PSOG: Enhanced particle swarm optimization by a unit vector of first and second order gradient directions

Particle swarm optimization (PSO) is one of the effective metaheuristic optimization methods that has been used in various design problems. As the number of design variables increases for multimodal design space, the efficiency of the approach will decrease. In the present paper, the method of PSO is combined with first and second order gradient directions and the robustness of the approach is greatly increased. Design problems are chosen from the literature and the results are compared with the original PSO. In structural optimization, the number of required analyses of the structure is an important factor in choosing an effective optimization approach. In the combined method, the number of initial particles can be reduced which in turn, the overall cost of the optimization process will be reduced. The new approach is not sensitive to the required optimization scaling parameters and it is stable. In addition, a modified penalty function is introduced with appropriate performance that is employed in the optimization process. To show the superiority of the proposed method, 25 test cases from CEC 2005 with 10 and 30 variables are chosen and the results of 10 PSO variants are compared. Also, 30 functions from CEC 2017 with 10, 30 and 50 variables are chosen for comparison.