A comparative study of evolutionary computation and swarm-based methods applied to color quantization

Color Quantization (CQ) is a complex and hard problem because selecting the best set of colors from many available colors and using that set to obtain a good quality image is an NP-complete problem. The use of evolutionary computation and swarm-based methods to solve search and optimization problems has increased dramatically in recent years. This article compares some of these methods in order to solve the CQ problem. The following methods were used to generate CQ images: Particle swarm optimization, Artificial bee colony, Adaptive differential evolution, Success-history based adaptive differential evolution (with and without linear population size reduction), Cuckoo search, Firefly algorithm and Shuffled-frog leaping algorithm. For the first two methods, two variants were considered. Thus, a total of ten metaheuristics were compared with four classical CQ methods (Variance-based, Median-cut, Binary splitting and Wu's methods) applying them to a set of benchmark images and considering four different palette sizes (32, 64, 128, and 256 colors). Three error measures were considered to compare the methods: the mean squared error, the mean absolute error and the peak signal-to-noise ratio. Some of the swarm-based methods analyzed include a recently proposed CQ method using ants. Although they have a slow computational speed in the experimental studies, the ant-based methods are significantly better than all other methods according to the Wilcoxon signed rank test. In general, despite their speed, classical methods underperform the other ten methods both qualitatively and quantitatively.