An improved memetic genetic algorithm based on a complex network as a solution to the traveling salesman problem

Authors: HADI MOHAMMADI, KAMAL MIRZAIE, Mohammad Reza Mollakhalili Meybodi

Abstract: A genetic algorithm (GA) is not a good option for finding solutions around in neighborhoods. The current study applies a memetic algorithm (MA) with a proposed local search to the mutation operator of a genetic algorithm in order to solve the traveling salesman problem (TSP). The proposed memetic algorithm uses swap, reversion and insertion operations to make changes in the solution. In the basic GA, unlike in the real world, the relationship between generations has not been considered. This gap is resolved using the proposed complex network to allow selection among possible solutions. The degree measure has been used for analysis the network. Different scenarios have been evaluated to solve seven TSPLib problems. For example, the results indicated that the memetic algorithm with a complex network, the memetic algorithm with the proposed local search and basic GA have 0.31%, 1.15% and 38% errors, respectively, when solving the TSP for 70 cities compared to the best solution in the TSPLib database. These results offered better performance of the memetic algorithm with a complex network compared to the memetic algorithm with the proposed local search and the basic GA. Also, the average run time of the algorithms showed their scalability.

Keywords: Travelling salesman problem, genetic algorithm, memetic algorithm, local search, complex network

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