of a femoral component for total hip arthroplasty incorporating variations in joint force orientation and cancellous bone properties. Beams on elastic foundation (BOEF) finite element models were developed to simulate the structural response. These simple models were chosen for their short computation time. This allowed us to represent the actual structural response surface by an exhaustive enumeration of the design and environmental variable space, and provided a means by which to validate the statistical predictor. We were able to predict the structural response and the optimal design accurately using only 16 runs of the computer code. The general trends predicted by the BOEF models were in agreement with previous three-dimensional finite element computer simulations, and experimental and clinical results, which demonstrated that the important features of intramedullary fixation systems were captured. These results indicate that the statistically based optimization methods are appropriate for optimization studies using computationally demanding models.

Use of tensor product splines in magnet optimization

Variational metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated.

Demand-side optimal selection of switching devices in radial distribution system planning

Optimal selection of distribution system switching devices is an important consideration in system planning and operation. The paper formulates the generalised optimisation problem of switching device selection incorporating customer demand-side considerations. This optimisation problem is nonlinear and nondifferentiable with a finite number of solutions. The paper presents a direct search technique and a bisection approach to solve this problem. The two techniques are illustrated and compared using practical distribution systems.

Self-adjusting dynamic binary phase holograms

An optical system constructed around a dynamic diffractive optic element, a ferroelectric liquid-crystal spatial light modulator in binary phase-only modulation mode, is investigated. The spatial light modulator is successively adjusted according to the direct binary search technique to diffract an incoming laser light beam into a predecided intensity distribution by use of feed back from the diffracted light. It was found that the feedback signal was noisy and that vibrations and limited bistability in the spatial light modulator's pixels were the main noise sources. The final diffraction efficiency depends on the degree of noise in the feedback signal, but even under fairly noisy conditions the iterations were found to converge properly.

A hybrid technique for the optimal design of electromagnetic devices using direct search and genetic algorithms

Genetic algorithms (GAs) have been successfully applied to optimization problems in a variety of applications in electromagnetics. In this paper, GAs are used along with a gradient-based direct search technique. The proposed hybrid optimization procedure was found to be efficient in most of the applications. The strengths of both techniques are used at different stages of the search. A magnetizer example is presented to show the effectiveness of the proposed technique.

Use of advanced techniques to optimize a multi-dimensional dairy model

Available methods for the optimization of agricultural systems vary widely, in terms of derivation, applicability and performance. A whole-farm dairying model with 16 separate, interacting managerial options was optimized by the hill-climbing (quasi-Newton), direct search (simplex), genetic algorithm (GENESIS) and simulated annealing (VFSR) techniques. The latter two clearly out-performed the former, with simulated annealing always identifying the global optimum.

Optimal design techniques applied to transverse-flux induction heating systems

In this paper an optimization procedure for the optimal design of a transverse-flux induction heating system is presented. Hooke and Jeeves (1961) direct search technique is used for the optimization procedure. The finite element method is used for the electromagnetic field calculation and the integral parameter determination. The results obtained by this procedure are compared with those available in literature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Numerical analysis of electrical defibrillation: The parallel approach

Numerical modeling offers a viable tool for studying electrical defibrilation, allowing the behavior of field quantities to be observed easily as the different system parameters are varied. One numerical technique, namely the finite-element method, has been found particularly effective for modeling complex thoracic anatomies. However, an accurate finite-element model of the thorax often requires a large number of elements and nodes, leading to a large set of equations that cannot be solved effectively with the computational power of conventional computers. This is especially true if many finite-element solutions need to be achieved within a reasonable time period (eg, electrode configuration optimization). In this study, the use of massively parallel computers to provide the memory and reduction in solution time for solving these large finite-element problems is discussed. Both the uniform and unstructured grid approaches are considered. Algorithms that allow efficient mapping of uniform and unstructured grids to data-parallel and message-passing parallel computers are discussed. An automatic iterative procedure for electrode configuration optimization is presented. The procedure is based on the minimization of an objective function using the parallel direct search technique. Computational performance results are presented together with simulation results.

