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

Abstract

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. Sowe propose theconcept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction.This concept of distance is a relative distance based on the configuration ofthe set of points located on a plane ornetwork. 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, forwarddirection nearness and bi-directional nearness. As a result, by using bi-directional nearness,we obtained goodapproximate solution of TSP. Moreover, the relation between AHP and ANP, through an example, is considered.