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Resumen En el diseño de experimentos es común el no uso de criterios para determinar los tratamientos y el número de réplicas que se deben realizar para la obtención de una buena estimación de los parámetros del modelo, debido principalmente al desconocimiento de estos y en muchas otras ocasiones por la dificultad en implementarlos. Los diseños óptimos tratan de resolver esta falencia al dar condiciones experimentales óptimas y los niveles de los factores donde se debe medir la respuesta, con el fin de obtener una mejora en la calidad de la inferencia estadística a un menor costo. En la búsqueda de diseños óptimos se utilizan criterios de optimalidad, los cuales son función de la matriz de información de Fisher. Uno de los problemas de estimación más frecuente en los modelos no lineales es la especificación de los valores locales para los parámetros del modelo, necesarios para la optimización del criterio de optimalidad. En este artículo se realiza un estudio de robustez de los diseños óptimos obtenidos en el modelo logístico, al considerar perturbaciones en los valores locales de los parámetros, con el fin de proporcionar al investigador un rango de maniobrabilidad en la selección de los valores locales y garantizando que el diseño óptimo resultante no pierda una eficiencia considerable con respecto al valor de referencia. Para ello, a partir de los datos de un ejemplo, se encuentran las eficiencias de cada uno de los diseños obtenidos con relación al valor sin perturbar; se construyen los diseños cD-óptimos locales para la estimación de la varianza del logit, se determinó que la magnitud de la perturbación en los diseños cD-óptimos locales obtenidos alcanzan una eficiencia alrededor de un 70 %, con un radio de 0.04 de perturbación sobre el valor de referencia. Abstract When experiments are designed, it is uncommon to use criteria to determine the treatments and number of replicates that should be conducted to properly estimate the parameters in the model under study. This is mainly due to a lack of knowledge of said criteria and, in many other cases, to the difficulty of interpreting them. Optimal designs try to overcome this difficulty by providing optimal experimental conditions and factor levels whose response should be evaluated in order to improve the quality of the statistical inference at a lower cost. Said designs also use optimality criteria, which are functions of the Fisher-information matrix. One of the most common estimation problems in nonlinear models is specifying local values for the parameters of the model, which is necessary to minimice the optimality criterion. This work examines the robustness of optimal designs obtained from logistic models when perturbations in the local values of the parameters are considered. The objective is to provide researchers with a wide range of action to select local values while guaranteeing that the efficiency of the resulting optimal designs is not considerably compromised compared to reference values. For that purpose, based on the data of an example, the efficiency of each resulting design was contrasted with the efficiency of unperturbed values. Furthermore, cD-optimal designs were created to estimate the logit variance. The impact of said perturbations on local cD-optimal designs resulted in an efficiency of approximately 70%, with a range of 0.04 of perturbation above the reference value.

The paper describes an application for visualization of four-dimensional graphs of a complex variable function. This application allowed us to construct an exact geometric algorithm for finding the real and complex roots of a polynomial on the same plane. A graph of an n-th order polynomial on the real plane allows us to define geometrically all the real roots. Number of real roots varies from 0 to n. The rest of the roots are complex and not determined by the graph. In the article, in addition to the graph of the basic polynomial, two auxiliary graphs are constructed, which allow us to represent all complex roots on the same real plane. Realization of this method is considered in detail for the solution of a cubic polynomial. In this case the method has exceptional features in comparison with polynomials of other degrees. We also propose an algorithm for constructing auxiliary functions for the general case of a polynomial of order n which have exact formulas for polynomials with order n ≤ 10. The algorithm for the first time builds the exact hodograph of poles for the control systems with feedback. We generalize the concepts of stationary and extremal points to the case of a complex function. The absence of the possibility of comparing the complex values of the objective function is compensated by an analysis of the behavior of the stationary point under small perturbations of the polynomial by linear functions. Optimality criteria are proposed using complex trajectories of stationary points.

For optimal design most parameters may be classified in size, shape, and topology, such as simple density variables and parameters for surface description. Density and surface can be rather directly visualized. Extending the design to material design in sense of design of distributions of constitutive matrices, a practical visualization is more complicated but may be based on classical laminate analysis. In rotational transformation of constitutive matrices, some practical quantities are often termed invariants, but the invariance relates to an unchanged reference direction. Rotating this reference direction, the practical quantities do change and this point is clarified with derived rotational transformation for these practical quantities. The theoretical and numerical background for design of optimal anisotropic constitutive matrices are presented. Then design results are applied in a 2D visualization of optimized constitutive matrices that are distributed in a finite element model where each element has a specific reference direction. The visualized distributions of physical quantities are stiffest material direction, material stiffest longitudinal constitutive component, level of anisotropy, absolute or relative shear stiffness, and test of orthotropy.

