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.
Highlights
The travelling salesman problem (TSP) is a popular problem, which finds smallest tour of the salesman that starts journey from a headquarters city and visits all outstanding n cities exactly once before comes back to his headquarters
It is seen that for asymmetric instances, HGA3 is placed in 2nd position and HGA4 is the best one
HGA2 is placed in 2nd position and HGA4 is the best one
Summary
The travelling salesman problem (TSP) is a popular problem, which finds smallest tour of the salesman that starts journey from a headquarters city and visits all outstanding n cities (nodes) exactly once before comes back to his headquarters. For finding better solution, within acceptable computational effort, to such type of problems, generally, heuristic/metaheuristic algorithms are applied. GAs are based on simulating the Darwinian survival-ofthe-fittest theory in the environmental biology [14] They are very robust, parallel, and global search metaheuristics that can solve large-sized problems quickly. They can automatically obtain and collect knowledge throughout the search procedure www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol 12, No 8, 2021 and can adaptively manage the search procedure to obtain the optimal/best solution. The hybrid genetic algorithms (HGAs) include a selected local search and perturbation procedure to the proposed SGA. The partially mapped crossover [15] along with swap mutation for perturbation procedure is to find better quality solution to the MSTSP
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