The artificial bee colony (ABC) algorithm is one of the classical bioinspired swarm-based intelligence algorithms that has strong search ability, because of its special search mechanism, but its development ability is slightly insufficient and its convergence speed is slow. In view of its weak development ability and slow convergence speed, this paper proposes the QABC algorithm in which a new search equation is based on the idea of quasi-affine transformation, which greatly improves the cooperative ability between particles and enhances its exploitability. During the process of location updating, the convergence speed is accelerated by updating multiple dimensions instead of one dimension. Finally, in the overall search framework, a collaborative search matrix is introduced to update the position of particles. The collaborative search matrix is transformed from the lower triangular matrix, which not only ensures the randomness of the search, but also ensures its balance and integrity. To evaluate the performance of the QABC algorithm, CEC2013 test set and CEC2014 test set are used in the experiment. After comparing with the conventional ABC algorithm and some famous ABC variants, QABC algorithm is proved to be superior in efficiency, development ability, and robustness.
Representations of the Affine Transformation Groups Acting Simply Transitively on Siegel Domains
