A novel hybrid method combining electromagnetism-like mechanism and firefly algorithms for constrained design optimization of discrete truss structures

Abstract

A new optimization method called Electromagnetism-like Firefly Algorithm (EFA), which is a novel hybrid between the Electromagnetism-like Algorithm (EM) and the Firefly Algorithm (FA) for discrete structural optimization is proposed. The EFA inherits the advantages of both the FA and the EM. This proposed optimization algorithm is then presented to improve both solution accuracy and convergence speed, as well as to treat constrained optimization problems with discrete design variables. In EFA, modified formulas of interactive forces are used to increase the diversification of the population, and the constraint violations are embedded into the charges of all electromagnetic fireflies to avoid becoming trapped in unfeasible domains. A mechanism called “current-to-best” electromagnetic movement is incorporated with traditional interactive movements to balance the exploration and the exploitation abilities of the EFA. In the local search phase, a newly bi-directional searching procedure is performed on the best firefly to intensify effectively its local optimum. In order to guarantee the convergence capability of the EFA, a harmonized selection mechanism combined with the traditional and elitist selections is proposed and applied if the algorithm cannot find a better optimal solution during a number of predetermined optimization loops. In addition, in this study, the FA and EM with some improvements in several phases are also proposed to solve the constrained optimization problems. Finally, a rounding technique is applied to the proposed EFA, FA and EM for solving discrete optimization problems. The improved performance of the EFA in comparison with the FA, EM as well as other optimization algorithms in the literature is demonstrated by six popular truss optimization problems with discrete variables.