Genetic algorithm to the bi-objective multiple travelling salesman problem

The travelling salesman problem (TSP) and its variants have been studied extensively due to its wide range of real-world applications, yet there are challenges in providing efficient algorithms to deal with some of its variants. The multiple travelling salesman problem (MTSP), is the generalization of TSP, which aims to determine m - routes for 'm' salesmen to cover a set of n - cities exactly once where each route starts and ends at a depot such that the total distance is least. In this, the number of cities in each route of the optimal solution may be distributed disproportionately. This paper presents, a bi-objective MTSP (BMTSP) with the load balancing constraint, where the first objective is to minimize the total travel distance and the second objective minimizes the total time. A metaheuristic based genetic algorithm with tournament selection (GATS) is designed by integrating with mixed strategies, such as flip, swap and scramble in mutation operation to obtain efficient Pareto solution for BMTSP. The computational experiments are carried out on different data sets, which are derived from the TSPLIB. The performance of GATS is compared with different genetic approaches and simulation results show that the proposed GATS obtained improved solutions on some of the benchmark instances.