Showing papers on "Optimal design published in 2008"

Orthogonal-maximin latin hypercube designs

Abstract: A randomly generated Latin hypercube design (LHD) can be quite struc- tured: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures for finding good LHDs by minimizing the pairwise correlations or by maximizing the inter-site distances. In this article we show that these two criteria need not be in close agreement. We propose a multi-objective optimization approach to find good LHDs by combining correlation and distance performance measures. We also propose a new exchange algorithm for efficiently generating such designs. Several examples are presented to show that the new algorithm is fast, and that the optimal designs are good in terms of both the correlation and distance criteria.

Designing Discrete Choice Experiments: Do Optimal Designs Come at a Price?

Abstract: In discrete choice experiments, design decisions are crucial for determining data quality and costs. While high statistical efficiency designs are desirable, they may come at a price if they increase the cognitive burden for respondents. We address this problem by designing 44 experiments that systematically vary numbers of attributes and attribute level differences. Our results for two product categories suggest that respondents systematically are less consistent in answering choice questions as statistical efficiency increases. This relationship holds regardless of the number of attributes and is statistically significant even if one accommodates preference heterogeneity. Implications for practice and future research are discussed.

A hierarchical model for concurrent material and topology optimisation of three-dimensional structures

Abstract: This paper presents an extension of the hierarchical model for topology optimisation to three-dimensional structures. The problem addressed covers the simultaneous characterisation of the optimal topology of the structure and the optimal design of the cellular material used in its construction. In this study, hierarchical suggests that the optimisation model works at two interconnected levels, the global and local levels identified, respectively, with the structure and its material. The class of cellular materials, defining the material microstructure, is restricted to single scale cellular materials, with the cell geometry locally optimised for the given objective function and constraints. The model uses the asymptotic homogenisation model to obtain the equivalent material properties for the specific local microstructures designed using a SIMP based approach. The necessary optimality conditions for the hierarchical optimal design problem are discussed and approximated numerically by a proper finite element discretisation of the global and local analysis and design problems. Examples to explore and demonstrate the model developed are presented.

Numerical methods for experimental design of large-scale linear ill-posed inverse problems

Abstract: While an experimental design for well-posed inverse linear problems has been well studied, covering a vast range of well-established design criteria and optimization algorithms, its ill-posed counterpart is a rather new topic The ill-posed nature of the problem entails the incorporation of regularization techniques The consequent non-stochastic error introduced by regularization needs to be taken into account when choosing an experimental design criterion We discuss different ways to define an optimal design that controls both an average total error of regularized estimates and a measure of the total cost of the design We also introduce a numerical framework that efficiently implements such designs and natively allows for the solution of large-scale problems To illustrate the possible applications of the methodology, we consider a borehole tomography example and a two-dimensional function recovery problem

Optimal Design of Water Networks Using a Modified Genetic Algorithm with Reduction in Search Space

Abstract: The efficient and effective search for the optimum design solution of a water distribution network using genetic algorithms (GAs) is governed by several factors such as representation scheme, population size, hydraulic simulation model, fitness function, penalty method, GA operators, number of generations, and more importantly the size of the search space. This paper proposes a modified GA that uses basic operators along with their derivatives randomly. Further, a methodology based on critical path method is suggested to reduce the search space. A software tool, GA-WAT, based on the proposed methodology is developed and first tested and verified for its efficiency and effectiveness on two previously published single source networks. Later, it is applied to the optimal design of a larger, two-source hypothetical network. The results obtained indicate that the modified GA with reduction in search space proposed herein is more effective, especially for large practical networks.

Minimum stress optimal design with the level set method.

Abstract: This paper is devoted to minimum stress design in structural optimization. We propose a simple and efficient numerical algorithm for shape and topology optimization based on the level set method coupled with the topological derivative. We compute a shape derivative, as well as a topological derivative, for a stress-based objective function. Using an adjoint equation we implement a gradient algorithm for the minimization of the objective function. Several numerical examples in 2-d and 3-d are discussed.

Optimal Designs for Dose-Finding Studies

Abstract: Understanding and properly characterizing the dose–response relationship is a fundamental step in the investigation of a new compound, be it a herbicide or fertilizer, a molecular entity, an environmental toxin, or an industrial chemical. In this article we investigate the problem of deriving efficient designs for the estimation of target doses in the context of clinical dose finding. We propose methods to determine the appropriate number and actual levels of the doses to be administered to patients, as well as their relative sample size allocations. More specifically, we derive local optimal designs that minimize the asymptotic variance of the minimum effective dose estimate under a particular dose–response model. We investigate the small-sample properties of these designs, together with their sensitivity to a misspecification of the true parameter values and of the underlying dose–response model, through simulation. Finally, we demonstrate that the designs derived for a fixed model are rather sensitive ...