We present a topology optimization based procedure aiming at the optimal placement (and design) of the supports in problems characterized by a time dependent construction process. More precisely, we focus on the solution of a time-dependent minimal compliance problem based on the classical Solid Isotropic Material with Penalization (SIMP) method. In particular, a continuous optimization problem with the state equation defined as the time-integral of a linear elasticity problem on a space-time domain is firstly introduced and the mean compliance over a time interval objective functional is then selected as objective function. The optimality conditions are derived and a fixed-point algorithm is introduced for the iterative computation of the optimal solution. Numerical examples showing the differences between a standard SIMP method, which only optimizes the shape at the final time, and the proposed time-dependent approach are presented and discussed.

Experimenters have come to a realization that a design can perform very well in terms of a particular statistical characteristic and still perform poorly in terms of a rival characteristic. Due to this studies have narrowed down to the area of optimality criteria. Some of these criteria include the alphabetic optimality criteria and compound optimality criteria. Compound optimality criteria are those that combine two or more alphabetic optimality criteria in one particular design. In this paper two alphabetic optimality D- and T- criteria are combined to obtain DT- compound optimality criteria for the existing second order rotatable designs using Balanced Incomplete Block Designs. The purpose of this paper is to bring a balance between to statistical properties; parameter estimation and model discrimination. This will aid those researchers who are interested in more than two desired traits in one design. In this analysis, we note that the more homogenous the design is the more optimal it becomes.

A practical approach to optimize a continuum/structural eigenfrequency is presented, including design of the distribution of material anisotropy. This is often termed free material optimization (FMO). An important aspect is the separation of the overall material distribution from the local design of constitutive matrices, i.e., the design of the local anisotropy. For a finite element (FE) model the amount of element material is determined by a traditional optimality criterion (OC) approach. In this respect the major value of the present formulation is the derivation of simple eigenfrequency gradients with respect to material density and from this values of the element OC. Each factor of this expression has a physical interpretation. Stated alternatively, the optimization problem of material distribution is converted into a problem of determining a design of uniform OC values. The constitutive matrices are described by non-dimensional matrices with unity norms of trace and Frobenius, and thus this part of the optimized design has no influence on the mass distribution. Gradients of eigenfrequency with respect to the components of these non-dimensional constitutive matrices are therefore simplified, and an additional optimization criterion shows that the optimized redesign of anisotropy are described directly by the element strains. The fact that all components of an optimal constitutive matrix are expressed by the components of a strain state, imply a reduced number of independent components of an optimal constitutive matrix. For 3D problems from 21 to 6 parameters, for 2D from 6 to 3 parameters, and for axisymmetric problems from 10 to 4 parameters.

A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic orthotropic model by appropriate assumptions. The design problem is given in the form of two minimization statements, reminiscent of a Nash game. After finite element discretization, the separate treatment of each of the two minimization statements follows from classical results and methods of structural optimization: the stiffest orientation of reinforcing fibers coincides with principal stresses and the separate selection of density of fibers is a convex problem that can be solved by optimality criteria iterations. Numerical solutions are shown for two particular configurations. The first for a statically determined structure and the second for a statically undetermined one. The latter shows related but non-unique solutions., 8 pages, 4 figures

Optimizing designs using robust (global) optimality criteria has been shown to be a more flexible approach compared to using local optimality criteria. Additionally, model based adaptive optimal design (MBAOD) may be less sensitive to misspecification in the prior information available at the design stage. In this work, we investigate the influence of using a local (lnD) or a robust (ELD) optimality criterion for a MBAOD of a simulated dose optimization study, for rich and sparse sampling schedules. A stopping criterion for accurate effect prediction is constructed to determine the endpoint of the MBAOD by minimizing the expected uncertainty in the effect response of the typical individual. 50 iterations of the MBAODs were run using the MBAOD R-package, with the concentration from a one-compartment first-order absorption pharmacokinetic model driving the population effect response in a sigmoidal EMAX pharmacodynamics model. The initial cohort consisted of eight individuals in two groups and each additional cohort added two individuals receiving a dose optimized as a discrete covariate. The MBAOD designs using lnD and ELD optimality with misspecified initial model parameters were compared by evaluating the efficiency relative to an lnD-optimal design based on the true parameter values. For the explored example model, the MBAOD using ELD-optimal designs converged quicker to the theoretically optimal lnD-optimal design based on the true parameters for both sampling schedules. Thus, using a robust optimality criterion in MBAODs could reduce the number of adaptations required and improve the practicality of adaptive trials using optimal design.

