In this paper, the design of fractional-order PID controller is considered in order to minimize certain performance indices such as integral absolute error, integral square error and integral time absolute error. The design-construction leads to a high-dimensional, multi-modal, complex optimization problem which is difficult to solve analytically. We show that it can be solved heuristically using an artificial bee colony (ABC) algorithm, which is a recently emerged ‘stochastic’ technique inspired from the intelligent foraging behavior of honey bee swarm. For the numerical examples under consideration, we further compare the performance of ABC with a ‘deterministic’ Nelder–Mead simplex algorithm.