Modified Memetic Self-Adaptive Firefly Algorithm for 2D Fractal Image Reconstruction

This work concerns the problem of 2D fractal image reconstruction with IFS: given a 2D fractal image, the goal is to obtain an IFS whose attractor approximates the input image accurately. This problem is known to be a difficult multivariate nonlinear continuous optimization problem. It is addressed in this paper through a modification of a popular nature-inspired metaheuristics: the firefly algorithm. Our approach, called memetic modified self-adaptive firefly algorithm (MMSA-FFA), enhances the original firefly algorithm with three additional features for better performance: the use of self-adaptation strategies on the control parameters, a new population model based on elitism, and the hybridization with the Luus-Jaakola local search heuristics. The method is applied to two illustrative examples of challenging fractal images comprised of four and forty-four contractive functions, respectively. Our experimental results show that the method performs very well, being able to capture the underlying structure of the fractal images with good visual quality and reasonable CPU times from totally random initial parameters.