Natela Ananiashvili

The traveling salesman problem belongs to the class of discrete optimization NP-hard problems [3]. Its solution is very important both from a practical and a theoretical point of view. This task involves finding the minimum weight Hamiltonian cycle in a weighted complete graph. Since the exact solution can be obtained through complete selection, which is impossible in the case of large dimensions, therefore, approximate algorithms are used, which obtain solutions close to the optimal in a short time interval [1, 2]. The paper proposes a genetic algorithm for solving the salesman’s problem for graphs for which the vertices are located on the plane and the distance between them is calculated according to the coordinates (in Cartesian rectangular coordinate system). With the proposed algorithm, it is possible to get a solution close to the optimal one. 

The task of medical data analysis is considered in order to identify frequent symptoms and symptom sets for each disease. For data analysis, the association rule mining method is used, which allows to assess the specificity ofthe symptoms found and the confidence of the diagnostic rules based on the identified associations. The proposed method was used to process the clinical data of a number of endocrinological diseases. Based on the obtained association rules, a knowledge base of the medical intelligent system designed for diagnosing endocrinological diseases was formed.

The main complexity of solution of optimization problems is related to non-linearity of functions and scales of problems [2]. Searching of optimal values with classical techniques sometimes finishes without results. In the given paper heuristic algorithm of solution of a problem of optimization is offered. The algorithm is based on main principles of classic genetic algorithm [1]. Genetic operators are considered. Selection is made with technique of inbreeding. Modified Operators of crossover and mutation is offered. Algorithm is approved for test problems. The quantitative results prove efficiency of our modified genetic operators and their combinations.

The heuristic algorithm of solution of generalized problems of finding of minimal set covering is developed. The necessity of solution of generalized problem of minimal set covering is revealed, when we search of multiple main center in the graph [1]. We can cite many practical problems of optimal location of service points for finding such centers. The proposed algorithm has selective characteristic and uses a search tree [2]. Algorithm realization software showed good results for test problems.

The problem of set covering is a NP-complex problem of combinatorial optimization. Algorithms of precise solution of this problem use techniques of branches and limits[1]. Time necessary for realization of such algorithms rapidly increases and when dimension of a problem also increases, it is impossible to get optimal values in real time [2]. This problem is a mathematical model for practical tasks, such as location of service centers, development of transport schedule, location of sources of power systems, etc. Therefore, it is very important to solve this problem in real time. When such problems are solved, heuristic algorithms are often used that find near optimal solutions in reasonable time interval. Approximate algorithms mainly imply partial selection of covering sets. In genetic algorithms, this process is similar to development of biological populations [3]. Heuristic algorithm of solution of problem of covering minimal summary weight of given set with subsets of non-uniform values is offered. The algorithm is based on genetic algorithm with operators of crossover and mutation. The results of computational experiments are given on the basis of knows test problems.

The article discusses the solution of the set partition problem. It is known that the set partition problem belongs to the class of NP complete problems. At present, there's no efficient algorithm for the solution of these problems for non private cases, also the time of the solution is dependent on the problem sizes and it can rapidly grow with the growth of the solution itself. We used a simple tree search algorithm. With the non-important complications of the programming techniques we were able to decrease the used memory and compilation time by approximately 32N times, here N is the number of the cover sets. For this we first wrote the set partition matrix compactly, then on the columns of the given matrix we compiled main operations with binary operators. We have written the program for the solution of this problem on an algorithmic language C++ and tested it on texts from OR-Library. This program also can be used to solve other problems from the graph theory, which can be derived to the Set Partition problem, or which are subproblems of this problem (eg ending dominant set of vertices in the graph).

In the given paper, we’re analyzing and modeling the reliability of complex wireless communication systems using the exponential distribution. We assume that the data is transmitted via unreliable environment. The transmitted message consists of n information blocks. The check of accuracy of getting information is made immediately after receiving the next block and the time spent on check is negligibly small, check is full. In the case of information distortion block transmission is repeated until it won’t be correctly received. It takes place with a help of control bits. It is assumed that there is a time redundancy.

Modeling based approach is described for analyzing and evaluating Internet server system reliability and availability in this paper. In the given model the states are defined by the different kinds of failures of the server system. The Markov model evaluates the probability of jumping from one known state into the next logical state. The probabilities between transitions of the states are a function of the failure rates of the transitional probabilities from one to another state. The number of first-order differential equations is equal the number of the states of the servers. First-order differential equations is developed by describing the probability of being in each state in terms of states of the model.

Nowadays, the practical realization of the optimization problems and a flexible software development is very important. The paperwork deals with the minimum search for the visualization method, for the local minimum and for the global minimum search of unconditional optimization tasks, as well. New modified late model is proposed for the heavy nucleus method, which is called "controllable". The term "controllable" means the opportunity to slow down or accelerate the heavy ball.

Optimal methods to create a universal software package is an important scientific - technical objective. In Multidimensional optimization tasks one dimensional optimization method is used to select the step. We consider interesting to research  effectiveness of the methods of gold section and the segment division into three equal parts while experimental error: We carried out a study of the efficiency criteria and observed time indicators of searching the extremum . The experiment showed that the best use of the bidding step is to choose the method of division into three equal parts, which is much more efficient in case of experimental errors. It is also important for the effectiveness of the extremum point of the interval boundaries of the location.

Doctoral Thesis Referee

Master Theses Supervisor

Doctoral Thesis Supervisor/Co-supervisor

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

Review of a scientific professional journal / proceedings

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

Participation in a project / grant funded from the state budget

Patent authorship

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

Monograph

Handbook

Research articles in high impact factor and local Scientific Journals

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus