Vol 77, No 11 (2016)

We propose an approach for solving the task prioritization problem in road surface repair under bounded resources; the idea is to use a combination of defect recognition and classification methods based on statistical analysis and machine learning (random forests) with original methods for solving infinite-dimensional optimization problems (optical-geometric analogy). We show the results of a computational experiment that indicate high performance of the developed algorithms, and the resulting solutions were evaluated highly by experts in road facilities management. Our results may encourage more efficient use of resources to improve the quality of motorways.

We consider the problem of estimating the probability of collision between shunting trains and passenger trains on a railroad station. We assume that the flow of shunting trains is Poisson for every turnout switch on which side collisions are possible. The data for computations include the station’s topology, timetable of passenger trains, and possible routes of their passing through the station together with the intensities of shunting trains moving through nonisolated turnout switches where collisions are possible, and also mean values of train lengths and their velocities. The proposed mathematical model of train motion can be regarded as a first approximation in modeling the collision process for trains on a railroad station. We also consider a real life example.

Consideration was given to the optimization model of assigning the locomotives to the freight trains. The model was formulated in terms of a dynamic problem of stochastic programming with probabilistic constraints. The state variables characterize positions of the locomotives and trains at each time instant. The variables defining the motion of locomotives and their assignment to trains at each time instant play the role of controls. The expectation of the total freight traffic is the criterial function of the problem. A two-stage hybrid algorithm to solve the problem was developed. It combines the coordinatewise search and a genetic algorithm. Results of the numerical experiment were given.

We consider the problems of designing the routes for freight cars from departure stations to destination stations and problems and planning model for the works and for finding the necessary number of trains to deliver a given number of freight cars from departure stations to destination stations.

We consider a servicing model for a stationary processor that services a finite collection of objects arriving in packets. A packet is considered to be serviced if all objects in this packet have finished servicing. For each packet, we know an individual penalty function which is monotone increasing from zero with the time a packet spends in the servicing system. We pose and study optimization problems with one and two criteria for evaluating the quality of servicing strategies. With the scheme shown in the paper, we construct a general solving algorithm based on the principle of dynamic programming and show examples of its implementation.

In this paper we propose a modification of the mirror descent method for non-smooth stochastic convex optimization problems on the unit simplex. The optimization problems considered differ from the classical ones by availability of function values realizations. Our purpose is to derive the convergence rate of the method proposed and to determine the level of noise that does not significantly affect the convergence rate.

Methods of MES construction concept for industrial production of processing type are considered: formation of its content, requirements to problems solved within it, strategy of creation planning, and MES components implementation.

We investigate the mean field games of N agents based on the nonlinear stable-like processes. The main result of the paper is that any solution of the limiting mean field consistency equation generates a 1/N-Nash equilibrium for the approximating game of N agents.

The paper suggests the concept of A-equilibrium that is a concretization of the “altruistic” Berge equilibrium adapted to the pure exchange models with externalities. In contrast to the classical markets, these models consider the external influence on the preferences of economic agents. In terms of an appropriate fuzzy domination, a cooperative characterization of the A-equilibrium allocations is given, and an analog of the classic core equivalence theorem is established.