Design Optimization for Integrated Neural Recording Systems

Abstract: Power and chip area are the most important parameters in designing a neural recording system in vivo. This paper reports a design methodology for an optimized integrated neural recording system. Electrode noise is considered in determining the ADC's resolution to prevent over-design of the ADC, which leads to unnecessary power consumption and chip area. The optimal transconductance and gain of the pre-amplifiers, which minimizes the power-area product of the amplifier, are mathematically derived. A numerical example using actual circuit parameters is shown to demonstrate the design methodology. A tradeoff between the power consumption of the system and the chip area in terms of the multiplexing ratio is investigated and the optimal number of channels per ADC is selected to achieve the minimum power-area product for the entire system. Following the proposed design methodology, a chip has been designed in 0.35 mum CMOS process, with the multiplexing ratio of 16:1, resulting in total chip area of 2.5 mm times 2.0 mm and power consumption of 5.3 mW from plusmn1.65 V.

Reliability-Redundancy Allocation for Multi-State Series-Parallel Systems

Abstract: Current studies of the optimal design of multi-state series-parallel systems often focus on the problem of determining the optimal redundancy for each stage. However, this is only a partial optimization. There are two options to improve the system utility of a multi-state series-parallel system: 1) to provide redundancy at each stage, and 2) to improve the component state distribution, that is, make a component in states with respect to higher utilities with higher probabilities. This paper presents an optimization model for a multi-state series-parallel system to jointly determine the optimal component state distribution, and optimal redundancy for each stage. The relationship between component state distribution, and component cost is discussed based on an assumption on the treatment on the components. An example is used to illustrate the optimization model with its solution approach, and that the proposed reliability-redundancy allocation model is superior to the current redundancy allocation models.

Sequential adaptive designs in computer experiments for response surface model fit

Abstract: Computer simulations have become increasingly popular as a method for studying physical processes that are difficult to study directly. These simulations are based on complex mathematical models that are believed to accurately describe the physical process. We consider the situation where these simulations take a long time to run (several hours or days) and hence can only be conducted a limited number of times. As a result, the inputs (design) at which to run the simulations must be chosen carefully. For the purpose of fitting a response surface to the output from these simulations, a variety of designs based on a fixed number of runs have been proposed. In this thesis, we consider sequential adaptive designs as an “efficient” alternative to fixed-point designs. We propose new adaptive design criteria based on a cross validation approach and on an expected improvement criterion, the latter inspired by a criterion originally proposed for global optimization. We compare these new designs with others in the literature in an empirical study and they shown to perform well. The issue of robustness for the proposed sequential adaptive designs is also addressed in this thesis. While we find that sequential adaptive designs are potentially more effective and efficient than fixed-point designs, issues such as numerical instability do arise. We address these concerns and also propose a diagnostic tool based on cross validation prediction error to improve the performance of sequential designs. We are also interested in the design of computer experiments where there are control variables and environmental (noise) variables. We extend the implementation of the proposed sequential designs to achieve a good fit of the unknown integrated response surface (i.e., the averaged response surface taken over the distributions of the environmental variables) using output from the simulations. The goal is to find an optimal choice of the control variables while taking into account the distributions of the noise variables.

Optimal observation times in experimental epidemic processes.

Abstract: This article describes a method for choosing observation times for stochastic processes to maximise the expected information about their parameters. Two commonly used models for epidemiological processes are considered: a simple death process and a susceptible-infected (SI) epidemic process with dual sources for infection spreading within and from outwith the population. The search for the optimal design uses Bayesian computational methods to explore the joint parameter-data-design space, combined with a method known as moment closure to approximate the likelihood to make the acceptance step efficient. For the processes considered, a small number of optimally chosen observations are shown to yield almost as much information as much more intensively observed schemes that are commonly used in epidemiological experiments. Analysis of the simple death process allows a comparison between the full Bayesian approach and locally optimal designs around a point estimate from the prior based on asymptotic results. The robustness of the approach to misspecified priors is demonstrated for the SI epidemic process, for which the computational intractability of the likelihood precludes locally optimal designs. We show that optimal designs derived by the Bayesian approach are similar for observational studies of a single epidemic and for studies involving replicated epidemics in independent subpopulations. Different optima result, however, when the objective is to maximise the gain in information based on informative and non-informative priors: this has implications when an experiment is designed to convince a naive or sceptical observer rather than consolidate the belief of an informed observer. Some extensions to the methods, including the selection of information criteria and extension to other epidemic processes with transition probabilities, are briefly addressed.

