NSABC: Non-dominated sorting based multi-objective artificial bee colony algorithm and its application in data clustering

This paper presents a non-dominated sorting based multi-objective artificial bee colony algorithm NSABC to solve multi-objective optimization problems. It is an extension of the artificial bee colony algorithm ABC, which is a single objective optimization algorithm, to the multi-objective optimization domain. It uses a novel approach in the employee bee phase to steer the solutions to simultaneously achieve both the orthogonal goals in the multi-objective optimization – convergence and diversity. The onlooker bee phase is similar to the ABC except for the fitness computation to exploit the promising solutions whereas there is no change in the scout bee phase, which is used to get rid of bad solutions and add diversity in the swarm by introducing random solutions. Along with a novel way of exploring new solutions, it uses non-dominated sorting and crowding distance, inspired by the NSGA-II, to maintain the best and diverse solutions in the swarm. It is tested on the 10 two-objective and three-objective unconstrained benchmark problems of varying nature and complexities from the CEC09 suite of test problems and is found better than or commensurable to thirteen state-of-the-art significant multi-objective optimization algorithms as well as other multi-objective variants of the ABC. Further, it is tested on the nine real-life data clustering problems considered from the UCI machine learning repository and proved itself better in comparison to the NSGA-II, MOVGA, and a recent multi-objective variant of the ABC named MOABC. Thus, it is observed that the NSABC is comparatively a simple, light, and powerful algorithm to solve multi-objective problems.