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Abstract: A Rosenbrock artificial bee colony algorithm (RABC) that combines Rosenbrock’s rotational direction method with an artificial bee colony algorithm (ABC) is proposed for accurate numerical optimization. There are two alternative phases of RABC: the exploration phase realized by ABC and the exploitation phase completed by the rotational direction method. The proposed algorithm was tested on a comprehensive set of complex benchmark problems, encompassing a wide range of dimensionality, and it was also compared with several algorithms. Numerical results show that the new algorithm is promising in terms of convergence speed, success rate, and accuracy. The proposed RABC is also capable of keeping up with the direction changes in the problems. [Copyright &y& Elsevier]