Discrete farmland fertility optimization algorithm with metropolis acceptance criterion for traveling salesman problems

Abstract

Traveling Salesman Problem (TSP) is an intricate discrete hybrid optimization problem that is categorized as an NP-Hard problem. The objective of the TSP is to find the shortest Hamilton route between cities to visit all existing cities and returning to the original city, from which the route started. Various researches have been carried out on TSP, and manifold solutions have been proposed to find the shortest route between cities, but none has been able to solve this problem completely. In this paper, a novel discrete version of the Farmland Fertility Algorithm is proposed, which uses three neighborhood searching mechanisms, and one Crossover operator. The Metropolis Acceptance Criterion has also been utilized to evade the local optimal traps. Furthermore, the Roulette Wheel selection technique is used to select neighboring mechanisms during the optimization process. Moreover, a local search mechanism is used to maximize the performance of the proposed algorithm. To prove the effectiveness of the contributions, and illustrate the efficiency of the proposed algorithm, the TSP library is evaluated on 37 data sets and compared with some well-known similar methods. The simulation results showed the superiority of the proposed algorithm against other comparative methods.