Finding Optimal Designs Research Articles

Pseudo-Bayesian [formula omitted]-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model

In the analysis of experiments with mixture, quadratic models have been widely used. Several authors considered finding optimum designs for the estimation of the parameters of the model. The optimum designs for the estimation of optimum mixing proportions in Scheffé’s quadratic mixture model has been studied by Pal and Mandal (2006) and Mandal et al. (2008a,b) using a pseudo-Bayesian approach. In this paper, we consider an additive quadratic mixture model, proposed by Darroch and Waller (1985), when the amount of mixture is taken into account, and obtain the A-optimal designs for the estimation of optimum proportions, adopting the approach of Pal and Mandal (2006). We show that, besides other support points, the origin and the vertices of the simplex are necessarily the support points of the optimum design.

Simultaneous kriging-based estimation and optimization of mean response

Robust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the "simulator" is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions.

Optimal designs for threshold-determining limiting dilution assays

In common with other non-linear models, the optimal design for a limiting dilution assay (LDA) depends on the value of the unknown parameter, θ, in the model. Consequently optimal designs cannot be specified unless some assumptions are made about the possible values of θ. If a prior distribution can be specified then a Bayesian approach can be adopted. A proper specification of the Bayesian approach requires the aim of the experiment to be described and quantified through an appropriate utility function. This paper addresses the problem of finding optimal designs for LDAs when the aim is to determine whether θ is above or below a specified threshold, θ0.

지반특성에 따른 동조질량감쇠기의 지진응답특성 및 최적설계변수

기존 동조질량감쇠기의 최적설계변수에 관한 연구는 풍하중과 같은 조화하중을 받는 구조물을 대상으로 연구가 수행되었다. 본 연구에서는 수치해석을 통하여 지진하중이 작용하는 건축물에 설치되는 동조질량감쇠기의 최적 감쇠비와 동조진동수비를 구하였다. 지반특성을 단단한 지반, 연약지반, 단층 근처 지반으로 분류하고, 이들 지반특성을 고려한 수치해석을 통해 구한 동조질량감쇠기의 설계변수를 기존 연구 결과와 비교하였다. 수치해석결과 본 연구로부터 구해진 동조질량감쇠기의 설계변수값을 적용한 경우 지진하중에 의한 응답제어에 기존 연구를 통해 얻어진 변수값을 적용한 경우에 비해 더 나은 제어효과를 얻을 수 있음을 알 수 있었다. Most previous studies for finding optimal design parameters of a tuned mass damper(TMD) have been focused on the harmonic excited single-degree-of freedom system. In this study, optimal values of damping ratio and tuning frequency ratio of a TMD applied to control a seismically excited structure are investigated through numerical analyses. Considering that the structural responses due to earthquake loads are strongly dependent on the soil condition, the site effects on the optimal parameters of the TMD are studied and compared to those presented by previous studies. Numerical analyses results indicate that better control performance can be obtained by using the parameters proposed by this study in the seismic application of the TMD.

BayesianL-Optimal Exact Design of Experiments for Biological Kinetic Models

SummaryData from experiments in steady state enzyme kinetic studies and radioligand binding assays are usually analysed by fitting non-linear models developed from biochemical theory. Designing experiments for fitting non-linear models is complicated by the fact that the variances of parameter estimates depend on the unknown values of these parameters and Bayesian optimal exact design for non-linear least squares analysis is often recommended. It has been difficult to implement Bayesian L-optimal exact design, but we show how it can be done by using a computer algebra package to invert the information matrix, sampling from the prior distribution to evaluate the optimality criterion for candidate designs and implementing an exchange algorithm to search for candidate designs. These methods are applied to finding optimal designs for the motivating applications in biological kinetics, in the context of which some practical problems are discussed. A sensitivity study shows that the use of a prior distribution can be essential, as is careful specification of that prior.

Optimal design and directional leverage with applications in differential equation models

We consider the problem of estimating input parameters for a differential equation model, given experimental observations of the output. As time and cost limit both the number and quality of observations, the design is critical. A generalized notion of leverage is derived and, with this, we define directional leverage. Effective designs are argued to be those that sample in regions of high directional leverage. We present an algorithm for finding optimal designs and then establish relationships to existing design optimality criteria. Numerical examples demonstrating the performance of the algorithm are presented.

Optimal Two-Level Fractional Factorial Designs for Location Main Effects with Dispersion Factors

In two-level fractional factorial designs, homogeneous variance is commonly assumed in analysis of variance. When the variance of the response variable changes when a factor changes from one level to another, we call that factor the dispersion factor. However, the problem of finding optimal designs when dispersion factors are present is relatively unexplored. In this article, we focus on finding optimal designs for the estimation of all location main effects when there are one or two dispersion factors, in the class of regular single replicated two-level fractional factorial designs of resolution III or higher. We show that by appropriate naming of the dispersion factors, D-optimal and A-optimal designs can be identified. Table of D-optimal resolution III designs with two dispersion factors is given.

Optimal experimental designs in RPLC at variable solvent content and pH based on prediction error surfaces

When pH is used as factor in reversed-phase liquid chromatographic (RPLC) separations, the need for providing quality and informative data with the minimal experimental effort becomes imperative. The most rational way to achieve this is by means of experimental designs. The interest in finding optimal designs involving solvent content and pH in RPLC is considerable, since these factors allow large variations in selectivity when ionisable compounds are involved. Unfortunately, the equations that describe the retention of these compounds with pH are nonlinear. As a consequence, factorial and other designs based on geometrical considerations are not well suited, whereas D-optimal and related designs can only be applied in an iterative fashion. In this work, an extension of G-optimal designs, aimed to enhance the quality of the predictions, is examined for problems involving solvent content and pH. The study was carried out with a set of probe ionisable compounds, for which information on retention behaviour was accurately known. A stepwise strategy was used to obtain a rapid estimation of the best design with a given number of experiments. The objective of the study was to investigate the distribution and number of points in the ideal design for compounds of different acid-base behaviour, and the possibility of finding common designs for groups of compounds. A further goal was to derive design construction rules containing the information requirements, without needing any further mathematical treatment.

Two Multi-Objective Genetic Algorithms for Finding Optimum Design of an I-beam

Many engineering design problems are characterized by presence of several conflicting objectives. This requires efficient search of the feasible design region for optimal solutions which simultaneously satisfy multiple design objectives. Genetic algorithm optimization (GAO) is a powerful search technique with faster convergence rates than traditional evolutionary algorithms. This paper applies two GAO-based approaches to multi-objective engineering design and finds design variables through the feasible space. To demonstrate the utility of the proposed methods, the multi-objective design of an I-beam will be presented.

Optimal designs for an interference model

Kunert and Martin (2000) determined optimal and efficient block designs in a model for field trials with interference effects, for block sizes up to 4. The present paper uses Kushner's (1997) method of finding optimal approximate designs to extend the work of Kunert and Martin (2000) to optimal designs with five or more plots per block. We give an overall upper bound a ⁎ t, b, k for the trace of the information matrix of any design and show that an universally optimal approximate design will have all its sequences from merely four different equivalence classes. We further determine the efficiency of a binary type I orthogonal array under a general Φ p ‐criterion . We find that these designs achieve high efficiencies of more than 0.94.

Expanded viewpoint for broadband antireflection coating designs

Examining spectral regions outside of the band where an antireflection coating is specified can aid in finding optimal design solutions. The reflectance versus wavenumber plots at low frequencies indicate the overall thickness of the design. These plots also point to whether the design will provide the minimum possible average reflectance in the specified band. It has been discovered that these patterns are nearly replicated by the plot of a quarter-wave stack at peak frequency. It is also found that optimal solutions exist only at quantized intervals.

A Geometric Characterization of Optimal Designs for Regression Models with Correlated Observations

We consider the problem of optimal design of experiments for random effects models, especially population models, where a small number of correlated observations can be taken on each individual, while the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving (1952) from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a nonlinear random effects population model, which is commonly used in pharmacokinetics.

An example of optimal phase II design for exposure response modelling

This paper presents an example of how optimal design methodology was used to help design a phase II clinical study. The planned analysis would relate the clinical endpoint to exposure (measured via the area under the curve (AUC)), rather than dose. Optimal design methodology was used to compare a number of candidate phase II designs, and an algorithm for finding optimal designs was employed. The sigmoidal E(max) with baseline (E₀) model was used to relate the clinical endpoint to individual subject AUCs, and the primary metrics were D optimality and the standard error (SE) of the AUC required to yield a clinically relevant change in the clinical endpoint. The performance of the candidate designs were compared across four different 'true' exposure response relationships (determined from the analysis of an earlier proof of concept (PoC) study). The results suggested the total sample size should be increased from the planned 540 individuals, and that the optimal design with 700 individuals would be equivalent to 812 individuals with the reference design (a 16% gain). The performance with this design was considered acceptable, although all designs performed poorly if the true exposure response relationship was very flat. This work allowed a prospective assessment of the likely performance and precision from the exposure response modelling prior to the start of the phase II study, and hence allowed the design to be revised to ensure the subsequent analysis would be of most value.

