Multilevel Graph Partitioning Scheme to Solve Traveling Salesman Problem

Abstract

Traveling salesman problem looks simple but it is an important combinatorial problem. This paper proposes a new hybrid scheme to find the shortest distance of tour in which each city is visited exactly one time, with the return back to the starting city. Traveling salesman problem is solved using multilevel graph partitioning approach. Although traveling salesman problem itself is a very difficult problem as it belongs to the NP-Complete problem class, yet one of the best possible solution is proposed using multilevel graph partitioning which also belongs to the NP-Complete problem class. To reduce the complexity, k-mean partitioning algorithm is used which divides the main problem into multiple partitions. Then solving each partition separately and thus finally improving the solution for overall tours by applying Lin Kernighan algorithm. From all of this analysis, an optimal solution is produced which tends to solve travelling salesman problem and could be used in more advance and complex applications.