### Article

## Анализ точности решения задачи коммивояжера с помощью «антижадного» алгоритма

In this paper the new "anti-greedy" algorithm for the Traveling Salesman Problem is under investigation. The idea of "anti-greedy" algorithm is consequent elimination of the longest edges from graph according to two rules: every node of the graph should have two incident edges as a minimum; the graph should not have cycles with less than n edges. This algorithm finds out more exact solutions than famous polynomial algorithms, especially for non-Euclidean graphs.

We consider the problem of planning the cousmonaut's time in ISS with given set of tasks, time planning horizon and load constraints. Shown that the problem is NP-hard in a strong sense. The heuristic algorithm was proposed. Proved that proposed algorithm is exact for problem with requirement of performing all tasks. Program C++ was written and algorithm's work was qualitatively analyzed.

Graph coloring problem is one of the classical combinatorial optimization problems. This problem consists in finding the minimal number of colors in which it is possible to color vertices of a graph so that any two adjacent vertices are colored in different colors. The graph coloring problem has a wide variety of applications including timetabling problems, processor register allocation problems, frequency assignment problems, data clustering problems, traffic signal phasing problems, maximum clique problem, maximum independent set problem, minimum vertex cover problem and others. In this paper a new efficient heuristic algorithm for the graph coloring problem is presented. The suggested algorithm builds the same coloring of a graph as does the widely used greedy sequential algorithm in which at every step the current vertex is colored into minimal feasible color. Computational experiments show that the presented algorithm performs graph coloring much faster in comparison with the standard greedy algorithm. The speedup reaches 5,6 times for DIMACS graphs.

The paper presents a formalized statement of the problem of selecting parameters and construction of a genomic classifier for medical test systemswith mathematical methods of machine learning without the use of biological and medical knowledge. A method is proposed to solve this problem. The results of testing the method using microarray datasets containing information on genome-wide transcriptome of the samples of estrogen positive breast tumors are discussed. Testing showed that the quality of classification provided by the constructed test system and implemented on the basis of assessments of expression of 12 genes is not inferior to the quality of classification carried out by such test systems as OncotypeDX and MammaPrint.

The theory of single upper and lower tolerances for combinatorial minimization problems has been formalized in 2005 for the three types of cost functions sum, product and maximum, and since then shown to be rather useful in creating heuristics and exact algorithms for the Traveling Salesman Problem and related problems. In this paper for these three types of cost functions we extend this theory from single to set tolerances and the related reverse set tolerances. In particular, we characterize specific values of (reverse) set upper and lower tolerances as positive and infinite, and we present a criterion for the uniqueness of an optimal solution to a combinatorial minimization problem. Furthermore, we present formulas or bounds for computing (reverse) set upper and lower tolerances using the relation to their corresponding single tolerance counterparts. Finally, we give formulas for the minimum and maximum (reverse) set upper and lower tolerances using again their corresponding single tolerance counterparts.

It is shown that the logarithm of the complexity (number of nodes in the decision tree of a branch and bound algorithm) of the individual traveling salesman problem is approximately normally distributed. We use a linear regression model (logarithm of the complexity — standard normal distribution) to estimate parameters of normal distribution, which fit the sample. Borders of the interval, which contains 90% of the sample of the logarithm of the complexity, are also given.

The routing problems are important for logistic and transport sphere. Basically, the routing problems related to determining the optimal set of routes in the multigraph. The Chinese postman problem (CPP) is a special case of the routing problem, which has many potential applications. We propose to solve the MCPP (special NP-hard case of CPP, which defined on mixed multigraph) using the reduction of the original problem into General Travelling Salesman Problem (GTSP). The variants of CPP are pointed out. The mathematical formulations of some problems are presented. The algorithm for reduction the MCPP in multigraph into GTSP is shown. The experimental results of solving MCPP in multigraph through the reduction into GTSP are presented.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.