MS 윈도우즈 운영체제 기반의 무선 네트워크 성능 분석 시뮬레이터의 설계 및 구현

To ensure accurate measurements of wireless network performance, it should be collected real-time data which are transmitted between a large number of nodes in the actual network environment. Therefore, it is necessary to develop simulation tool for finding optimal network system design method such as media access control, routing technique, ad-hoc algorithm of node deployment while overcoming spatial and temporal constraints. Our research attempts to provide an improved architecture and design method of simulation tool for wireless network is an application of multi-threading technique in these issues. We finally show that usability of the proposed simulator by comparing results derived from same test environment in the wireless LAN model of our simulator and widely used network simulation package, NS-2.

Design of tensegrity structures using parametric analysis and stochastic search

Tensegrity structures are lightweight structures composed of cables in tension and struts in compression. Since tensegrity systems exhibit geometrically nonlinear behavior, finding optimal structural designs is difficult. This paper focuses on the use of stochastic search for the design of tensegrity systems. A pedestrian bridge made of square hollow-rope tensegrity ring modules is studied. Two design methods are compared in this paper. Both methods aim to find the minimal cost solution. The first method approximates current practice in design offices. More specifically, parametric analysis that is similar to a gradient-based optimization is used to identify good designs. Parametric studies are executed for each system parameter in order to identify its influence on response. The second method uses a stochastic search strategy called probabilistic global search Lausanne. Both methods provide feasible configurations that meet civil engineering criteria of safety and serviceability. Parametric studies also help in defining search parameters such as appropriate penalty costs to enforce constraints while optimizing using stochastic search. Traditional design methods are useful to gain an understanding of structural behavior. However, due to the many local minima in the solution space, stochastic search strategies find better solutions than parametric studies.

Optimum covariate designs in split-plot and strip-plot design set-ups

The problem considered is that of finding optimum covariate designs for estimation of covariate parameters in standard split-plot and strip-plot design set-ups with the levels of the whole-plot factor in r randomised blocks. Also an extended version of a mixed orthogonal array has been introduced, which is used to construct such optimum covariate designs. Hadamard matrices, as usual, play the key role for such construction.

Visual RBF network design based on Star Coordinates

The performance of neural networks is greatly affected by their design, yet the question of finding optimal designs remains open and inspires a considerable amount of research. Most of the researches have been focused on developing automatic algorithms for neural network configuration. This paper addresses the problem of Radial Basis Function Network (RBFN) design definition with a visual technique, called Star Coordinates. The purpose of this approach is to enable the RBFN design revision and refining process, capitalizing on the power of visualization and interactive operations.

Intelligent Design and Modelling of Natural Gas Storage Facilities

Underground gas storage reservoirs provide an efficient and economical way to match the constant supply of gas from long-distance pipelines to the variable, weather-driven demand of the natural gas market. The most important design specifications for underground natural gas storage facilities in terms of startup and operation costs are its capacity, maximum reservoir pressure, number of wells required for drainage, flowing wellhead pressure, and the ratio between working gas and cushion gas. The relationships between these variables are quite complex, and a need exists for a reliable predictive tool. Despite these complexities, the optimal combination of these design parameters can be reached using artificial neural network (ANN) technology. In this study, ANN technology creates an intelligent system capable of learning the complex relationships between input parameters and output responses, which can quantify the importance of each relationship and design variables critical to the determination of optimal design.

Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors

For paired comparison experiments involving pairs of multifactor options differing in a specified number of factors the problem of finding optimal designs is considered, when only main effects are to be estimated. It is presumed that the set of factors can be partitioned into two groups such that the number of levels is constant within each group. The optimal designs for this frequently encountered case are also optimal for the corresponding choice experiments under the hypothesis that the parameters in the multinomial logit model are equal to zero.

가중평균대리모델을 사용한 천음속 압축기 블레이드 최적화

The main purpose of the present study is to perform shape optimizations of transonic compressor blade in order to enhance its performance. In this study, the Latin hypercube sampling of design of experiments and the weighted average surrogate model with the help of a gradient based optimization algorithm are used within design space by the lower and upper limits of each design variable and for finding optimum designs, respectively. 3-D Reynolds-averaged Navier-Stokes solver is used to evaluate the objective functions of adiabatic efficiency and pressure ratio. Six variables from lean and airfoil thickness profile are selected as design variables. The results show that the adiabatic efficiency is nhanced by 1.43% by efficiency optimization while the pressure ratio is increased very small, and <BR>pressure ratio is increased by 0.24% by pressure ratio optimization.