Comparison of different implementations of the travelling sailsman problem

Andraž Gregorčič (2013) Comparison of different implementations of the travelling sailsman problem. EngD thesis.

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Abstract

The Traveling Salesman Problem is a well known problem from computer science. We know that the salesman must travel through all the cities, which are represented as vertices in a graph. He must visit each vertex exactly once and return back to his starting point. It is important that his path is as short as possible and of course the cheapest. In graph theory this is called a Hamiltonian cycle. In the Traveling Salesman Problem we are searching for the shortest Hamiltonian cycle. The problem was already encountered in the 19th century. Irish mathematician W. R. Hamilton began working on it and the cycle was later named after him. Today we can say with certainty that this problem is one of most studied problems in optimization. It belongs to the Non-deterministic Polynomial-time hard(NP-hard) class of problems. These are problems for which exact polynomial solutions are not known. This thesis presents a part of graph and algorithm theory. Some exact and approximate algorithms that are used to solve this problem are shown. We encounter concrete situations that require solving the problem. Implementation and working of a program we created are described, as are individual tests that were executed on the program.

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