Abstract
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.
Highlights
The travelling salesman problem (TSP) is a well-known problem in computer science and operations research that aims to find a minimum cost Hamiltonian circuit in any network
The percentage of difference between the best and average solutions obtained by hybrid genetic algorithm (HGA), AC2OptGA, GA with local operators (GAL), Table 5: Comparative study of HGA, AC2OptGA, GAL, SW + ASelite, M-GELS, modified GA (MGA), and NMACO
A sampling approach for creating initial population, sequential constructive crossover, swap mutation operator, and a local search approach along with an immigration technique are used in our proposed HGA
Summary
The travelling salesman problem (TSP) is a well-known problem in computer science and operations research that aims to find a minimum cost Hamiltonian circuit in any network. The problem has application in school bus scheduling that finds a bus filling structure so that the number of tours as well as the distance toured by the busses is minimum provided that no bus is overcrowded and the time needed to cross any way does not surpass the maximum allowable time [4] Another application of the MTSP is reported as crew scheduling in [5] where the problem of scheduling numerous groups of photographers to several schools is investigated. Crossover operators which were proposed for the usual TSP are applied to the MTSP Majority of these operators cannot obtain good GAs for the problem. A hybrid GA (HGA) is developed using a heuristic method for creating initial population, SCX, swap mutation, local search approach, and an immigration approach for finding highquality solution to the reduced problem.
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