This paper presents the development, results and conclusions obtained with a solid topology optimization code, using truss lattices as an alternative to continuum elements. Truss elements are used for the simplicity of the implementation in a new code, in all aspects: boundary conditions, loadings, elemental stiffness matrix. Blocked structures, well posed mechanical equilibrium problems are assured by a proper truss arrangement, lattice driven, similar to structured or unstructured meshing.

Transportation networks are subject to significant travel time uncertainty as a result of traveler behavior, recurring congestion, capacity variability (construction zones, traffic incidents), variation in demand, and so on. Therefore, interest is growing in modeling and optimizing travel time reliability in such networks. This paper proposes an efficient algorithm to compute the path of maximum travel time reliability on a network with normally distributed and correlated link travel times. For this optimal reliability path (ORP) problem, it is shown that the subpath optimality condition for the deterministic shortest path problem does not hold, and consequently, a new bounds-based optimality criterion is proposed using the K shortest expected time paths and the minimum path variance on the network. An algorithm is developed to solve the ORP problem on the basis of the proposed optimality criterion and an efficient path generation procedure. Computational experiments on various test networks show the proposed algorithm to be efficient, requiring limited path enumeration. With as few as five shortest paths and 50 Monte Carlo draws, the proposed algorithm is able to find the most reliable path for realistic network sizes. Empirical investigations highlight the unreliability of the least expected time path and suboptimality of the independence assumption. The study also underscores the role of risk attitudes (reflected by reliability threshold) on the benefits of the ORP. The algorithm and empirical results have important applications for developing reliability-based routing applications for congestion mitigation and intelligent transportation systems.

The paper describes how to take into consideration the presence of transmissible loads in a topology optimization method based on optimality criteria. The optimization problem has been defined as a total potential energy maximization problem with stress, displacement or stiffness constraints. The final volume of the optimal structural configuration has not to be specified a priori and is a consequence of the imposed structural constraints. The implementation of the proposed method is quite simple and leads to the identification of well defined optimal structures. The results obtained by solving several benchmark problems are shown.

Conjoint analysis is a research technique for measuring consumer preferences, and it is a method for simulating consumers' possible reactions to changes in current products or newly introduced products into an existing competitive market. One of the most critical steps in Conjoint analysis application is experimental designs construction. The purpose of an experimental design is to give a rough overall idea as to the shape of the experimental response surface, while only requiring a relatively small number of runs. These designs are expected to be orthogonal and balanced in an ideal case. In practice, though, it is hard to construct optimal designs and thus constructing of near optimal and efficient designs is carried out. There are several ways to quantify the relative efficiency of experimental designs. The choice of measure will determine which types of experimental designs are favored as well as the algorithms for choosing efficient designs. In this paper it is proposed the algorithm which combines one standard and one non-standard optimality criteria. The computational experiments were made, and results of comparison with algorithm implemented in commercial package SPSS confirm the efficiency of the proposed algorithm. .

The present paper deals with the formulation of novel closed-form algorithms for the kinematic synthesis of quasi-constant transmission ratio planar four-bar and slider–crank linkages. The algorithms are specific for both infinitesimal and finite displacements. In the first case, the approach is based on the use of kinematic loci, such as centrodes, inflection circle, and cubic of stationary curvature, as well as Euler–Savary equation. In the second case, the design equations follow from the application of Chebyshev min–max optimality criterion. These algorithms are aimed to obtain, within a given range of motion, a quasi-constant transmission ratio between the driving and driven links. The numerical examples discussed allow a direct comparison of structural errors for mechanisms designed with different methodologies, such as infinitesimal Burmester theory and the Chebyshev optimality criterion.

The paper shows the results obtained by using a topology optimisation code to solve a three-dimensional problem concerning a real automotive component. The implemented optimisation method is based on the maximisation of the total potential energy with a volume constraint by optimality criteria. The volume of the optimal solution depends on the imposed static (displacement, stress, stiffness) and dynamic (natural frequency) constraints and has not to be specified a priori. The optimisation process converges toward a quite well defined structure made of the base material with a very little percentage of elements characterised by intermediate material properties.

