Optimality conditions to the acyclic travelling salesman problem

This paper views an optimal solution (tour) of the n-station acyclic Travelling Salesman problem as consisting of n−1 elements of the distance matrix. Considering lower bound for elements a theoretical basis for identifying and eliminating non-optimal elements was suggested. This concept of element elimination was then used to define optimality conditions. Finally, an iterative algorithm which converges at the optimal sequence was proposed and applied to some numerical examples.