Hessian-based model reduction for large-scale systems with initial-condition inputs

Abstract: Reduced-order models that are able to approximate output quantities of interest of high-fidelity computational models over a wide range of input parameters play an important role in making tractable large-scale optimal design, optimal control, and inverse problem applications. We consider the problem of determining a reduced model of an initial value problem that spans all important initial conditions, and pose the task of determining appropriate training sets for reduced-basis construction as a sequence of optimization problems. We show that, under certain assumptions, these optimization problems have an explicit solution in the form of an eigenvalue problem, yielding an efficient model reduction algorithm that scales well to systems with states of high dimension. Furthermore, tight upper bounds are given for the error in the outputs of the reduced models. The reduction methodology is demonstrated for a large-scale contaminant transport problem.

Design optimization of low-speed axial flow fan blade with three-dimensional RANS analysis

Abstract: This work presents a numerical optimization procedure for a low-speed axial flow fan blade with polynomial response surface approximation model. Reynolds-averaged Navier-Stokes equations with SST turbulence model are discretized by finite volume approximations and solved on hexahedral grids for flow analyses. The blade profile as well as stacking line is modified to enhance blade total efficiency, i.e., the objective function. The design variables of blade lean, maximum thickness and location of maximum thickness are selected, and a design of experiments technique produces design points where flow analyses are performed to obtain values of the objective function. A gradient-based search algorithm is used to find the optimal design in the design space from the constructed response surface model for the objective function. As a main result, the efficiency is increased effectively by the present optimization procedure. And, it is also shown that the modification of blade lean is more effective to improve the efficiency rather than modifying blade profile.

Optimal Structural Design of Vehicle Components Using Topology Design and Optimization

Abstract: In order to meet today's vehicle design requirements and to improve the cost and fuel efficiency, there is an increasing interest to design light-weight and cost-effective vehicle components. In this study, a topology design approach, which aims at defining of an optimum model at design stage, is used to decrease product cost and lead time to markets. An example of a vehicle component design is presented to illustrate the application of the topology optimisation approach for the optimal design of vehicle components.

Shape optimization of an axial compressor blade by multi-objective genetic algorithm

Abstract: In this study, a multi-objective optimization of an axial compressor rotor blade has been performed through genetic algorithm with total pressure and adiabatic efficiency as objective functions. The non-dominated sorting of genetic algorithm-II has been implemented and confidence check has been performed at k-means clustered points among all the Pareto-optimal solutions. Reynolds-averaged Navier—Stokes equations are solved to obtain the objective function and flow field inside the compressor annulus. The objective functions are used to generate Pareto-optimal front. The design variables are selected from blade lean and thickness through the Bezier polynomial formulation. By this optimization, maximum efficiency and total pressure are increased by 1.76 and 0.41 per cent, respectively, when two extreme clustered points are considered as optimal designs.

Thermal buckling load optimization of laminated composite plates

Abstract: In this study, the applicability of the Modified Feasible Direction (MFD) method on the thermal buckling optimization of laminated plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminated plates and the fiber orientation is considered as design variable. The first-order shear deformation theory is used in the mathematical formulation. For this purpose, a program based on FORTRAN is used for the optimization of laminated plates. Finally, the effect of aspect ratio, antisymmetric lay-up, boundary condition, material anisotropy, ratio of coefficients of thermal expansion, and hybrid laminates on the results is investigated and the results are compared.

Pitfalls of using a single criterion for selecting experimental designs

Abstract: For surrogate construction, a good experimental design (ED) is essential to simultaneously reduce the effect of noise and bias errors. However, most EDs cater to a single criterion and may lead to small gains in that criterion at the expense of large deteriorations in other criteria. We use multiple criteria to assess the performance of different popular EDs. We demonstrate that these EDs offer different trade-offs, and that use of a single criterion is indeed risky. In addition, we show that popular EDs, such as Latin hypercube sampling (LHS) and D-optimal designs, often leave large regions of the design space unsampled even for moderate dimensions. We discuss a few possible strategies to combine multiple criteria and illustrate them with examples. We show that complementary criteria (e.g. bias handling criterion for variance-based designs and vice versa) can be combined to improve the performance of EDs. We demonstrate improvements in the trade-offs between noise and bias error by combining a model-based criterion, like the D-optimality criterion, and a geometry-based criterion, like LHS. Next, we demonstrate that selecting an ED from three candidate EDs using a suitable error-based criterion helped eliminate potentially poor designs. Finally, we show benefits from combining the multiple criteria-based strategies, that is, generation of multiple EDs using the D-optimality and LHS criteria, and selecting one design using a pointwise bias error criterion. The encouraging results from the examples indicate that it may be worthwhile studying these strategies more rigorously and in more detail. Copyright © 2007 John Wiley & Sons, Ltd.