A pattern recognition lexi search approach to generalized time-dependent travelling salesman problem

In this paper the “Generalized Time-dependent Travelling Salesman Problem” is a three dimensional travelling salesman problem where the cost matrix C (i, j, k) is the cost of the salesman visiting from city i to city j at time (facility) k. The cost matrix C(i,j,k) [i,j = 1,2,3,…..,n;k = 1,2,3,…..,m] is given. There are n cities and N = {1, 2, 3,…, n}. We are given a partition of cities into groups and we require to find a minimum length tour that includes at least one city from each group. The problem is to find a feasible tour for m(Lexi Search algorithm based on Pattern Recognition Technique for solving “Generalized Time-dependent Traveling Salesman Problem” with an illustrative example. For this problem a computer program is developed for the algorithm and is tested. It is observed that it takes less time for solving fairly higher dimension problem also.