The aim of this paper is to address optimality of control strategies for stochastic control systems subject to uncertainty and ambiguity. Uncertainty corresponds to the case when the true dynamics and the nominal dynamics are different but they are defined on the same state space. Ambiguity corresponds to the case when the true dynamics are defined on a higher dimensional state space than the nominal dynamics. The paper is motivated by a brief summary of existing methods dealing with optimality of stochastic systems subject to uncertainty, and a discussion on its shortcoming when stochastic systems are ambiguous. The issues which will be discussed are the following. 1) Modeling methods for ambiguous stochastic systems, 2) formulation of optimal stochastic control systems subject to ambiguity, 3) optimality criteria for ambiguous stochastic control systems. © 2011 IFAC. 18 4459 4464

The aim of this paper is to address optimality of control strategies for stochastic discrete time control systems subject to conditional distribution uncertainty. This type of uncertainty is motivated from the fact that the value function involves expectation with respect to the conditional distribution. The issues which will be discussed are the following. 1) Optimal stochastic control systems subject to conditional distribution uncertainty, 2) optimality criteria for stochastic control systems with conditional distribution uncertainty, including principle of optimality and dynamic programming. © 2011 IEEE. 6407 6412

We state a new implicit optimality criterion for convex semi-infinite programming (SIP) problems. This criterion does not require any constraint qualification and is based on concepts of immobile index and immobility order. Given a convex SIP problem with a continuum of constraints, we use an information about its immobile indices to construct a nonlinear programming (NLP) problem of a special form. We prove that a feasible point of the original infinite SIP problem is optimal if and only if it is optimal in the corresponding finite NLP problem. This fact allows us to obtain new efficient optimality conditions for convex SIP problems using known results of the optimality theory of NLP. To construct the NLP problem, we use the DIO algorithm. A comparison of the optimality conditions obtained in the paper with known results is provided.

This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented. The original publication is available at www.springerlink.com:Anders Klarbring and Bo Torstenfelt, Dynamical systems and topology optimization, 2010, Structural and multidisciplinary optimization, (42), 2, 179-192.http://dx.doi.org/10.1007/s00158-010-0479-9Copyright: Springer Science Business Mediahttp://www.springerlink.com/

In large structures it is often necessary to estimate the reliability of the system by use of parallel systems. Optimality criteria-based algorithms for calculation of the joint design point in a parallel system are described and efficient active set strategies are developed. Three possible algorithms are tested in two examples against well-known general non-linear optimization algorithms. Especially one of the suggested algorithms seems to be stable and fast. In large structures it is often necessary to estimate the reliability of the system by use of parallel systems. Optimality criteria-based algorithms for calculation of the joint design point in a parallel system are described and efficient active set strategies are developed. Three possible algorithms are tested in two examples against well-known general non-linear optimization algorithms. Especially one of the suggested algorithms seems to be stable and fast.

http://www.springer.com/978-0-387-79935-3; We study the family of gradient algorithms for solving quadratic optimization problems, where the step-length gamma_k is chosen according to a particular procedure. In order to carry out the study, we re-write the algorithms in a normalized form and make a connection with the theory of optimum experimental design. We provide the results of a numerical study which shows that some of the proposed algorithms are extremely efficient.

Gustav Elfving contributed to the genesis of optimal experimental design theory with several papers mainly in the 1950s. These papers are presented and briefly analyzed. The connections between Elfving’s results and the results of his successors are elucidated to stress the relevance of Elfving’s impact on the development of optimal design theory.

We express Gittins indices for multi-armed bandit problems as Laurent expansions around discount factor 1. The coefficients of these expan-sions are then used to characterize stationary optimal policies when the optimality criteria are sensitive-discount optimality (otherwise known as Blackwell optimality), average-reward optimality and average-overtaking optimality. We also obtain bounds and derive optimality conditions for policies of a type that continue playing the same bandit as long as the state of that bandit remains in prescribed sets.

