Complexity indices for the traveling salesman problem continued

An Approach for Solving Traveling Salesman Problem

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...

The traveling salesman problem

Complexity Indices for the Travelling Salesman Problem and Data Mining

We extend our previous work on complexity indices for the travelling salesman problem (TSP) using graph spectral techniques of data mining. A complexity index is an invariant of an instance I by which we can predict the execution time of an exact algorithm for TSP for I. We consider the symmetric travelling salesman problem with instances I represented by complete weighted graphs G. Intuitively...

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...

The Computational Complexity of the Traveling Salesman Problem

In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer. Disclaimer: This article was authored by Craig Alan Feinstein in his private capacity. No official support or endorsement by the U.S. Government is intended or should be inferred. Consider the following well-known NP-hard problem: Traveling Salesman Problem A traveling salesman...