Novel GA for metropolitan stations of Indian railways when modelled as a TSP

Abstract

In this paper, seven cities that have a direct connection link by Indian railways are modeled as a travelling salesman problem. Then genetic algorithm (GA) is used to solve it by considering three different objective functions, namely: distance, cost and time. For the implementation of GA, the fourth variation of order crossover (OX4) as proposed in Deep and Mebrahtu (Int J Comb Optim Probl Inform 2(3):1–23, 2011a) with inversion mutation and inverted displacement mutations are used. These are programmed in C++ and implemented on the distance, cost and time data obtained from the Indian railways. The minimum and maximum distances of travel, costs of travel and time taken to cover the stations are evaluated. According to the analysis of results that is based on numerical experimentations the sequence of choosing stations really matters. This is observed by the big difference between the minimum and maximum distance, cost and time of travel evaluated. Especially the difference between the minimum and maximum results of distance travelled and time taken to cover the tours is almost twice.