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Subdata selection methods provide flexible tradeoffs between computational complexity and statistical efficiency in analyzing big data. In this work, we investigate a new algorithm for selecting informative subdata from massive data for a broad class of models, including generalized linear models as special cases. A connection between the proposed method and many widely used optimal design criteria such as A-, D-, and E-optimality criteria is established to provide a comprehensive understanding of the selected subdata. Theoretical justifications are provided for the proposed method, and numerical simulations are conducted to illustrate the superior performance of the selected subdata. [ABSTRACT FROM AUTHOR]

The possibility of constructing a multi-position direction finding system for the case of a priori uncertainty, based on the application of the principles of multiplication of single marks of the location of the emitting target (multistructure principle) and their subsequent partition into classes (clustering principle) is considered. The criteria and algorithms for detecting the resulting cluster and for constructing the optimal estimation of target location stable to anomalous measurement errors are presented, taking into account the time costs of their computer realization. Practical recommendations and results of comparative analysis of different algorithms are given. [ABSTRACT FROM AUTHOR]

Existing criteria for optimal coke quality used in practice in batch formulation are reviewed. The chemical and petrographic parameters of the optimal batches are presented for various Russian coke plants and for the production of high-quality coke. It is found that the economic indices of blast-furnace operation—such as the coke consumption and productivity—depend more on the mechanical strength M10 of the coke than on M25. A cost–quality criterion is proposed for finding the optimal coke. In contrast to previous criteria, the cost–quality criterion is based on a model for M10, ignoring M25. That simplifies the calculations required to find the optimal batch. [ABSTRACT FROM AUTHOR]

Multi criteria optimization of complicated catalytic reactions based on a kinetic model is relevant for both manufacturing and laboratory processes. However, this is not enough just to calculate all effective trajectories, values of variable parameters and optimality criteria. Information about feasible interval for optimal mode changes is important when applying the calculated modes in practice. This article provides mathematical formulation of the task of the Pareto front parameter analysis and solution algorithm. For benzyl butyl ether catalytic synthesis reaction, the conditions multi criteria optimization task was resolved, and acceptable interval of changing the optimal values of temperature, mole ratio of initial reagents and reaction time was calculated in order to prevent significant change of optimality criteria values. [ABSTRACT FROM AUTHOR]

Sigmund's 2001 educational paper with a self-contained 99-line MATLAB code had far-reaching impact to teaching and research of topology optimization. This brief note aims to close the gaps on self-contained content desirable for classroom teaching. The goal is to add clarity to the theoretical foundation, and to enable students' learning of the complete iterative optimization solution with minimum additional effort. [ABSTRACT FROM AUTHOR]

The problem of subsample selection among an enormous number of combinations arises when some covariates are available for all units, but the response can be measured only for a subset of them. When estimating a Bayesian prediction model, optimized selections can be more efficient than random sampling. The work is motivated by environmental management of aquatic systems. We consider data on 4360 Finnish lakes and aim to find an approximately optimal subsample of lakes in the sense of Bayesian D-optimality. We study Bayesian two-stage selection where the choice of lakes to be measured at the second stage depends on the measurements carried out at the first stage. The results indicate that the two-stage approach has a modest advantage compared to the single-stage approach. [ABSTRACT FROM AUTHOR]

In this study, the method of inscribed hyperspheres (IHS) is presented and applied for the optimal design of 2-D steel moment frame structures. The weight of the structures, which is a function of the design variables (cross-sectional areas), is optimized subject to stress, displacement, size limits, and the variables' linkage constraints. The IHS approach is employed to find the acceptable centers. The basic idea of this method is to inscribe the largest possible sphere in a closed space that has been created by the objective function and linearized constraints in each step. The obtained results were presented in discrete and continuous variables and compared to the results reported in the literature. This comparison showed the efficiency of this method. Also, a new mixed method of combining the optimality criteria (OC) method and the IHS method is presented in this study. It was observed that the number of iterations needed to reach the optimal solution using this new method is less than that of the above two methods when used individually, and the problem is converged to the optimal answer with extremely low iterations. [ABSTRACT FROM AUTHOR]

