Optimum design of truss structures with frequency constraints by an enhanced particle swarm optimization method with gradient directions based on emigration philosophy

In this article, the combined method of particle swarm optimization (PSO) with gradient directions (PSOG) is further extended to increase the capabilities of exploration and exploitation. Four different enhancements are added to the PSOG, based on emigration ideas. To investigate the power of the presented methods, 29 complicated functions are optimized with several local optima. Then, the suggested approaches are used in structural design problems with multiple frequency constraints containing sizing and shape design variables for two- and three-dimensional truss structures. The results are compared with some of the methods in the literature and the superiority of the suggested techniques is demonstrated.