This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

In early generation variety trials, large numbers of new breeders' lines (varieties) may be compared, with each having little seed available. A so-called unreplicated trial has each new variety on just one plot at a site, but includes several replicated control varieties, making up around 10% and 20% of the trial. The aim of the trial is to choose some (usually around one third) good performing new varieties to go on for further testing, rather than precise estimation of their mean yields. Now that spatial analyses of data from field experiments are becoming more common, there is interest in an efficient layout of an experiment given a proposed spatial analysis and an efficiency criterion. Common optimal design criteria values depend on the usual C-matrix, which is very large, and hence it is time consuming to calculate its inverse. Since most varieties are unreplicated, the variety incidence matrix has a simple form, and some matrix manipulations can dramatically reduce the computation needed. However, there are many designs to compare, and numerical optimisation lacks insight into good design features. Some possible design criteria are discussed, and approximations to their values considered. These allow the features of efficient layouts under spatial dependence to be given and compared. (c) 2006 Elsevier Inc. All rights reserved.

Este trabajo describe brevemente el debate científico que se produjo en su momento en el ámbito de la optimización de estructuras entre los partidarios de los métodos matemáticos de optimización de problemas no lineales y los de los criterios optimizantes. En ese sentido recuerda el planteamiento que investigadores como A. B. Templeman llevaron a cabo y que conceptualmente consistía en establecer una propuesta probabilista de los criterios optimizantes, cuyo mérito radicaba en ser completamente racional y no prejuzgar las condiciones que iban a ser activas en el diseño óptimo. Tras revisar el estado de la cuestión, se ha desarrollado una nueva formulación que simplifica y mejora las anteriores y transforma el problema de optimización en otro consistente en resolver sucesivamente sistemas de ecuaciones de la misma dimensión que el número de variables del problema. El algoritmo requiere la obtención de las sensibilidades de primer orden, con lo que también puede ser considerado como un nuevo método de gradiente. Tras la descripción teórica, el método se ha aplicado para resolver 2 ejemplos de optimización de estructuras de celosía muy comunes en la literatura de esta disciplina científica. Los resultados numéricos que se muestran permiten concluir que esta formulación obtiene la solución óptima con gran precisión. This work reviews A. B. Templemans research in the maximum entropy principle applied to structural optimization, which consists in defining a probabilistic approach for the optimality criteria. This new reasoning does not assume aprioristically which conditions could be active in the optimum point, giving a completely rational point of view to the optimization problem. After reviewing the state of the art, a new formulation, which simplifies and improves previous methodologies, is developed. This new method turns the optimization problem into solving successively systems of equations with the same dimension as the number of design variables. Since this algorithm requires obtaining first order sensitivities, it can be considered as a new gradient method. After the theoretical description, the algorithm is tested with two examples of truss structures. Results show a good performance of the algorithm, based on comparisons with other alternatives found in the literature.

The paper concerns the application of a non-classical performance measure, a late work criterion (Y, Yw), to scheduling problems. It estimates the quality of the obtained solution with regard to the duration of the late parts of tasks not taking into account the quantity of this delay. The paper provides the formal definition of the late work parameter, especially in the shop environment, together with its practical motivation. It contains general complexity studies and the results of investigating open-shop scheduling cases, i.e. two polynomial time algorithms for problems O | pmtn, ri | Yw and O2 | di = d | Y, as well as the binary NP-hardness proof for O2 | di = d | Yw.

This paper presents a possible generalization of geometric programming problems. Such a generalization was proposed by Peterson [6], based on Rockafellar's [8] conjugate function theory. Using their results, we define a slightly different, more symmetric dual pair of general unconstrained geometric programming problems. In the second chapter the conjugate function is defined and some of its properties are demonstrated. In the third chapter the general unconstrained geometric programming problem and its dual pair are introduced and some of its fundamental properties are proved. The primal optimality criteria is based on Peterson's papers [6,7] and the dual optimality criteria completes our examinations.

This paper examines the relationships between optimality criteria which are commonly used for undiscounted, discrete-time, countable state Markovian decision models. One approach, due to Blackwell, is to maximize the expected discounted total return as the discount factor approaches 1. Another, due to Veinott, is to maximize the Cesaro means of the finite horizon expected returns as the horizon tends to infinity. Derman's is to maximize the long-run average gain. Denardo, Miller and Lippman showed that Blackwell's and Veinott's approaches are equivalent for finite state and action spaces. As shown here, that equivalence breaks down when the state space is countable. Also, policies optimal according to Blackwell's or Veinott's approach need not be optimal according to Derman's. On the positive side, fairly weak conditions are given under which Blackwell's and Veinott's criteria imply Derman's, and somewhat stronger conditions under which Blackwell's and Veinott's criteria are equivalent.