We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund (Struct Multidiscip Optim 62:2211–2228, 2020a), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions. [ABSTRACT FROM AUTHOR]

In this work, interval programming problems are considered for financial investment and optimality criteria. An order relation, defined by Ishibuchi and Tanaka for maximization problems, is used to obtain the solution of the problems. A real-life example, related to investment, and its solution are given. Necessary and sufficient optimality criteria including weak and strongly solution for interval programming problems are introduced via basic calculus rule, scalarization, and vectorization. [ABSTRACT FROM AUTHOR]

In topology optimization, the bisection method is typically used for computing the Lagrange multiplier associated with a constraint. While this method is simple to implement, it leads to oscillations in the objective and could possibly result in constraint failure if proper scaling is not applied. In this paper, we revisit an alternate and direct method to overcome these limitations. The direct method of Lagrange multiplier computation was popular in the 1970s and 1980s but was later replaced by the simpler bisection method. In this paper, we show that the direct method can be generalized to a variety of linear and nonlinear constraints. Then, through a series of benchmark problems, we demonstrate several advantages of the direct method over the bisection method including (1) fewer and faster update iterations, (2) smoother and robust convergence, and (3) insensitivity to material and force parameters. Finally, to illustrate the implementation of the direct method, drop-in replacements to the bisection method are provided for popular Matlab-based topology optimization codes. [ABSTRACT FROM AUTHOR]

We study the sensitivity of some optimality criteria based on progressively type-II right censored order statistics scheme changes and explain how the sensitivity analysis helps to find the optimal censoring schemes. We find that determining an optimal censoring plan among a class of one-step censoring schemes is not always recommended. We consider optimality criteria as the model output of a sensitivity analysis problem and quantify how this model depends on its input factor and censoring scheme, using local and global sensitivity methods. Finally, we propose a simple method to find the optimal scheme among all possible censoring schemes. [ABSTRACT FROM AUTHOR]

SAP2000 is well-known commercial software for analysis and design of structural systems that is equipped with an open application programming interface (OAPI). In this work, a code written in C# able to solve three-dimensional topology optimization problems is presented, where a topology optimization framework was integrated into SAP2000 taking advantage of its OAPI feature. The code is partially based on the 99 and 88 line codes written by Sigmund (Struct Multidiscip Optim 21(2):120-127, 2001) and Andreassen et al. (Struct Multidiscip Optim 43(1):1-16, 2011). The code solves the problem of minimum compliance while through OAPI it takes advantage of all modelling capabilities of SAP2000. The paper covers the theoretical aspects of topology optimization incorporated in the code and provides detailed description of their numerical implementations. Special effort was made to the latter one, describing in detail all numerical aspects of the code, in order to facilitate the reader to understand the code, and therefore being able to further enhance its capabilities. The complete code can be downloaded from GitHub (https://github.com/nikoslagaros/TOCP). [ABSTRACT FROM AUTHOR]

Numerical optimization is an indispensable part of the design process of laminated composite structures. Several optimality criteria-based algorithms exist which rely on a sequential resizing and scaling approach. This paper presents a novel design algorithm applicable for stiffness and eigenfrequency optimization of composite structures with concurrent consideration of resizing and scaling operations. A method is introduced that allows for an efficient consideration of nonlinear constraints. This is done by determining stable concurrent scaling parameters from first-order constraint change ratio estimations. Optimization is carried out using optimality criteria in three independent steps, namely with respect to fiber angles, ply thickness ratios, and total laminate thickness. Sensitivity analyses are performed analytically at low computational costs. Numerical examples demonstrate the efficiency and fast convergence of the method. Compared to established algorithms, the number of required function evaluations is reduced significantly. [ABSTRACT FROM AUTHOR]

