Opposition and dimensional based modified firefly algorithm

• The proposed modified firefly algorithm gives more optimal solution than original FA.
• The time complexity of the modified FA is also less as compared to FA.
• The dimensional FA helps FA not to stuck in the local optima and gives global optima.
• The opposition FA improves initialization of fireflies so they converge faster.

This paper presents the modified Firefly Algorithm (FA) originally proposed by Yang.Firefly Algorithm is based on the idealized behavior of the flashing characteristics of the fireflies. Though firefly is powerful in local search, it does not search well globally due to being trapped in local optimum. Due to this reason, the convergence is generally slow. The FA also doesn't give efficient solution in high dimensional problems. The proposed approach gives more efficient solution with reduced time complexity in comparison to original FA. Two modifications made are: (1) Opposition-based methodology is deployed where initialization of candidate solutions is done using opposition based learning to improve convergence rate of original FA, which includes initializing the opposite number of positions of each firefly. This also ensures efficient searching of the whole search space, (2) The dimensional-based approach is employed in which the position of each firefly is updated along different dimensions. This results in more optimal solution. This algorithm works for High Dimensionality problems, especially in terms of accuracy in finding the best optimal solution and in terms of fast convergence speed as well. Several complex multidimensional standard functions are employed for experimental verification. Experimental results include comparison with other Evolutionary algorithms which show that the Opposition and Dimensional based FA (ODFA) gives more accurate optimal solution with high convergence speed than the original FA and those achieved by existing methods.