Enhanced Firefly Algorithm with Implicit Movement

Abstract

The question for an optimal solution to a certain real-world problem often turns into a complex optimization problem. The sizing of the cross sections for bars of a truss structure is generally hampered by interdependencies. This prevents local search methods from finding a sufficient optimum. For those issues, there is a demand for fast and reliable global optimization algorithms. The Firefly Algorithm is a swarm-intelligence-based method frequently used for solving multi-modal optimization problems. The algorithm maintains a set of individuals, each corresponding to a point within the solution space. During the optimization process, the individuals move within the solution space under certain rules in order to find the global optimum. This paper presents an enhancement of the Firefly Algorithm by an implicit backward Euler movement. Therefore, in each iteration a linear system of equations must be solved to determine the new positions of the individuals. To evaluate the performance of the implicit movement, it is applied to continues benchmark optimization functions. The optimization process is compared to the basic Firefly Algorithm to specify the effect of implicit movement. Furthermore, a discrete parameter optimization of a ten-bar truss in the sense of a weight reduction is carried out. The optimization results are compared to the basic Firefly Algorithm as well as to the results of four state-of-the-art algorithms. The implicit movement provides an intuitive and an easy to implement modification of the Firefly Algorithm. Simulation results show that the implicit movement causes a significant improvement in the convergence behavior compared to the basic Firefly Algorithm and outperforms state-of-the-art algorithms in terms of the solution quality and convergence behavior. Due to its generality, the proposed implicit movement can be implemented to several swarm-intelligence-based algorithms and offers a promising universal approach for enhancement.