An improved version of Minty's algorithm to solve TSP with penalty function

The traveling salesman problem has been studied for many years since the model can be used for various applications such as vehicle routing, job sequencing, clustering a data array, and so on. In this paper one of the typical exact algorithms for TSP, Minty's, will be modified to improve the performance of the algorithm on the applications without losing simplicity. The Little's algorithm gives good results, however, the simple and plain Minty's algorithm for solving shortest-route problems has the most intuitive appeal. The suggested Minty's modification is based on the creation of penalty-values on the matrix of a TSP. Computer experiments are made to verify the effectiveness of the modification.