We consider a bilevel “defender-attacker” model built on the basis of the Stackelberg game. In this model, given is a set of the objects providing social services for a known set of customers and presenting potential targets for a possible attack. At the first step, the Leader (defender) makes a decision on the protection of some of the objects on the basis of his/her limited resources. Some Follower (attacker), who is also limited in resources, decides then to attack unprotected objects, knowing the decision of the Leader. It is assumed that the Follower can evaluate the importance of each object and makes a rational decision trying to maximize the total importance of the objects attacked. The Leader does not know the attack scenario (the Follower’s priorities for selecting targets for the attack). But, the Leader can consider several possible scenarios that cover the Follower’s plans. The Leader’s problem is then to select the set of objects for protection so that, given the set of possible attack scenarios and assuming the rational behavior of the Follower, to minimize the total costs of protecting the objects and eliminating the consequences of the attack associated with the reassignment of the facilities for customer service. The proposed model may be presented as a bilevelmixed-integer programming problem that includes an upper-level problem (the Leader problem) and a lower-level problem (the Follower problem). The main efforts in this article are aimed at reformulation of the problem as some one-level mathematical programming problems. These formulations are constructed using the properties of the optimal solution of the Follower’s problem, which makes it possible to formulate necessary and sufficient optimality conditions in the form of linear relations. [ABSTRACT FROM AUTHOR]

A topology optimization approach based on the boundary element method (BEM) and the optimality criteria (OC) method is proposed for the optimal design of sound absorbing material distribution within sound barrier structures. The acoustical effect of the absorbing material is simplified as the acoustical impedance boundary condition. Based on the solid isotropic material with penalization (SIMP) method, a topology optimization model is established by selecting the densities of absorbing material elements as design variables, volumes of absorbing material as constraints, and the minimization of sound pressure at reference surface as design objective. A smoothed Heaviside-like function is proposed to help the SIMP method to obtain a clear 0-1 distribution. The BEM is applied for acoustic analysis and the sensitivities with respect to design variables are obtained by the direct differentiation method. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem for exterior boundary-value problems. A relaxed form of OC is used for solving the optimization problem to find the optimal absorbing material distribution. Numerical tests are provided to illustrate the application of the optimization procedure for 2D sound barriers. Results show that the optimal distribution of the sound absorbing material is strongly frequency dependent, and performing an optimization in a frequency band is generally needed. [ABSTRACT FROM AUTHOR]

In this paper, the element free Galerkin method (EFG) is applied to carry out the topology optimization of continuum structures with displacement constraints. In the EFG method, the matrices in the discretized system equations are assembled based on the quadrature points. In the sense, the relative density at Gauss quadrature point is employed as design variable. Considering the minimization of weight as an objective function, the mathematical formulation of the topology optimization subjected to displacement constraints is developed using the solid isotropic microstructures with penalization interpolation scheme. Moreover, the approximate explicit function expression between topological variables and displacement constraints are derived. Sensitivity of the objective function is derived based on the adjoint method. Three numerical examples are used to demonstrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We investigate the possibility of extending some results of Pázman and Pronzato (Ann Stat 42(4):1426-1451, 2014) to a larger set of optimality criteria. Namely, the problems of computing D-, A-, and $$E_k$$ -optimal designs in a linear regression model are reformulated here as 'infinite-dimensional' linear programming problems. The same approach is applied to combination of these optimality criteria and to the 'criterion robust' problem of Harman (Metrika 60:137-153, 2004). Approximate optimum designs can then be computed by a relaxation method (Shimizu and Aiyoshi in IEEE Trans Autom Control 25(1):62-66, 1980), and this is illustrated on various examples. [ABSTRACT FROM AUTHOR]

