Showing papers on "Optimal design published in 1974"
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01 Jan 1974
2,486 citations
TL;DR: For general optimality criteria, this article obtained criteria equivalent to $\Phi$-optimality under various conditions on ''Phi'' and showed that such equivalent criteria are useful for analytic or machine computation of ''phi''-optimum designs.
Abstract: For general optimality criteria $\Phi$, criteria equivalent to $\Phi$-optimality are obtained under various conditions on $\Phi$. Such equivalent criteria are useful for analytic or machine computation of $\Phi$-optimum designs. The theory includes that previously developed in the case of $D$-optimality (Kiefer-Wolfowitz) and $L$-optimality (Karlin-Studden-Fedorov), as well as $E$-optimality and criteria arising in response surface fitting and minimax extrapolation. Multiresponse settings and models with variable covariance and cost structure are included. Methods for verifying the conditions required on $\Phi$, and for computing the equivalent criteria, are illustrated.
736 citations
01 Feb 1974
TL;DR: A mixed-integer linear programming approach to the planning of electrical-power networks is described, based on an interpretation of fixed-cost transportation-type models, and includes both network security and costs of network losses.
Abstract: A mixed-integer linear programming approach to the planning of electrical-power networks is described. The method is based on an interpretation of fixed-cost transportation-type models, and includes both network security and costs of network losses. Both single-period and multitime-period planning problems are considered. A large general-purpose mathematical programming system is used to obtain solutions using branch-and-bound algorithms, and the practical aspects of organising the problems and controlling the branch-and-bound tree search within a modern m.p.s. package are discussed. Three case studies are presented for illustration: the optimal design of a 132 kV subtransmission system, the optimal time-phased design of the same system over. eight years, and the optimal layout and cable selection for a new housing-estate low-voltage network. The paper concludes by indicating potential further applications of the method for scheduling, for example, new plant at substations.
135 citations
TL;DR: In this paper, a methodology for optimal design and/or operation of a water distribution system that is to operate under one or several loading conditions is developed for optimal optimization of water distribution systems, where the objective function may include the initial cost of the design, the cost of operation, the physical measures of performance, and penalties for violating constraints.
Abstract: A methodology is developed for optimal design and/or operation of a water distribution system that is to operate under one or several loading conditions. Decision variables may be design variables, such as pipe diameters, or control variables, such as heads and flows. The objective function may include the initial cost of the design, the cost of operation, the physical measures of performance, and the penalties for violating constraints. Constraints may be imposed on the decision variables and on the performance of the system under each loading. Flow solutions are obtained by a modified Newton-Raphson method employing sparse matrix techniques. Optimization is obtained by a combination of the generalized reduced gradient and penalty methods. Implementation in a computer program and its use on a test problem in both batch and time-sharing modes are described, and it is concluded that the method is computationally feasible. The many different ways in which it can be used to analyze, design, and operate water distribution systems are outlined.
119 citations
TL;DR: In this paper, an extension of the Kiefer-Wolfowitz general equivalence theorem is used to establish properties of the procedures and some difficulties in the Bayesian analysis of discrimination experiments are considered.
Abstract: SUMMARY Results in the theory of optimum regression designs are used to develop experimental designs for discriminating between several regression models. An extension of the Kiefer-Wolfowitz general equivalence theorem is used to establish properties of the procedures. A sequential data-dependent strategy is described and its properties investigated for specific examples. In conclusion, some difficulties in the Bayesian analysis of discrimination experiments are considered.
108 citations
TL;DR: In this article, the optimality of connected block designs has been discussed and a partitioning of the family of connected designs in the above fashion has been proposed, namely locally connected, globally connected and pseudo-globally connected designs.
