Properties of three computational forms of r-algorithms differentiated by their complexities (number of calculations per iteration) are considered. The results on convergence of the limit variants of r-algorithms for smooth functions and r μ (α)-algorithm for nondifferentiable functions are presented. A variant of r(α)-algorithms with a constant coefficient of space dilation α and adaptive step adjustment along the normalized anti-subgradient in the transformed space of variables is discussed. Octave-functions ralgb5 and ralgb4 of r(α)-algorithms with adaptive step adjustment are described. The results of computational experiments for substantially ravine piecewise quadratic function and ravine quadratic and piecewise linear functions are presented.

Shor’s r-Algorithms: Theory and Practice

Until recently, the statistical approach was the main technique in solving the prediction problem. In the framework of static models, the tasks of forecasting, the identification of hidden periodicity in data, analysis of dependencies, risk assessment in decision making, and others are solved. The general disadvantage of statistical models is the complexity of choosing the type of the model and selecting its parameters. Computing intelligence methods, among which artificial neural networks should be considered at first, can serve as alternative to statistical methods. The ability of the neural network to comprehensively process information follows from their ability to generalize and isolate hidden dependencies between input and output data. Significant advantage of neural networks is that they are capable of learning and generalizing the accumulated knowledge. The article proposes a method of neural networks training in solving the problem of prediction of the time series. Most of the predictive tasks of the time series are characterized by high levels of nonlinearity and non-stationary, noisiness, irregular trends, jumps, abnormal emissions. In these conditions, rigid statistical assumptions about the properties of the time series often limit the possibilities of classical forecasting methods. The alternative methods to statistical methods can be the methods of computational intelligence, which include artificial neural networks. The simulation results confirmed that the proposed method of training the neural network can significantly improve the prediction accuracy of the time series.

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Neural network time series prediction based on multilayer perceptron

A general approach and methods are proposed for matched system solution of the following sequence of interconnected problems: the construction of a set of objective functions from empirical data under conceptually uncertain conditions, the determination of a Pareto set under the condition of a rational mutual matching of the set of values and the domain of objective functions, and a multicriterion choice of a rational solution on a Pareto set under the condition of a compromise between inconsistent objectives. As a result, new possibilities are opened up for finding rational compromises in multicriterion problems of conceptual design, situation prediction, and innovation planning.

A Rational Compromise in the System Problem of Disclosure of Conceptual Uncertainty

In this paper the primary components of a Decision Support System (DSS) for on line control of various activities of a Computer Integrated Manufacturing System (CIMS) will be delineated More specifically, the interrelationships among various decision making components of such a system will be discussed

Components of a decision support system for computer integrated manufacturing

Three classes of methods to generate pseudorandom sequences based on arithmetic principles are given. A class of matrix nondifferentiable optimization problems is analyzed and a method is proposed to solve them based on r-algorithms. An application is given.

Arithmetic modeling of random processes and r-algorithms

This article examines some topics of optimization of computations, which have been discussed at 25 seminar-schools and symposia organized by the V.M. Glushkov Institute of Cybernetics of the Ukrainian Academy of Sciences since 1969. We describe the main directions in the development of computational mathematics and present some of our own results that reflect a certain design conception of speed-optimal and accuracy-optimal (or nearly optimal) algorithms for various classes of problems, as well as a certain approach to optimization of computer computations.

Optimization of computations

Program package for solving large-scale production and transportation planning problems (PLANNER)

The paper describes the features of the DISNEL package for interactive solution of a wide range of discrete and nonlinear optimization problems of ES computers.

V. S. Mikhalevich

Papers

Optimization of computations

Program package for solving large-scale production and transportation planning problems (PLANNER)

Disnel: An application package for solving discrete and nonlinear optimization problems

Оптимизационные задачи производственно-транспортного планирования : модели, методы, алгоритмы

Investigation of optimization methods and their applications