Vol 77, No 12 (2016)

We consider the planning problem for freight transportation between two railroad stations. We are required to fulfill orders (transport cars by trains) that arrive at arbitrary time moments and have different value (weight). The speed of trains moving between stations may be different. We consider problem settings with both fixed and undefined departure times for the trains. For the problem with fixed train departure times we propose an algorithm for minimizing the weighted lateness of orders with time complexity O(qn² log n) operations, where q is the number of trains and n is the number of orders. For the problem with undefined train departure and arrival times we construct a Pareto optimal set of schedules optimal with respect to criteria wL_max and C_max in O(n² max{n log n, q log v}) operations, where v is the number of time windows during which the trains can depart. The proposed algorithm allows to minimize both weighted lateness wL_max and total time of fulfilling freight delivery orders C_max.

The paper is concerned with scheduling trains moving in both directions between two stations connected by a single-track railway with a siding. The paper presents dynamic programming based algorithms which minimizes two objective functions: maximum lateness and total weighted completion time. The complexity of these algorithms is O(n²).

A new approach was proposed to analyze the stability of the linear continuous stationary dynamic systems. It is based on the decomposition of a square H₂ norm of the transfer function of the dynamic system into parts corresponding either to particular eigenvalues of the system matrix, or to pairwise combinations of these eigenvalues. The spectral decompositions of a square H₂ norm of the transfer function with multiple poles were obtained using the residues of the transfer function and their derivatives. Exact analytical expressions for calculation of the quadratic forms of the corresponding expansions were derived for an arbitrary location of the eigenvalues in the left half-plane. The obtained decompositions allow one to characterize the contribution of individual eigen-components or their pairwise combinations into the asymptotic variation of the system energy. We propose the energy criterion for estimation of the system stability margins that uses an evaluation of energy accumulated in a group of weakly stable system modes. This approach is illustrated by calculating the energy of a band-pass filter.

Consideration was given to a method of analysis of the automatic control systems described by the mathematical model with cubic characteristic equation. The possibility was demonstrated of fast and simple selection of the PID-controller parameters on the operational amplifier with the aim of providing aperiodic character of the transient in the closed-loop system.

Consideration was given to the two-step problem of stochastic optimization with a bilinear model which describes the problem of forming the securities portfolio consisting of some risk assets and one riskless asset. The probability of exceeding the given threshold of capital is used as the optimality criterion. At the second step, the piecewise constant control is used as the capital control. Determined were the upper and lower estimates of the probability functional. The problems of maximizing the upper and lower estimates of the probability functional were reduced to the problems of mixed integer linear programming by means of discretizing the probabilistic measure. An algorithm to seek an approximate solution to the original problem was proposed, and an example was considered.

We construct a semi-Markov model for a queueing system GI/G/1/0 with an unreliable server, where after the server’s failure it is subject to minimal emergency restoration, and after reaching certain total time of operation it is subject to complete maintenance with full restoration of its reliability characteristics. We define stationary reliability and economical system parameters and perform bicriterial optimization of the maintenance period.

The paper considered the distributions of random finite sequences occurring in the theory of collective conformity behavior. A theorem stating that the full principle of large deviations is satisfied for such sequences was formulated and proved. The corresponding action functional was determined.

The problem of selection the most informative features is reduced to an optimization problem for the average risk functional whose maximization is equivalent to maximization of informational distance between distributions of features in two classes. We consider a maximization procedure for the average risk functional via empirical risk, estimating the divergence between them, with Rademacher complexity. The proposed method has been applied efficiently to problems of selection parameters important to separate the states of technological processes. We show an experimental comparison of the developed approach with other widely known feature selection techniques.

We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all the players from the coalition are strictly benefited. Such deviations define a coalitional better-response (CBR) dynamics that is in general stochastic. The CBR dynamics either converges to a K-stable equilibrium or becomes stuck in a closed cycle. We also assume that at each time a selected coalition makes mistake in deviation with small probability that add mutations (perturbations) into CBR dynamics. We prove that all K-stable equilibria and all action profiles from closed cycles, that have minimum stochastic potential, are stochastically stable. Similar statement holds for strict K-stable equilibrium. We apply the CBR dynamics to study the dynamic formation of the networks in the presence of mutations. Under the CBR dynamics all strongly stable networks and closed cycles of networks are stochastically stable.

In article the basic is constructive-technological decisions applied in galvanic isolators (GI) with giant magnetoresistive by effect are considered. Results of research of spin-valve magnetoresistive (SVMR) nanostructures with an antiferromagnetic film (Ta–FeNiCo–CoFe–Cu–CoFe–FeNiCo–FeMn–Ta) for creation on their basis domestic digital GI are presented. Are received magnetoresistive elements on the basis of the developed technological processes of formation nanostructures with size SVMR of effect 7–8%, at a room temperature.

To solve a reactor system static optimization problem by simulation and control theory methods were created a reactor node simulation model and control theory model. The static optimization problem is set and solved.