A hybridization of grey wolf optimizer and genetic algorithm for the traveling salesman problems

In this study, grey wolf optimizer (GWO), genetic algorithm (GA), and K-Opt operation are combined to develop a metaheuristic named GWO-GA for the traveling salesman problems (TSPs). The alteration of the positions of two nodes of a potential solution (sequence of nodes or route) of a TSP is defined as a swap operation and a sequence of such swap operations is defined as a swap sequence. Using swap operations and swap sequence, the perturbation rules of the basic GWO are modified for the perturbation of any potential route (solution) of a TSP. The proposed approach consists of two phases. In the first phase, the operations of GWO are applied to a randomly generated set of potential solutions of the target problem for a predefined number of iterations. At the end of each iteration, the 3-Opt operation is applied to the solutions for which better movement is not found using GWO operations. In the second phase of the algorithm, the GA is applied for another number of iterations on the output set of the GWO phase. In the GA phase, the Roulette wheel selection process and multi-point cyclic crossover operation are used in a different approach. K-Opt operation for \(K=3\) $K=3$ is used in place of mutation operation. K-Opt operation is again applied to the best-found solution after the end of the second phase for a fixed number of iterations for a possible improvement. The efficiency of the algorithm is tested on a set of benchmark test instances of different sizes from the TSPLIB. The performance of the proposed GWO-GA is compared with a set of state-of-the-art algorithms on TSPs using statistical tests and its superiority is established using comparison tables of the results as well as statistical tests. Obtained optimal routes are also presented to support the concluding remarks. It is observed that the algorithm shows a 100% success rate for problem size up to 144 and optimum route up to problem size 264.