Over the next ten years, air traffic management in the world will change dramatically, bringing both challenges and opportunities. The biggest of those challenges is the continuing rise in traffic volumes and will increase the movement of airbuses around the airport due to busy runways. This air traffic congestion will increase the running cost of flights due to unwanted movement of airbuses around the airport and it will also increase the chances of the airbus collision. This paper considers the problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace. Aircraft can not get closer to each other than a given safety distance in order to avoid possible conflicts between different airplanes. For such system of multiple aircraft, we consider the path planning problem among given waypoints avoiding all possible conflicts. In this paper we have proposed Adaptive Resonance Theory Map Neural networks (ART1) to produce optimize solution. Our result shows that the average expected conflict time of aircrafts using ARTMAP has been increased to more than 20 minutes.