Solving Travelling salesman problem using Harmony search algorithm and other metaheuristics

Abstract

Travelling salesman problem belongs in basic problems of operations research. It is a NP-hard problem. The number of possible solutions of this problem is very high – it increases with the factorial of the number of the nodes at the graph. So even with nowadays computers it takes very large amount of time to solve TSP with exact methods. Therefore TSP is now usually solved with a heuristic (or metaheuristic) techniques, which provides a satisfactory solution in real-time. This paper is focused on one novel metaheuristic method – Harmony Search, which is inspired by the improvisation process of musicians. Several instances of travelling salesman problem are solved in this paper with this method and gained results are compared with the optimal solution of each instance and with results computed by other metaheuristic methods.