P-Path Minimum Distance Connectivity from Head Quarter to the Cities

Many Combinatorial programming problems are NP-hard (Non Linear Polynomial), and we consider one of them called P path minimum distance connectivity from head quarter to the cities. Let there be n cities and the distance matrix D(i, j, k) is given from ithcity to jthcity using kthfacility. There can be an individual factor which influences the distances/cost and that factor is represented as a facility k. We consider m<n cities are in cluster and to connect all the cities in subgroup (cluster) from others by using same facility k. The problem is to find minimum distance to connect all the cities from head quarter (say 1) threw p-paths subject to the above considerations. For this problem we developed a Pattern Recognition Technique based Lexi Search Algorithm, we programmed the proposed algorithm using C. we compared with the existed models and conclude that it suggested for solving the higher dimensional problems.