Optimum Shunt Capacitor for Power Factor Compensation in the Presence of Harmonics.(Dept.E)

Power consumers require both reliable service and a acceptable voltage profile. The presence of nonlinear loads in power system generate harmonics which affect, in particular, the shape and magnitude of the supplied voltage, Classical design of capacitors for power factor compensation has been based on the undamental frequency analysis. However, the presence of harmonics and distortion, the compensated power factor is the short circuit generally worse. Additionally, according to capacity at the load bus, the calculated capacitor value could result in harmonic resonant conditions. A direct search technique known as Fibonacci Method (II) has been employed to determine the optimum capacitor bank size, and at the same time avoiding harmonic resonance in a power system with harmonic distortion. The method takes into account the effect of time variation of harmonic distortion, load level and short circuit impedance at load bus on the optimal solution. The proposed method has been illustrated through some actual cases of industrial loads existing in an Egyptian distribution network. The results highlighting the influence of harmonic distortion level, load level, and short circuit impedance have also been discussed in this paper.

An Integrated Computer-Aided Optimization System for Process Planning

Designing a manufacturing operation is a major activity of process planning, especially in the case of processes requiring a comprehensive selection of the operating parameters. This activity includes three hierarchical stages : procedure design, schedule design, and tolerance design. A new approach for process modelling and optimization has been devised to address the problems to solve at each stage. The methodology is based on sequential experimentation to model the feasible domain of the process and on a direct search technique to optimize for quality and process robustness. An integrated computer-aided system has been designed to manage the manufacturing data and the strategies for optimization and variation reduction. Applications to various manufacturing processes are presented.

Optimizing electromagnetic devices combining direct search methods with simulated annealing

Problems of optimization in computational electromagnetics are discussed with particular reference to the determination of the global minimum of practical objective functions. An optimizing environment is described which uses integral methods for calculating user-defined objective functions. Results are presented which combine stochastic and direct search techniques to find a satisfactory design optimum of practical problems. >

Index selection with nonlinear profit function as a tool to achieve simultaneous genetic gain

Simultaneous improvement of several, and often negatively correlated, traits is frequently a desired objective in forest tree breeding. A profit function that includes a combination of both linear weights and weights for the cross-products of trait combinations facilitates the construction of a linear index, with an attractive response in all traits. A detailed algorithm for finding the index coefficients is provided, along with three examples of applications in tree breeding. The index is also a powerful tool in optimizing the selection for a ratio of two traits. It is argued that a more equal progress in several traits provides a safetey net when faced with economic uncertainties. The provided algorithm eliminates the need for direct search techniques. Existence of a dual set of linear weights means that the statistical properties of the index based on nonlinear profit functions are identical to those of the classical Smith-Hazel type of index.

Optimum matching of ohmic loads to the photovoltaic array

Optimum matching of loads to the photovoltaic (PV) generator is most desirable for more accurate sizing, higher system performance and maximum utilization of the costly solar array generator. The quality of load matching depends on the PV array characteristics, the load characteristics, and the insolation profile. A matching factor is defined as the ratio of the load energy to the array maximum energy over a one day period. Optimum matching is achieved by determining the optimal array parameters with respect to the load parameters. Optimization is done using direct-search techniques. Results show that the theoretical optimum matching factor for an ohmic load is 94.34%. For an electrolytic load the matching factor could reach 99.83%. A maximum power tracker can be eliminated if optimum matching is achieved.

Multicriteria optimization for combined reliability and redundancy allocation in systems employing mixed redundancies

The present paper provides a new mathematical formulation of a combined reliability and redundancy allocation involving multiple objective functions in the reliability design of a system employing mixed type of redundancy. The paper proposes an easily computerizable procedure for solving a variety of design problems. The proposed solution technique is a combination of the direct search technique [9,10] and a random search procedure for optimizing redundancy and reliability at the same time at each subsystem and uses multicriteria optimization procedure based on min-max approach [11,12] for obtaining Pareto optimal solutions. The procedure is illustrated through several examples. A general computer code, called ESMOP (Efficient Search Multi-Objective Programming), for the use on IBM compatible PCs has also been developed. The code takes into account all kinds of redundancies including multiple discrete choices for component reliabilities, and a wide variety of resource coefficients and constraint functions.