Bi-directional nearness in a network by AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process)

In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP (Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance. Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. So we propose the concept of bi-directional nearness defined by AHP's synthesizing of weights "for" direction and "from" direction. This concept of distance is a relative distance based on the configuration of the set of points located on a plane or network. In order to confirm the usefulness of our study we apply the proposed nearness to solving methods of TSP (Traveling Salesman Problem), where to find an approximate solution of TSP we improved Nearest Neighbor Method. Some numerical experiments of TSP were carried out. To decide a nearest point we used two kind of nearness, forward direction nearness and bi-directional nearness. As a result, by using bi-directional nearness, we obtained good approximate solution of TSP. Moreover, the relation between AHP and ANP, through an example, is considered.