Showing papers on "Discrete optimization published in 1984"
Book•
01 Feb 1984
TL;DR: This book contains the edited version of lectures and selected papers presented at the NATO ADVANCED STUDY INSTITUTE on computer aided optimal design: Structural and Mechanical Systems, held in Tr6ia, Portugal, 29th June to 11th July 1986.
Abstract: This book contains the edited version of lectures and selected papers presented at the NATO ADVANCED STUDY INSTITUTE ON COMPUTER AIDED OPTIMAL DESIGN: Structural and Mechanical Systems, held in Tr6ia, Portugal, 29th June to 11th July 1986, and organized by CEMUL -Center of Mechanics and Materials of the Technical University of Lisbon. The Institute was attended by 120 participants from 21 countries, including leading scientists and engineers from universities, research institutions and industry, and Ph.D. students. Some participants presented invited and contributed papers during the Institute and almost all participated actively in discussions on scientific aspects during the Institute. The Advanced Study Institute provided a forum for interaction among eminent scientists and engineers from different schools of thought and young reseachers. The Institute addressed the foundations and current state of the art of essential techniques related to computer aided optimal design of structural and mechanical systems, namely: Vari ational and Finite Element Methods in Optimal Design, Numerical Optimization Techniques, Design Sensitivity Analysis, Shape Optimal Design, Adaptive Finite Element Methods in Shape Optimization, CAD Technology, Software Development Techniques, Integrated Computer Aided Design and Knowledge Based Systems. Special topics of growing importance were also pre sented.
1,256 citations
TL;DR: A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments and the performance is compared to that of other existing hyper cube structures such as Boolean n-cube and nearest neighbor mesh computers.
Abstract: A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments. The interconnection is based on a mixed radix number system and the technique results in a variety of hypercube structures for a given number of processors N, depending on the desired diameter of the network. A cost optimal realization is obtained through a process of discrete optimization. The performance of such a structure is compared to that of other existing hypercube structures such as Boolean n-cube and nearest neighbor mesh computers.
786 citations
TL;DR: Some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem, and the results will be applied to a certain class of approximation problems.
Abstract: In this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem. This will be done for weakly minimal and minimal solutions, respectively. Finally the results will be applied to a certain class of approximation problems.
137 citations
59 citations
TL;DR: A comprehensive study of most of the available computer optimization codes, which may be used for metal cutting operations, has been carried out, and a short description of each of these codes is given showing its features and limitations.
55 citations
Posted Content•
TL;DR: A new methodology called INDTREES (for INdividual Differences in TREE Structures) for fitting various(discrete) tree structures to three-way proximity data for relieving three common types of maladies.
Abstract: Models for the representation of proximity data (similarities/dissimilarities) can be categorized into one of three groups of models: continuous spatial models, discrete nonspatial models, and hybrid models (which combine aspects of both spatial and discrete models). Multidimensional scaling models and associated methods, used for the spatial representation of such proximity data, have been devised to accommodate two, three, and higher-way arrays. At least one model/method for overlapping (but generally non-hierarchical) clustering called INDCLUS (Carroll and Arabic 1983) has been devised for the ease of three-way arrays of proximity data. Tree-fitting methods, used for the discrete network representation of such proximity data, have only thus far been devised to handle two-way arrays. This paper develops a new methodology called INDTREES (for individual Differences in TREE Structures) for fitting various (discrete) tree structures to three-way proximity data. This individual differences generalization is one in which different individuals, for example, are assumed to base their judgments on the same family of trees, but are allowed to have different node heights and/or branch lengths. We initially present an introductory overview focussing on existing two-way models. The INDTREES model and algorithm are then described in detail. Monte Carlo results for the INDTREES fitting of four different three-way data sets are presented. In the application, a single ultrametric tree is fitted to three-way proximity data derived from intention-to-buy-data for various brands of over-the-counter pain relievers for relieving three common types of maladies. Finally, we briefly describe how the INDTREES procedure can be extended to accommodate hybrid modelling, as well as to handle other types of applications.
47 citations
TL;DR: In this article, the authors present the capabilities of the ADS-1 program and demonstrate its application to structural synthesis, which solves the general nonlinear constrained optimization problem in the standard form at each level of the optimization process.
Abstract: Today, numerous programs are available which may be coupled with finite element analysis or other analysis techniques to perform the optimization function in the solution of structural synthesis problems. However, most of these codes include only one or two algorithms and many have not been tested on problems of significant size and complexity. There is, therefore, a need for a reliable, general-purpose, publicly available code, containing a variety of modern algorithms for use in structural synthesis as well as general engineering design. The ADS-1 program (Automated Design Synthesis: Version 1) was written in response to this need. The present investigation has the objective to present the capabilities of the ADS program and to demonstrate its application to structural synthesis. The ADS program solves the general nonlinear constrained optimization problem in the standard form. At each level of the optimization process, several options are available.
33 citations
TL;DR: In this paper, the authors present a review of the development of the discrete maximum principle and present a new approach to optimization of the multi-stage optimization problems called the upper boundary approach.
Abstract: In this paper we present a review of the development of the discrete maximum principle. In the presentation, the emphasis is on a geometrical interpretation. The crucial assumptions in the theory developed are pointed out, and the attempts to overcome the limitation in the resulting theorems ore exposed. Following the review, we present a new approach to optimization of the multi-stage optimization problems called the ’ upper boundary approach ’. The classical methods of solving this problem are shown to fit smoothly into the new approach. Moreover, using this approach a number of new results have been developed, among these a new generalized version of the discrete maximum principle. The new version does not require the assumption of directional convexity.
