We consider the multiple travelling salesman Problem (MTSP) that is one of the generalization of the travelling salesman problem (TSP). For solving this problem genetic algorithms (GAs) based on numerous crossover operators have been described in the literature. Choosing effective crossover operator can give effective GA. Generally, the crossover operators that are developed for the TSP are applied to the MTSP. We propose to develop simple and effective GAs using sequential constructive crossover (SCX), adaptive SCX, greedy SCX, reverse greedy SCX and comprehensive SCX for solving the MTSP. The effectiveness of the crossover operators is demonstrated by comparing among them and with another crossover operator on some instances from TSPLIB of various sizes with different number of salesmen. The experimental study shows the promising results by the crossover operators, especially CSCX, for the MTSP.

The multiple travelling salesman problem (MTSP), an extension of the well-known travelling salesman problem (TSP), is studied here. In MTSP, starting from a depot, multiple salesmen require to visit all cities so that each city is required to be visited only once by one salesman only. It is NP-hard and is more complex than the usual TSP. So, exact optimal solutions can be obtained for smaller sized problem instances only. For large-sized problem instances, it is essential to apply heuristic algorithms, and amongst them, genetic algorithm is identified to be successfully deal with such complex optimization problems. So, we propose a hybrid genetic algorithm (HGA) that uses sequential constructive crossover, a local search approach along with an immigration technique to find high-quality solution to the MTSP. Then our proposed HGA is compared against some state-of-the-art algorithms by solving some TSPLIB symmetric instances of several sizes with various number of salesmen. Our experimental investigation demonstrates that the HGA is one of the best algorithms.