Showing papers on "Discrete optimization published in 1973"

Waveform Segmentation Through Functional Approximation

Abstract: Waveform segmentation is treated as a problem of piecewise linear uniform (minmax) approximation. Various algorithms are reviewed and a new one is proposed based on discrete optimization. Examples of its applications are shown on terrain profiles, scanning electron microscope data, and electrocardiograms. The processing is sufficiently fast to allow its use on-line. The results of the segmentation can be used for pattern recognition, data compression, and nonlinear filtering not only for waveforms but also for pictures and maps. In the latter case some additional preprocessing is required and it is described in [19].

Optimal discrete systems with pure delays

Abstract: Necessary and sufficient conditions for the optimization of multivariable discrete systems containing pure delays in dynamics, in performance index, and in constraints are investigated. Using nonlinear programming, it is shown that a discrete maximum principle similar to the one derived by Pearson and Sridhar [1] is valid for a subclass of these problems, that is, systems with linear dynamics, convex inequality constraints, and convex performance index.

Discrete Gradient Optimization of Water Systems

Abstract: With the present optimization techniques, diameter of pipes is assumed to be continuous. At the end of the optimization process, the diameter of pipes is then rounded to the nearest available size. This will give an approximate minimum at best, and possibly a nonfeasible solution. A discrete optimization technique that treats pipe diameter as discrete variable and flow and head loss as continuous variable is formulated. It has been applied to a fairly large water transmission system with good results. This technique can be used to design a completely new system as well as an expanding one. Other pipe networks, such as oil pipeline and aircraft fuel system, can also be designed by means of this technique.

Discrete optimization and the planning of electric power networks

Abstract: Power system transmission planning is expressed as a large finite Markovian sequential process over time involving 1) a known planning horizon divided into finite number of stages; 2) a large number of alternative additions (type, size, and place of new facilities) at each stage; 3) analysis and criteria for evaluating network acceptance (performance, reliability, security, cost, etc.) for each alternative at each stage; 4) a searching method to find the optimum plan. Forward dynamic programming is used to maximize the utility of the transmission network over the period of the planning horizon ensuing adequate service, and the results show the effects of economy of scale as the planning horizon is increased. However, dynamic programming is limited by the number of alternatives considered at each stage. Thus a new method, discrete dynamic optimizing (DDO), is also introduced.

The estimation of continuous-time systems using discrete data

Abstract: and several in teres t ing special cases, when the dependent and independent vector variables y(t) and z(t) are observed only at the d iscre te , equally-spaced time-points t = 1, ..., N . The vector x[t) i s a residual and 6 and B are respectively a vector and matrix of parameters to be estimated, with T(T; 8) a possible nonlinear function of 6 . Clearly (l) cannot be directly estimated when only discrete data are available, so we consider the approximation

The solution of discrete linear optimization problems by neighborhood-search techniques

Abstract: A process and apparatus for forming a wide variety of air-laid nonwoven webs, with the apparatus including plural pairs of spaced parallel oppositely rotating lickerins, each pair having a movable divider plate therebetween. The lickerins individualize fibers from separate fibrous sources, which may be similar or dissimilar, and high speed air streams are caused to flow past each individual lickerin, through a mixing zone between each pair of lickerins to form combined streams, and into a common mixing zone above a fiber collecting means to form a composite stream. The individualized fibers are doffed from the lickerins by the high speed air streams and are entrained therein, and divider plates between each pair of lickerins are adjustable through a range of positions for controlling the degree of intermixing of the entrained fibers in the combined streams. A further divider plate is mounted in adjustable relationship with respect to the common mixing zone to control the degree to which the combined streams and entrained fibers intermix in forming the composite stream. The air streams may be generated by a single suction source below the fiber collecting means, or by separate individually controlled suction sources on opposite sides of the further divider plates, which may be individually adjusted to further vary the web that is formed on the fiber collecting means. The further divider plate is preferably removably mounted so that a further material, such as a reinforcing material or an adhesive can be introduced into the composite stream and resulting web, if desired.

Finite State Representations of Discrete Optimization Problems

Abstract: This paper is concerned with the representation of a discrete optimization problem given in the form of a $ddp$ (discrete decision process) by a G-$sdp$ (G-sequential decision process). A G-$sdp$ is a finite state model of discrete optimization problem, consisting of a finite number of states and a rule specifying the transition from one state to another corresponding to each decision applied to it. A cost function, taken from a given family of functions G, is associated with each transition. A necessary and sufficient condition for a given $ddp$ to be represented by a G-$sdp$, which is valid for most important G’s, is obtained ; it turns out that various representation theorems obtained in the earlier paper [3] are special cases of this theorem. Furthermore, a case in which the existence of the unique minimal representation is guaranteed to exist receives special attention, and some sufficient conditions are discussed.

Discrete linear optimal control systems with quadratic cost functionals

Abstract: This paper presents a functional analysis solution to the discrete optimal control problem with quadratic cost functional, dealing with the case of unconstrained control and fixed endpoints.

Optimal control of a linear discrete system.

Abstract: Recently, increasing attention has been paid to the theory of systems; this is manifested by the great number of articles published all over the world. Application of this theory to the problems of control has led to the construction of new algorithms for the synthesis of dynamic systems which could not be obtained by classical methods in control engineering. Moreover, implementation of these algorithms necessitates utilization of digital computer.

A discrete maximum principle for systems with pure delays

Abstract: This paper deals with necessary arid sufficient conditions for the optimization of nonlinear multivariate discrete systems containing pure delays in dynamics, in performance index, and in constraints. Using non-linear programming, it is shown that a discrete maximum principle similar to the one derived by Pearson and Sridhar (1966) is valid for a subclass of these problems, that is systems with linear dynamics, concave inequality constraints, and convex performance index. As an application, the optimal piceewise constant control with optimal non-uniform sampling of systems described by differential equations is derived.

Nonlinear constrained optimization of filled polyesters

Abstract: An efficient method for optimization of a formulation problem subject to nonlinear constraints was demonstrated. Specifically, a nine-variable polyester-filler system was investigated experimentally. The investigation included selection of an efficient experimental design, regression analysis, and study of optimization methods. Recommended procedures are reported, along with examples and discussion of several typical applications.