Minimax optimal placement problem for special-form objects on a multiply connected domain

An optimal placement problem for special-form objects on a multiply connected domain is considered. The objects must be disjoint and belong to a convex region that contains forbidden areas. The performance criterion is described by a function of maximum of differentiable functions. The method of feasible directions and the method of directed transition were adapted to solve this problem. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 128–137, May–June 2007.     

Memory-based neuro-fuzzy system for interpolation of reflection coefficients of printing inks

The problem of interpolation of a two-dimensional function on a nonuniform axial rectangular grid is considered. To solve the problem, a memory-based neuro-fuzzy system is proposed. This system is computationally simple and provides a high-quality interpolation. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–11, September–October 2008.     

A nonlinear compromise scheme in multicriteria evaluation and optimization problems

The concept of a nonlinear compromise scheme in multicriteria problems of evaluation and optimization is presented. It is shown that the problem is to approximate correctly the utility function and construct a substantial mathematical model (scalar convolution) adequate to the given situation to solve various multicriteria problems. In analysis problems, this convolution is an objective function. Its extremization results in a compromise-optimal vector of arguments. An illustrative example is given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 106–114, July–August 2009.     

Solution of continuous problems of optimal covering with spheres using optimal set-partition theory

The paper considers a continuous problem of optimal c-sphere covering of a compact set from Ω from E _n with a given number of spheres of minimum radius and a problem of covering a set with the minimum number of spheres of given radius. Algorithms are proposed and substantiated to solve the problems using optimal set-partition theory and Shor’s r-algorithm. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 98–117, May–June 2009.     

Optimizing a mathematical model of a 3D body surface

A general method is proposed to select the number and arrangement of horizontal and vertical sections of a surface sufficient to describe this surface by splines of two variables with an accuracy sufficient from the technological point of view. An analytical review is given to methods that can be used to solve the problem posed (spline-interpolation, spline-interlineation of functions, R-functions, the theory of polynomial operator interpolation). The results of a computation experiment are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 103–112, January–February 2006.     

Pursuit problem in distributed control systems

A pursuit problem in distributed parabolic control systems without mixed derivatives with variable coefficients is considered. The finite-difference method is used to solve this problem. Necessary conditions for the termination of a pursuit are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 153–158, March–April 2009.     

Solving a continuous nonlinear problem of optimal set partition with arrangement of subset centers in the case of a convex objective functional

A continuous nonlinear single-commodity problem of optimal partition of a set Ω in an n-measurable Euclidean space into disjoint subsets with arrangement of their centers is analyzed using equality and inequality constraints in the case of a convex objective functional. A method and algorithm are proposed to solve this problem. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 134–152, March–April 2008.     

Capabilities of the system maple in studying dynamic systems of magnetically interacting free bodies

The problem of n magnetically interacting free bodies is considered. Its dynamic model of order 12n is obtained based on the Lagrangian formalism. The Maple software is used to numerically solve the Cauchy problem and to plot phase portraits. The model is relevant to magnetic levitation. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 178–183, November–December 2007.     

Using artificial neural networks for classification of black-and-white images

This work is devoted to the problem of automatic classification of binary images. To solve this problem, neural networks are used. Experiments based on a database of faxgrams are performed with neural networks of different types. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 184–187, March–April 2008.     

A method of multicriteria evaluation and optimization of hierarchical systems

It is shown that any multicriterion problem can be represented by a hierarchical system. Individual properties of the object are evaluated at the lower level of the system, using a criterion vector; and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriterion problems of evaluation and optimization. It is based on nested scalar convolutions of vector-valued criteria and allows simple structural and parametrical synthesis of multicriterion hierarchical systems. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–92, May–June 2007.     

The quasi-newtonian method of solution of convex variational inequalities with descent decomposition

The problem of numerical solution of convex variational inequalities with nonlinear constraints is considered. An equivalent optimization problem is constructed. To solve it, a Newtonian-type method with descent decomposition with respect to direct and dual variables of a variational inequality is developed. The nonlocal convergence of the algorithm and the superlinear rate of convergence in a neighborhood of the solution are proved. Translated from Kibemetika i Sistemnyi Analiz, No. 4, pp. 90–105, July–August, 1999.     

