Finding the Shortest Hamiltonian Cycle Using the Combined Approach of Swarm Intelligence based on Complex Networks

In this paper, Hamiltonian cycle was used in a standard and theoretical problem called TSP as well as a practical problem called finding the shortest Hamiltonian cycle to cover all provinces of Iran. These kinds of problems can be solved using swarm intelligence algorithms derived from natural, environmental and social factors. Accordingly, the PSO Algorithm, which is one of the algorithms of swarm intelligence, was used . Search was also used to improve the results of each particle. Besides, a complex network was used in order to enhance the better exchange of information between particles and to select the next most appropriate position for each particle. In this network of nodes in which a better solution is maintained, the degree of that node is always greater. In the complex network, two criteria, degree and neighborhood degree, are used to find the best solution. The TSPLib standard problems were used to compare the results.  The findings showed that the particle swarm optimization technique with a complex network local search was more cost-effective than the optimization of the particle swarm with local search and standard particle swarm in a way that the percentage of error to the best solution in TSPLib was reduced in the particle swarm optimization algorithms with complex network local search and the particle swarm optimization in the local search compared to the standard particle swarm method, respectively. To solve the ST70 in network and basic algorithms, the average cost of solving the problem is 705 and 797, respectively.