Multiple traveling salesman problem using novel crossover and group theory

This paper propose a new technique which uses novel crossover with multi chromosome representation using group theory for tour construction for solving the multiple traveling salesmen problem (MTSP) using a genetic algorithm (GA) for near-optimal solutions. In the proposed algorithm, we use group tour construction method to get population having rich diversity. In group tour construction method each individual / initial tour is distinct provided that population size is less than the total number of cities. We also use multi chromosome representation technique, which minimizes the search space. We evaluated and compare the proposed technique with four different crossover methods for two MTSP objective functions, namely, total travel of the cost of m tours of the m salesman and longest tour cost travel by any one salesman. In this MTSP, we minimize these objective functions. Computational results obtained from proposed crossover with group tour construction is better than T CX, ORX+A, CYX+A, PMX + A crossover based method.