Abstract: The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.
Abstract: An envy behavioral game theoretical model with two
types of homogeneous players is considered in this paper. The
strategy space of each type of players is a discrete set with only
two alternatives. The preferences of each type of players is given
by a discrete utility function. All envy strategies that form Nash
equilibria and the corresponding envy Nash domains for each type
of players have been characterized. We use geometry to construct
two dimensional envy tilings where the horizontal axis reflects the
preference for players of type one, while the vertical axis reflects
the preference for the players of type two. The influence of the envy
behavior parameters on the Cartesian position of the equilibria has
been studied, and in each envy tiling we determine the envy Nash
equilibria. We observe that there are 1024 combinatorial classes of
envy tilings generated from envy chromosomes: 256 of them are
being structurally stable while 768 are with bifurcation. Finally, some
conditions for the disparate envy Nash equilibria are stated.
Abstract: This paper introduces an original method for
guaranteed estimation of the accuracy for an ensemble of Lipschitz
classifiers. The solution was obtained as a finite closed set of
alternative hypotheses, which contains an object of classification with
probability of not less than the specified value. Thus, the
classification is represented by a set of hypothetical classes. In this
case, the smaller the cardinality of the discrete set of hypothetical
classes is, the higher is the classification accuracy. Experiments have
shown that if cardinality of the classifiers ensemble is increased then
the cardinality of this set of hypothetical classes is reduced. The
problem of the guaranteed estimation of the accuracy for an ensemble
of Lipschitz classifiers is relevant in multichannel classification of
target events in C-OTDR monitoring systems. Results of suggested
approach practical usage to accuracy control in C-OTDR monitoring
systems are present.