Fitting the skills of the natural vision is an appealing perspective for artificial vision systems, especially in robotics applications dealing with visual perception of the complex surrounding environment where robots and humans mutually evolve and/or cooperate, or in a more general way, those prospecting human–robot interaction. Focusing the visual attention dilemma through human eye-fixation paradigm, in this work we propose a model for artificial visual attention combining a statistical foundation of visual saliency and a genetic tuning of the related parameters for robots’ visual perception. The computational issue of our model relies on the one hand on center-surround statistical features’ calculations with a nonlinear fusion of different resulting maps, and on the other hand on an evolutionary tuning of human’s gazing way resulting in emergence of a kind of artificial eye-fixation-based visual attention. Statistical foundation and bottom-up nature of the proposed model provide as well the advantage to make it usable without needing prior information as a comprehensive solid theoretical basement. The eye-fixation paradigm has been considered as a keystone of the human-like gazing attribute, molding the robot’s visual behavior toward the human’s one. The same paradigm, providing MIT1003 and TORONTO image datasets, has served as evaluation benchmark for experimental validation of the proposed system. The reported experimental results show viability of the incorporated genetic tuning process in shoving the conduct of the artificial system toward the human-like gazing mechanism. In addition, a comparison to currently best algorithms used in the aforementioned field is reported through MIT300 dataset. While not being designed for eye-fixation prediction task, the proposed system remains comparable to most of algorithms within this leading group of currently best state-of-the-art algorithms used in the aforementioned field. Moreover, about ten times faster than the currently best state-of-the-art algorithms, the promising execution speed of our approach makes it suitable for an effective implementation fitting requirement for real-time robotics applications.