Abstract: Connectedness is an important property which every block design must possess if it is to provide an unbiased estimator for all elementary treatment contrasts under the usual linear additive model. We have classified the family of connected designs into three subclasses: locally connected, globally connected and pseudo-globally connected designs. Basically, a locally connected design is one in which not all the observations participate in the estimation. A globally connected design is one in which all observations participate in the estimation. Finally, a pseudo-globally connected design is a compromise between locally and globally connected designs. Theorems and corollaries are given which characterize the different classes of connected designs. In our discussion on the optimality of connected designs we show that there is much to be gained by partitioning the family of connected designs in the above fashion. Our optimality criteria are $S$-optimality suggested by Shah, which selects the design with minimum trace of the information matrix squared and $(M, S)$-optimality which selects the $S$ optimal design from the class of designs with maximum trace of the information matrix. Using these optimality criteria, we have been able to derive some new results which we hope to be of interest to the users and researchers in the field of optimum design theory. To be specific, let BD $\{v, b, (r_i), (k_u)\}$ denote a block design on a set of $v$ treatments with $b$ blocks of size $k_u, u = 1,2, \cdots, b$ and treatment $i$ is replicated $r_i$ times. Then we have shown that for the family of connected block designs BD $\{v, b, (r_i), k\}$ with (i) less than $k - 1$ treatments having replication equal to one and binary (0, 1) the $S$-optimum design is pseudo-globally connected; (ii) the $S$-optimum design is globally connected if $r_i > 1$ and the designs are binary; and (iii) at least one treatment with replication greater than $b$, then the $(M, S)$-optimum design is pseudo-globally connected. In the final part of this paper we mention some unsolved problems in this area.
107 citations
TL;DR: In this paper, a mathematical optimization problem based on the equilibrium conditions and the stress constraints is formulated to obtain an approximate design which avoids merely local optima, which is close to the exact global optimum obtained by enforcing the compatibility conditions and is therefore a good starting point for an optimizing procedure.
42 citations
TL;DR: In this article, the authors considered the problem of designing optimal observers for linear time-invariant systems and showed that the optimal observer is constructed by a reduced (minimal-order) observer with constant gains.
Abstract: This paper considers the problem of designing optimal observers for linear time–invariant systems. The optimal criterion introduced here is the time–integral of the mean–square estimation error. A canonical form of the observers is given for simplifying the discussion. A necessary and sufficient condition to this optimal design problem is presented. The result states that the optimal observer is constructed by a reduced (minimal–order) observer with constant gains, which are determined by solving a matrix Riecati equation.
20 citations
01 Nov 1974
TL;DR: This paper generalized the approach of Ref.
Abstract: This paper generalized the approach of Ref. [1] for the design of optimal inputs to MIMO systems with process or driving noise. First an expression for the information matrix is derived and it is shown to consist of two parts, one depending on the designed input and the other depending on the process noise input. The equivalence relationships between D-optimal designs and min-max designs are obtained leading up to numerical algorithms for computing globally optimal designs. Easily computable bounds are derived for the loss in performance due to suboptimal designs. It is shown that the optimal input may be chosen to have a discrete spectrum with a finite number of frequencies.
18 citations
TL;DR: In this paper, it was proved that in a sequential design of a regression problem, the variance of the 1s estimate for the response surface in the n-th sequential point tends to zero with n \rightarrow \infty.
Abstract: It is proved that in a sequential design of a regression problem the variance of the 1s estimate for the response surface in the $n$th sequential point tends to zero with $n \rightarrow \infty$ This allows the proof of the convergence of certain procedures for computing $D_s$-optimum designs
16 citations
TL;DR: In this article, an elastic structure is postulated to consist of members which are taken from a given set of available cross sections, and the structure is to be designed, for given total volume, so as to be as stiff as possible.
TL;DR: In this article, an optimal design procedure for sandwich structures subject to frequency and section constraints is developed from direct comparison theorems for different designs, derived from the Rayleigh quotient for the structure.
Abstract: An optimal design procedure for sandwich structures subject to frequency and section constraints is developed from direct comparison theorems for different designs. These theorems are derived from the Rayleigh quotient for the structure. Applications to the axial motion of a bar and to the vibration of a portal frame are given.
TL;DR: In this article, a new statistical variability criterion for optimal design and comparative evaluation of thin film RC active filters is proposed, which is more realistic and useful in designing and/or deciding on the merits of the filter for large-scale manufacture than any of the multiparameter sensitivity functions suggested so far.
Abstract: A new statistical variability criterion for optimal design and comparative evaluation of thin film RC active filters is proposed. The manufacturing industries should find this criterion to be more realistic and useful in designing and/or deciding on the merits of the filter for large-scale manufacture than any of the multiparameter sensitivity functions suggested so far. Four biquadratic bandpass circuits have been chosen to illustrate the usefulness of the criterion and their optimum variability measure is compared.
TL;DR: The optimal design of system reliability which takes into account the quantitative aspect of systems throughput or capacity is proposed and is based on the concept of an r-out-of-n configuration instead of the conventional parallel 1-out of-N configuration.
