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Artificial bee colony algorithm as a recent meta-heuristic algorithm, inspired from the foraging behavior of honey bees, can be considered as a proper technique to handle optimization problems. In this paper, a multi-objective artificial bee colony algorithm is introduced in which an archive is defined to store non-dominated solutions. Furthermore, to reduce computations and to have evenly distributed solutions, the archive is pruned using a technique based on neighborhood radius concepts. A group of bees that is responsible for improvement of the solutions chooses and exploits one solution of the archive. Because of the definition of neighborhood radius and retaining adjacent solutions, the remaining solutions have an equal chance to be selected by onlooker bees. In order to examine the proposed algorithm, some benchmark functions are used and the results are compared with true Pareto fronts. Moreover, the algorithm is utilized to optimize the coefficients of a new combined controller applied to a ball-beam system. In fact, the proposed controller is a combination of robust decoupled sliding mode and adaption laws based on the gradient decent method. The objective functions are considered as the integral time of absolute of errors of the ball position and the beam angle that should be minimized with a constraint on the control effort. To evaluate and validate the suggested approach, the obtained time responses of the ball-beam system are compared with those of other recently reported controllers.

A New Multi-objective Artificial Bee Colony Algorithm for Optimal Adaptive Robust Controller Design