The requirements for highly dynamic drives, which are characterized by a number of contradictory indicators, such as weight-size, power, and dynamic indicators, are presented. Methods for the design of highly dynamic electrical drives and motors for them are reviewed. One possible design method of the electrical drives and motors under consideration is a comprehensive approach that takes into account the effect of different parts of the drive on each other. Possibilities of modern software that make it possible to implement such a complex approach are shown. Possible design stages using the suggested software and integrated approach are analyzed. In the case of the integrated approach, the following design stages can be selected: preliminary electromagnetic calculation of the electric motor, optimization by methods of the nonlinear programming using a genetic algorithm, field calculation using the finite element method, electric motor simulation modeling, interdisciplinary electromagnetic and thermal calculations, 3D modeling, and mechanical calculations. The results of calculations, simulation modeling of the electric drive, and experimental data of the prototype are given. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of characterizing Pareto optima (efficient solutions) for the difference of two mappings vector-valued in a finite or infinite-dimensional preordered space. Closely related to the well-known optimality criterion of scalar DC optimization, a mixed vectorial condition is obtained in terms of both strong (Fenchel) and weak (Pareto) $$\epsilon $$ -subdifferentials that completely characterizes the exact or approximate weak efficiency. This condition also allows to deal with some special restricted mappings. Moreover, the condition established in the literature in terms of strong $$\epsilon $$ -subdifferentials for characterizing the strongly efficient solutions (usual optima), is shown here to remain valid without assuming that the objective space is order-complete. [ABSTRACT FROM AUTHOR]

In a free material formulation, the problem of minimizing a weighted sum of compliance's from multiple load cases, subject to an active constraint on material volume, is solved in a formulation with two optimality criteria. The first optimality criterion for the distribution of material volume densities is equal value for the weighted elastic energy densities, as a natural extension of the optimality criterion for a single load case. The second optimality criterion for the components of a constitutive matrix (of unit norm) is proportionality to corresponding weighted strain components with the same proportionality factor $\widehat \lambda $ for all the components, as shortly specified by $C_{i j k l} = \widehat \lambda \sum _{n} \eta _{n} (\epsilon _{i j})_{n} (\epsilon _{k l})_{n}$, in traditional notation (n indicate load case). These simple analytical results should be communicated, in spite of the practical objection against design for weighted sum of compliance's, as compared to worst case design and design considering strength. The application of the approach of the two optimality criteria is illustrated by a 2D example with 8 load cases. Stable and fast convergence is shown. [ABSTRACT FROM AUTHOR]

A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization solver; internal solver. The coupling between these incomplete solutions is ensured using an outer iteration strategy based on the block coordinate descend method. The presented algorithm provides a general framework to extend the traditional binary phase topology optimization solvers for the solution of multiphase topology optimization problems. Interesting features of the presented algorithm are:generality, simplicity and the ease of implementation. The presented algorithm is used to solve multimaterial minimum structural and thermal compliance topology optimization problems based on the classical optimality criteria method. Details of MATLAB implementation are presented and the complete program listings are provided as the Supplementary Materials. The success and performance of the presented method are studied through several two dimensional numerical examples. [ABSTRACT FROM AUTHOR]

Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff-St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings. [ABSTRACT FROM AUTHOR]

In this paper the nonlinear analysis and design optimization of guyed masts is addressed. The mast is modeled as a 3D truss and is supported by catenary cable elements that have nonlinear elastic behavior. For nonlinear static analysis, an innovative procedure is proposed that divides the structure into linear and nonlinear parts and analyzes them separately. The proposed method satisfies the equilibrium and compatibility by establishing and solution of a set of nonlinear equations. The optimization problem employs the sizes of members, initial cable tensions and the positions of anchor on the ground and tie level of cables on the mast as design variables. To facilitate the optimization solution, a compatible sensitivity analysis procedure is proposed. Sensitivities of objective function, displacement and strength constraints in the mast and cables, subjected to a variety of load combinations including dead, wind and ice loads are calculated. Numerical examples are provided to show the nonlinear analysis procedure and the applicability of the algorithm to optimum design of practical guyed masts. [ABSTRACT FROM AUTHOR]

The paper proposes a model of subjective expected utility with respect to the additive probability measure whose formalism is based on the formally logical principles of optimality, unlike the Anscombe-Aumann SEU model defined in behavioristic traditions. [ABSTRACT FROM AUTHOR]

We consider bilevel optimization from the optimistic point of view. Let the pair ( x, y) denote the variables. The main difficulty in studying such problems lies in the fact that the lower level contains a global constraint. In fact, a point ( x, y) is feasible if y solves a parametric optimization problem L( x). In this paper we restrict ourselves to the special case that the variable x is one-dimensional. We describe the generic structure of the feasible set M. Moreover, we discuss local reductions of the bilevel problem as well as corresponding optimality criteria. Finally, we point out typical problems that appear when trying to extend the ideas to higher dimensional x-dimensions. This will clarify the high intrinsic complexity of the general generic structure of the feasible set M and corresponding optimality conditions for the bilevel problem U. [ABSTRACT FROM AUTHOR]

