Abstract
We consider the maximum scatter travelling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the shortest edge in the tour that travels each city only once in the given network. It is a very complicated NP-hard problem, and hence, exact solutions are obtainable for small sizes only. For large sizes, heuristic algorithms must be applied, and genetic algorithms (GAs) are observed to be very successful in dealing with such problems. In our study, a simple GA (SGA) and four hybrid GAs (HGAs) are proposed for the MSTSP. The SGA starts with initial population produced by sequential sampling approach that is improved by 2-opt search, and then it is tried to improve gradually the population through a proportionate selection procedure, sequential constructive crossover, and adaptive mutation. A stopping condition of maximum generation is adopted. The hybrid genetic algorithms (HGAs) include a selected local search and perturbation procedure to the proposed SGA. Each HGA uses one of three local search procedures based on insertion, inversion and swap operators directly or randomly. Experimental study has been carried out among the proposed SGA and HGAs by solving some TSPLIB asymmetric and symmetric instances of various sizes. Our computational experience reveals that the suggested HGAs are very good. Finally, our best HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that our best HGA is better.