Vol 80, No 7 (2019)

We give a survey of approaches for analyzing the sensitivity of non-dominated alternatives to changes in the parameters of partial quasi-orderings that define preferences. Such parameters can include values of importance coefficients for different criteria or boundaries of interval estimates of the degrees of superiority in the importance of some criteria over others, boundaries of intervals of criteria value tradeoffs uncertainty and others.

The problem of finding an optimal location of the vertices of a tree network in an assembly space representing a finite set is considered. The optimality criterion is the minimum total cost of location and communications in all points of this space. Different vertices of the tree can be located in a single point of the assembly space. This problem is well-known as the Weber problem. The representation of the Weber problem as a linear programming problem is given. It is proved that the set of all optimal solutions to the corresponding relaxed Weber problem for the tree network contains an integer solution. This fact can be used to improve the efficiency of algorithms for the problems differing from the Weber problem by the presence of additional constraints: it allows us to find the optimal value of the objective function, which in turn significantly reduces the complexity of calculating the optimal solution itself, e.g., by the branch-and-bound method.

It is noted that the aircraft landing problem is one of the main tasks in the planning and regulation of air traffic flows, which requires the use of a sufficiently serious mathematical apparatus. A brief overview of the main approaches to the formulation and solution of this problem is presented.

This paper proposes a dynamic game-theoretic statement of the resource allocation problem in an organizational system. The application of evolutionary modeling algorithms for solving such problems is considered. Some illustrative examples are given.

This paper studies stability of carrier coalitions in a cooperative inventory routing game (CIRG). Difficulty of this study is not only in a computational complexity of the class of routing problems, but also in the task of constructing a characteristic function, since heuristic solutions that are usually used in routing problems can’t guarantee the subadditivity property in the general case. In its turn, violation of subadditivity can lead to instability of a coalition, because a player could get more profit in a different coalition or individually. To solve routing problems, Adaptive large neighborhood search (ALNS) and its modification with the Dynamic adaptation method, DALNS, are used in this work. A special Direct coalition induction algorithm (DCIA) is used to construct a subadditive characteristic function, and four different concepts of cooperative game solutions are considered. The analysis of extensive computational experiments allows to illustrate the dependence of the stability of a grand coalition on such factors as a routing algorithm, an algorithm for a characteristic function construction, and a solution concept for a cooperative game.

The paper examines the influence of bluff body’s shape on vortex shedding stability in a liquid flow. It shows that the expansion of stable vortex existence domain enables the extension of velocity measurement range for vortex flowmeters. Numerical simulation of eddy flows generated by various bluff body shapes is undertaken with the appropriate comparative analysis of flow characteristics. A bluff body with the best flow parameters enabling the improvement of flowmeter’s measurement performance is selected.

The history of development and the current state-of-the-art in the stability theory of systems with delay based on an effective generalization of the direct Lyapunov method are presented. This method uses “classical” Lyapunov functions in combination with the Razumikhin condition.

We present the results of the analysis and comparison of the properties of two concepts in state filtering problems for nonlinear stochastic dynamic observation systems with discrete time: sigma-point Kalman filter based on a discrete approximation of continuous distributions and conditionally minimax nonlinear filter that implements the conditionally optimal filtering method based on simulation modeling. A brief discussion of the structure and properties of the estimates and justifications of the corresponding algorithms is accompanied by a significant number of model examples illustrating both positive applications and limitations of the efficiency for the estimation procedures. The simplicity and clarity of the considered examples (scalar autonomous regressions in the state equation and linear observations) allow us to objectively characterize the considered estimation methods. We propose a new modification of the nonlinear filter that combines the ideas of both considered approaches.

A game-theoretic model of the Principal-agent type is considered, in which the result of an agent’s activity depends not only on his/her choice but also on some random factor. The Principal is assumed to choose the total probability of all negative events that he/she will exclude from consideration; in the other respects, he/she is cautious. The structure of the Principal’s optimal strategies is found. Two models differing by the Principal’s awareness of the partner’s actions are studied.