24 citations
TL;DR: The combination of simulation and optimization for probabilistic models with continuous decision variables is discussed and the stochastic quasigradient method which is a well known technique in Stochastic optimization may also successfully applied for simulation-optimization problems.
Abstract: A major part of all simulation models contains a number of decision variables. For such models the problem of optimal decision arises in a natural way. The combination of simulation and optimization for probabilistic models with continuous decision variables is discussed in this paper. Several important techniques for solving the combined problem are presented. In particular the stochastic quasigradient method which is a well known technique in stochastic optimization may also successfully applied for simulation-optimization problems.
13 citations
TL;DR: The structural and computational aspects of two decomposition algorithms suitable for dynamic optimization of nonlinear interconnected networks are examined.
Abstract: The structural and computational aspects of two decomposition algorithms suitable for dynamic optimization of nonlinear interconnected networks are examined. Both methods arise from a decomposition based on Lagrangian duality theory of the addressed dynamic optimization problem, which is the minimization of energy costs over a given time period, subject to the requirement that the network equations and inequality restrictions are satisfied. The first algorithm uses a spatial decomposition of the state space into subgroups of state variables associated with particular network zones. This leads to a number of lower-dimensional optimization problems which can be solved individually at one level and coordinated at a higher level to account for interactions between these zones. The second algorithm uses time decomposition to solve a sequence of static optimization problems, one for each time increment into which the interval is subdivided, which are then coordinated to take account of dynamic interaction between the time increments. Computational results from an actual network in the United Kingdom are presented for both methods.
01 Jan 1984-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: An approach to classification is described where an evaluation function is available, and the major difference between this approach and previous optimization attempts is the use of deterministic ratter than probabilistic classifications.
Abstract: An approach to classification is described where an evaluation function is available. Deterministic classifications are evaluated by a heuristic function, and a special search procedure is applied to find a classification optimizing this function. A specific application to image segmentation is presented, including several examples. The major difference between this approach and previous optimization attempts is the use of deterministic ratter than probabilistic classifications.
Dissertation•
01 Jan 1984
TL;DR: In this paper, the authors present a survey of statistics and optimization in the field of statistical and optimization for the application of computer vision. But their work is limited to a single application.
Abstract: (1984). Statistics and Optimization: The Interface. American Journal of Mathematical and Management Sciences: Vol. 4, Statistics and Optimization: The Interface, pp. 1-5.
TL;DR: Relations between efficient solutions to discrete multicriteria decision problems and optimal solutions to corresponding parametric single-criterion problems are analyzed.
Abstract: Relations between efficient solutions to discrete multicriteria decision problems and optimal solutions to corresponding parametric single-criterion problems are analyzed. In particular we consider such decision problems where one criterion is a sum function while the remaining criteria are bottleneck functions. In this case the multi-criteria problem can be reduced to a linear parametric sum problem. Depending upon the nature of its feasible set, the sum problem may belong to a class of computationally tractable optimization problems, By solving it parametrically we can then generate the set of all efficient solutions to the original multicriteria problem.
01 May 1984
TL;DR: In this paper, three different classes of multiple points location-allocation problems in the Euclidean plane are considered under a discrete optimization criterion which minimizes the maximum cost based on certain interpoint distances.
Abstract: Three different classes of multiple points location-allocation problems in the Euclidean plane are considered under a discrete optimization criterion which minimizes the maximum cost based on certain interpoint distances. Each of these classes of geometric optimization problems is studied with three different distance metrics (Euclidean, Rectilinear, Infinity) as well as for feasible solution sets in the plane which are both discrete and infinite. All of these problems are shown to be polynomial-time reducible to each other and furthermore D^{p} complete.
01 Jan 1984
TL;DR: In treating vector optimization problems, dialogue methods play an ever increasing role (see e.g. R. Wierzbicki, et al. /).
Abstract: In treating vector optimization problems, dialogue methods play an ever increasing role (see e.g. R. Dupre et al /2/, A. Wierzbicki /1 1 /, A. Lewandowski et al /8/, S. Zionts et al /13 /).
01 Jan 1984
TL;DR: In studying physical and engineering systems, one usually starts with a mathematical model which is obtained by considering some physical laws and/or empirical formulae and the behaviour of the system is described by the evolution of appropriate variables over time or over frequencies.
Abstract: In studying physical and engineering systems, one usually starts with a mathematical model which is obtained by considering some physical laws and/or empirical formulae. The behaviour of the system is then described by the evolution of appropriate variables (dependent variables) over time or over frequencies (the independent variable). For a broad class of systems, the values of the dependent variables are only known, or can only be defined, at discrete time instants. Typical examples of this are found in the fields of information processing, digital filters, managerial systems, environmental systems, certain command and control systems, socioeconomic systems, to name but a few. In addition, the rapid growth in computing capabilities and the improved technology of microprocessorshhas attracted systems analysts and modellers to utilise digital computers extensively in solving their problems. This is the case with many industrial processes where digital devices are often used. In such industrial applications, we have batch information processing in contrast to the continuous information processing which was required when traditional analog equipment was used.
06 Jun 1984
TL;DR: A recursive equation is provided for the computation of the 2.D Faddeva matrices of the algorithm given in [1].
Abstract: The purpose of this paper is to provide a recursive equation for the computation of the 2.D Faddeva matrices of the algorithm given in [1]. It will be shown that with this equation, the algorithm becomes computationally much simpler.