Abstract: The optimal design of system reliability which takes into account the quantitative aspect of systems throughput or capacity is proposed. It is based on the concept of an r-out-of-n configuration instead of the conventional parallel 1-out-of-n configuration and is especially suitable for treating problems which arise in process systems. The problem is solved by the pseudo-Boolean programming method of Lawler and Bell.
TL;DR: In this article, the authors have considered design behaviour at various loading stages and pressures, as an input in the design process called synthesis and geometric properties are generated as an output, for checking accepted design behaviour or safe pressure carrying capacity.
TL;DR: In this article, the authors present a method of synthesizing optimal control in such a way as to minimize not only a certain cost function, but also the sensitivity of the cost function and trajectory sensitivity.
Abstract: The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic performance index subject to the system dynamics constraint. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory due to the departure of the system parameters from their nominal values or due to the divergence between the mathematical model and the physical system. In an attempt to resolve this difficulty, the paper presents a method of synthesizing optimal control in such a way as to minimize not only a certain cost function, but also the sensitivity of the cost function and trajectory sensitivity. It is shown that the optimal control so obtained will result in a system whose cost function and transient response are little sensitive to first-order variations in plant parameter values. A numerical example involving a synchronous machine swinging against an infinite bus is used to demonstrate the feasibility of incorporating sensitivity consider...
TL;DR: In this paper, a comprehensive model of drainage design suitable for optimization is developed, and a problem dependent algorithm is developed based upon Dynamic Programming, which is shown in actual designs to produce optimal drainage designs simply and cheaply.
Abstract: This paper derives from a research project investigating the systematic use of formal optimization techniques in computer aided building design. A comprehensive model of drainage design suitable for optimization is developed. After limited success with a very powerful general purpose optimization program based upon the Geometric Programming technique, a problem dependent algorithm is developed based upon Dynamic Programming. The latter technique is shown in actual designs to produce optimal drainage designs simply and cheaply.
TL;DR: In this article, the authors presented a method of synthesizing optimal control in such a way as to minimize a certain cost function, while choosing the system controllable parameters in the region of near zero sensitivity.
Abstract: The usual procedure for the optimal design of linear regulators for synchronous machines is to minimize a chosen quadratic cost function subject to the system dynamics constraints. However, the optimal control synthesized in such a straightforward fashion is unsatisfactory, since it is dependent on the particular choice of system control parameters made by the investigators. Furthermore, in practice, there may be a departure of these parameters from their nominal values. In an attempt to resolve these difficulties, the paper presents a method of synthesizing optimal control in such a way as to minimize a certain cost function, while choosing the system controllable parameters in the region of near-zero sensitivity. Considering a three-machine system as an illustrative example, this method is used as a basis for the selection of voltage regulator gains. It is shown that choosing the gains in the region of low sensitivity of the optimal cost function enhances the system transient response. The method is simple and is capable of handling multi-parameter sensitivity analysis in the framework of optimal control.
TL;DR: In this article, the authors present a finite element analysis for the design of large oil tankers with respect to a particular tanker transverse problem and the sensitivity of the optimum design to changes in certain key parameters of the design problem is investigated.
Abstract: There is considerable interest at the present time in the development of rational approaches to the design of ship structure. Particularly important is the design of structure for large oil tankers. These ships now represent about half the world's demand for tonnage and the increase in their size rapidly outstrips traditional evolutionary design methods. In Section 2 of the paper the development of a design scheme for ship structure is described. Broadly the system consists of a finite element analysis routine linked to an optimization algorithm. In Section 3 detailed results are presented for an application of the scheme to a particular tanker transverse problem. In Section 4 the sensitivity of the optimum design with respect to changes in certain key parameters of the design problem is investigated. In Section 5 some alternative ways of using the design scheme are discussed.
01 Jan 1974
TL;DR: The basic problem is identified as one in mathematical programming, in general nonlinear programming, and the difficulties are indicated that are experienced in the application of standard methods of non linear programming.
Abstract: The paper is concerned with methods of optimal structural design. Typical ingredients of structural optimization problems are discussed in Sect. 1. The basic problem is identified as one in mathematical programming, in general nonlinear programming, and the difficulties are indicated that are experienced in the application of standard methods of nonlinear programming. The following three sections deal with optimal plastic design, which is the most developed area of structural optimization because linear programming is applicable to it. Sections 2 and 3 are respectively concerned with the optimal plastic design of a truss of given layout and the determination of the optimal layout of a truss that has to transmit given loads to a given foundation. Optimal plastic design of beams and grillages is discussed in Sect. 4. Section 5 is devoted to optimal design of elastic trusses and beams. Computational aspects of structural optimization are discussed in Sect. 6,and some new ideas are mentioned in Sect. 7.