The material-replacement method is presented to improve the efficiency of topology optimization of a continuum structure with tension-only or compression-only material. Traditionally, a structure with tension-only or compression-only material should be considered as nonlinear in finite element analysis and many times of reanalysis are required to obtain the accurate physical fields for the update of the design variables in optimization. To improve the efficiency of structural optimization, the material-replacement method is proposed, in which the original tension/compression only material is replaced with an isotropic material with the same effective elasticity. The method contents two major ideas. One is the structural reanalysis for nonlinearity of material is put into the global iteration of optimization. The other is that the local stiffness will be modified step by step according to the local stress state. Numerical results show the validity of the method. [ABSTRACT FROM AUTHOR]

When non-zero prescribed support displacements are involved in addition to design independent loads for a continuum/structure, then the objectives of minimum compliance (total elastic energy) and of maximum strength lead to different designs. This is verified by the presented sensitivities. Designs from neither of the two objectives are characterized by uniformly distributed energy density. However, simple iterations with the goal of obtaining uniform energy density show that the strength is favored by this approach. These observations leads to a rejection of the objectives of compliance minimization as well as that of direct strength maximization; we choose the objective of obtaining uniform energy density and show by examples that the obtained solutions are close to fulfilling also strength maximization, with the price of increased compliance. Optimal design examples are presented and discussed in detail for different combinations of non-zero prescribed support displacements and design independent loads. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Composite plates are designed in order to maximize the performance with respect to eigenfrequencies. The plates are considered to be laminates where the individual plies consist of orthotropic material. The design task is the orientation of the orthotropic material in each element of the discretization and the ratio between the amounts of material put in the two directions of the fiber-net. The optimizations are performed using the finite element method for analysis and the optimization approach is a two-step method. In the first step we first find the best design on the basis of a recursive optimization procedure based on an optimality criterion (OC). In the second step mathematical programming (MP) and sensitivity analysis are applied to find the final optimized design. [ABSTRACT FROM AUTHOR]

In early generation variety trials, large numbers of new breeders’ lines need to be compared, and usually there is little seed available for each new line. A so-called unreplicated trial has each new line on just one plot at a site, but includes several (often around five) replicated check or control (or standard) varieties. The total proportion of check plots is usually between 10% and 20%. The aim of the trial is to choose some good performing lines (usually around 1/3 of those tested) to go on for further testing, rather than precise estimation of their mean yield. 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. Some possible design criteria are discussed, and efficient layouts under spatial dependence are considered. [ABSTRACT FROM AUTHOR]

This paper presents a new multi-objective topology optimization algorithm for continuum structures under multiple loading cases. An expert evaluation method of weights based on grey system theory is proposed to calculate the objective weights when the compromise programming approach is employed as a multi-objective optimization scheme converting the multi-objective problem to a single objective problem. A modified updating scheme with a self-adaptive move limit for design variables is also suggested, SIMP is regarded as density-stiffness interpolation scheme and the optimality criteria method is used as the optimizer. Numerical instabilities, such as checkerboards and mesh dependencies, are also discussed. The validities of these methods in this paper are demonstrated by some numerical applications. [ABSTRACT FROM AUTHOR]

The paper presents a topology optimisation method based on optimality criteria for total potential energy maximisation with a volume constraint. The final volume of the optimal structural configuration has not to be specified a priori and is directly controlled by the stress, displacement or stiffness constraints defined at the design problem layout phase. The proposed method leads to the identification of well defined structures characterised by a small number of discrete elements with intermediate material properties within a limited number of iterations. The results obtained by solving several two dimensional benchmark problems are shown. [ABSTRACT FROM AUTHOR]

A proximity theorem is a statement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for L-convex and M-convex functions, this paper establishes proximity theorems for larger classes of discrete convex functions, L2-convex functions and M2-convex functions, that are relevant to the polymatroid intersection problem and the submodular flow problem. [ABSTRACT FROM AUTHOR]

The nonlinear regression model with N observations yi=η( xi,θ) +εi, and with the parameter θ subject to q nonlinear constraints Cj (θ)=0; j=1, ..., q, is considered. As an example, the spline regression with unknown nodes is taken. Expressions for the variances (variance matrices) of the LSE are discussed. Because of the complexity of these expressions, and the singularity of the variance matrix of the LSE for θ, the optimality criteria and their properties, in particular the convexity and the equivalence theorem are considered from different aspects. Also the possibility of restriction to designs with limited values of measures of nonlinearity is mentioned. [ABSTRACT FROM AUTHOR]

A characterization of optimal vector unbiased predictor is obtained. Some properties of optimal unbiased predictors are established. It is shown that simultaneous prediction of future random variables is equivalent to marginal prediction of these random variables. Following Kale and Chandrasekar (1983) and Chandrasekar (1984), it is shown that the criteria proposed by ishii (1969) based on matrices and the one proposed by Bibby and Toutenburg (1977) based on quadratic loss in the class of vector unbiased predictors are equivalent. The above approach is illustrated with some examples. [ABSTRACT FROM AUTHOR]

This paper presents a computer-based method for the optimal design of three-dimensional Reinforced Concrete (RC) structures having beams subjected to shear force and bending moment, columns subjected to biaxial moments, biaxial shears and axial loads, and shear walls subjected to pure shear. Regarding the beams and columns, the design variables are the width, depth and area of longitudinal reinforcement of member sections. The design variables for the shear walls are the thickness of the wall, the area of vertical reinforcement, horizontal distance between the vertical stirrups, the area of horizontal reinforcement, vertical space between the horizontal stirrups, and the area of vertical flexural reinforcement. The Optimality Criteria (OC) method is applied to minimize the cost of the concrete, steel and formwork for the structure. ACI code [1] provisions concerning the strength and ductility of beams, columns and shear walls are taken as constraints. The constraints also impose upper and lower bounds on the dimensions of beams and columns, and on shear wall thickness, reinforcement area and the maximum and minimum vertical and horizontal spaces between the stirrups of the shear walls. Sensitivity analysis is conducted for both internal forces and the capacities of the sections of the beams, columns and shear walls. The features of the design method are illustrated by a solved example. [ABSTRACT FROM AUTHOR]

Statistically motivated algorithms for the solution of stochastic programming problems typically suffer from their inability to recognize optimality of a given solution algorithmically. Thus, the quality of solutions provided by such methods is difficult to ascertain. In this paper, we develop methods for verification of optimality conditions within the framework of Stochastic Decomposition (SD) algorithms for two stage linear programs with recourse. Consistent with the stochastic nature of an SD algorithm, we provide termination criteria that are based on statistical verification of traditional (deterministic) optimality conditions. We propose the use of ‘bootstrap methods’ to confirm the satisfaction of generalized Kuhn-Tucker conditions and conditions based on Lagrange duality. These methods are illustrated in the context of a power generation planning model, and the results are encouraging. [ABSTRACT FROM AUTHOR]

The minisum multifacility location problem is regarded as hard to solve, due to nondifferentiabilities whenever two or more facilities coincide. Recently, several authors have published conditions for the coincidence of facilities. In the present paper, these conditions are extended to more general location problems and improved with respect to new sufficient coincidence conditions for location problems with mixed asymmetric gauges. Some of these conditions are formulated only in terms of the given weights and certain values from a preprocessing step. [ABSTRACT FROM AUTHOR]

In optimal design research, designs are optimized with respect to some statistical criterion under a certain model for the data. The ideas from optimal design research have spread into various fields of research, and recently have been adopted in test theory and applied to item response theory (IRT) models. In this paper a generalized variance criterion is used for sequential sampling in the two-parameter IRT model. Some general principles are offered to enable a researcher to select the best sampling design for the efficient estimation of item parameters. [ABSTRACT FROM AUTHOR]