A Novel Codebook Generation by Lévy Flight Based Firefly Algorithm

Abstract

Nature inspired metaheuristic algorithms are become more powerful and useful in image processing algorithms especially by the developments in microprocessor technology. In the last several decades the Linde-Buzo-Gray algorithm is a powerful technique for local optimum codebook generation in image compression. Fuzzy C-Means and C-Means are the alternative ones for the same process. On the other hand nature-inspired metaheuristic algorithms have also become other alternate technics for designing the optimum codebook. In this paper the Firefly technique is enhanced by the Lévy flight function to achieve the global optimum codebook. The Firefly technique contains two sub search mechanisms to reach the global minimum solution. The first one is the attraction of any firefly by a brighter one. This process strongly guides to the firefly on the global minimum way especially if it is attracted by the brightest one. The second one is the random search of a firefly in a circle with a radius of a. On the other hand if a is determined so big, the firefly may lose its way and come to a location that is much far away from the firefly group and possibly there is no brighter firefly to be followed. On the contrary, if a is determined so small, this time the fireflies fall into a local minimum and can not escape. Therefore we need to have such an a that in most of the iterations its value changes in a small random value interval, but in rare iterations its value must be relatively big in order to escape local minimums. Therefore if a firefly is captured by a local minimum point by accidentally, Lévy Flight step provides an opportunity to escape from it easily. Numerical results suggest that the new introduced Lévy Flight based Firefly Algorithm is better than the classical techniques and provides the global optimum codebook for image compression. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.