Matemaatika instituut. Kuni 2015

Permanent URI for this communityhttps://hdl.handle.net/10062/14971

2016 moodustas koos Matemaatilise Statistika Instituudiga Matemaatika ja Statistika Instituudi.

Browse

Browsing Matemaatika instituut. Kuni 2015 by Subject "algoritmi kirjeldus"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Rändkaupleja ülesande lahendamine sipelgaalgoritmiga
    (Tartu Ülikool, 2013) Laas, Teele; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
    Complex combinatorial optimization problems have arised in many different fields. However, often this kind of problems are very hard to solve in practice, scientists have worked out many algorithms for solving combinatorial optimization problems. Ant Algorithm is a recent metaheuristic method that is one of the applicable algorithms for solving optimization problems. The first chapter of this bachelor’s thesis gives an overview of Ant Algorithm. Ant Algorithm was first introduced by Dorigo and his colleagues in early 1990s and it is inspired by the behavior of real ants. People have explored the nature and have tried to understand different kinds of processes around us. A very interesting aspect of the behavior of several ant species is their ability to find shortest paths between the ant’s nest and the food sources. In the Ant Algorithm there are several artificial ants’ capabilities used to find solutions to the problem. Although the Ant Algorithm is quite new method, it is a well defined and good performing method that is more and more often applied to solve a variety of complex combinatorial problems. One of the Ant Algorithm’s successful applications is Travelling Salesman Problem, which was the first famous combinatorial problem solved by Ant Algorithm. Ant Algorithm is one of the most efficient algorithms for Travelling Salesman Problem. The second chapter of this bachelor’s thesis is dedicated to introducing the Travelling Salesman Problem. Travelling Salesman Problem is easy to describe but it is so difficult to solve. Travelling Salesman Problem is a well known and extensively studied problem and it has wide application background. We can’t imagine how many problems of our real life can be solved as Travelling Salesman Problems. In this chapter an overview of current applications is given. The last chapter of this thesis is a practical part of it. A certain Travelling Salesman Problem is solved with the Ant Algorithm there. The task was to find the shortest route between 15 different counties’ centers of Estonia. In this chapter the description and importance of different parameters in Ant Algorithm is given and the relationship between Ant Algorithm’s parameters is analyzed. Ant Algorithm is led by five parameters. The result of the task was a 948.79 km long tour through all these 15 cities which was found in 1.91 seconds. It was the fastest time to find the solution. Ant Algorithm showed good performance for solving this problem. Computings were realized in MATLAB environment. This thesis is interesting to read for those who would like to get some knowledge about mathematical optimization problems. It is interesting to know the practical side of math. In addition, this thesis is useful for those who want to solve different kinds of optimization problems using Ant Algorithm.