Analysis of mathematical models and methods of solving combinatorial optimization problems on game-type permutations

The paper is concerned with an optimization problem on game-type permutations, where one or both players have combinatorial constraints on their strategies. A mathematical model of such problems is constructed and analyzed. A modified graphical method is proposed to solve (2xn)-and (mx2)-dimensional problems. High-dimensional problems are reduced to linear programming and combinatorial optimization problems. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 103–114, November–December 2007.     

Analysis and formation of acoustic fields in inhomogeneous waveguides

The problem of numerical modeling and formation of acoustic fields with definite properties in an axisymmetric inhomogeneous underwater waveguide is considered. A numerical method to solve a boundary-value and extremal problems for a parabolic Schr?dinger-type wave equation with a complex nonself-adjoint operator is proposed and investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 62–71, March–April 2009.     

Solving optimization problems with linear-fractional objective functions and additional constraints on arrangements

The paper proposes an exact method to solve an optimization problem on arrangements with a linear-fractional objective function and additional linear constraints. The efficiency of the solution algorithm is analyzed by means of numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 79–85, September–October 2006.     

Optimization of the synthesis of hyperplane clusters and neurofunctional transforms in signal classification systems

The paper continues the analysis of clustering and signal classification problems. For problems of point-set clustering in a feature space, an optimal algorithm to synthesize hyperplane clusters and an algorithm to solve a problem on linear separability of a finite point set are obtained, criteria for linear strip separability of points in a feature space into two classes are formulated, and methods of finding optimal nonlinear transform of a coordinate of the feature vector in given classes of functions and its index are developed. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 50–58, November–December 2008.     

A regularization algorithm for singular controls of parabolic systems

A practically convenient method of regularization is proposed to solve an optimal control problem for a parabolic equation with a delta function on its right-hand side. The corresponding regularized analogue is proved to converge to a delta function in a negative space. The differential characteristics of the performance criterion are analyzed. An algorithm for finding the optimal control is developed for a regularized problem. Results from a numerical testing of the algorithm are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 86–94, January–February 2006.     

A finite element/Monte–Carlo method for polymer dilute solutions

A finite element/Monte–Carlo method is proposed for solving the flow of a polymer dilute solution. The mass and momentum equations are supplemented with stochastic differential equations which model the dynamics of the polymer chains. Finite elements and a Monte–Carlo method are used to solve the problem. A theoretical analysis is performed on a simplified, deterministic, Oldroyd-B problem. Numerical results are compared to experimental ones. Received: 22 December 2000 / Accepted: 30 May 2001     

A Relaxation Approach for Estimating Origin–Destination Trip Tables

The problem of estimating origin-destination travel demands from partial observations of traffic conditions has often been formulated as a network design problem (NDP) with a bi-level structure. The upper level problem in such a formulation minimizes a distance metric between measured and estimated traffic conditions, and the lower level enforces user-equilibrium traffic conditions in the network. Since bi-level problems are usually challenging to solve numerically, especially for large-scale networks, we proposed, in an earlier effort (Nie et al., Transp Res, 39B:497–518, 2005), a decoupling scheme that transforms the O–D estimation problem into a single-level optimization problem. In this paper, a novel formulation is proposed to relax the user equilibrium conditions while taking users’ route choice behavior into account. This relaxation approach allows the development of efficient solution procedures that can handle large-scale problems, and makes the integration of other inputs, such as path travel times and historical O–Ds rather straightforward. An algorithm based on column generation is devised to solve the relaxed formulation and its convergence is proved. Using a benchmark example, we compare the estimation results obtained from bi-level, decoupled and relaxed formulations, and conduct various sensitivity analysis. A large example is also provided to illustrate the efficiency of the relaxation method.     

Shrinkage of arcs in solving systems of linear inequalities with graph structure

To solve systems of linear equalities with graph structure, it is necessary to execute operations of sequential shrinkage of terminal and intermediated arcs. The paper deals with an algorithm of shrinkage of these arcs for a graph specified as an adjancency matrix. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 167–170, March–April, 2000.     

A rescue robot designed for ease of use: development of exploration system using behavior of bombycid

Rescue operation is one of most effective applications of robots. However, previous rescue systems that use robots have a serious problem that is a shortage of professional operators. In this paper, we develop an exploration system of survivors using carbon dioxide, and to solve the problem we apply searching mechanism of bombycid to our system. To demonstrate the effectiveness of the proposed system, experiments have been conducted. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008