01 Jun 1974
TL;DR: In this paper, a railway vehicle is modeled as a linear, stable, strictly dissipative multi-degree of freedom dynamic system, and non-linear mathematical programming techniques are used to minimize the nonlinear objective function representing the maximum resonant response at a point of the system.
Abstract: The minimax response of a complex dynamic system, such as a railroad vehicle, can be obtained by choosing certain (optimum) values of the stiffness and damping elements in the system. The railway vehicle is mathematically modeled as a linear, stable, strictly dissipative multi-degree of freedom dynamic system. The system is excited at more than one point by synchronous harmonic forces. A minimax principle reduces the problem to that of finite dimensional optimal design problem. Non-linear mathematical programming techniques are used to minimize the non-linear objective function representing the maximum resonant response at a point of the system, and subjected to linear or non-linear constraints, over a certain frequency range. The frequency range may be finite or infinite. Dynamic response of the system before and after optimization is shown, and three-dimensional plots for the constrained and unconstrained objective function versus the two most important design parameters are illustrated.
TL;DR: In this article, the authors characterized classes of uniformly optimal designs under different conditions on the availability or observations, i.e. in different sets of admitted designs, and in cases where D and A optimal designs do not exist, they gave a particular resut, in particular optimality statements concerning incomplete designs such as those presented by J. KIEFER.
Abstract: In a goneral three way layout without interactions: a particular choice of the system {n ijk } of numbers of observations at the levels i, j, k of the three factors represent a specific (nomandomized) design of the three way layout. Classes of uniformly optimal designs under different conditions on the availability or observations, i.e. in different sets of admitted designs, are characterized. In cases where uniformly optimal designs do not exist, D and A optimal designs are given. A particular resut is the following: If the numbers of observations are restricted by the systems {n i }, {n j }, {n j } of the total numbers of observations at each level of every factor, then a design dealing with inference with respect to the first factor is uniformly if and only if it satisfics the conditions {n ij = n i n j /n} and {n ik =n k /n} for all i and j. The results obtained establish, in particular optimality statements concerning incomplete designs such as those presented by J. KIEFER in [Ann. Math. Statist. 29 ...
01 May 1974
TL;DR: In this, the first of four connected reports, the authors survey the published material on mixtures experiments and optimal design construction, and provide a bibliography for each area.
Abstract: : In this, the first of four connected reports, the authors survey the published material on mixtures experiments and optimal design construction, and provide a bibliography for each area. (Author)
TL;DR: In this article, the optimal time in stochastic control and optimal design of stochastically optimal control are discussed. But the authors do not consider the problem of optimal design.
Abstract: CONTENTSIntroduction § 1. Optimal time in a stochastic control § 2. Optimal time and optimal design § 3. Stationary quasi-variational inequalities References
01 Apr 1974
TL;DR: In this article, a dynamic model of an automatic vehicle system is analyzed and formulated as an optimal design problem, and the design concept adopted is to find the design parameters such that the gun barrel has a desirable property of least possible disturbance from a perturbation due to continuous bursts under uncertainty of environments such as road conditions and the azimuth angle.
Abstract: : A dynamic model of an automatic weapon-vehicle system is analyzed and formulated as an optimal design problem. The design concept adopted is to find the design parameters such that the gun barrel has a desirable property of least possible disturbance from a perturbation due to continuous bursts under uncertainty of environments such as road conditions and the azimuth angle. Thus, the optimal design problem becomes a 'parametric optimal design' problem with a system of highly nonlinear differential equations that describe the state of the system. A numerically implementable transcription is given such that the formulation fits into the finite dimensional parametric optimal design problem.
TL;DR: In this article, the optimal design of an elastic truss carrying a single system of loads, subject to stress constraints and nonzero minimum stiffness constraints, is studied and necessary and sufficient conditions for local optimality of a fully stressed design are derived by the method of Lagrange multipliers.
Abstract: This paper is concerned with the optimal design of an elastic truss carrying a single system of loads, and subject to stress constraints and nonzero minimum stiffness constraints. Necessary and sufficient conditions for local optimality of a fully stressed design are derived by the method of Lagrange multipliers. The form of the optimality conditions for some special cases of the general problem are considered and their application is illustrated by examples.