Swarm robotics is an area of research that has attracted several researchers. This field is part of the collective robotics approach that is inspired by the self-organized behaviors of social animals. From interactions between agents, guided by simple rules, it is possible to design emerging collective behaviors capable of performing complex tasks in an organized manner, for the coordination and control of a large number of robots. In this article, we proposed a new model that combines different techniques of natural and evolutionary computing: we mainly focus on ideas and concepts about cellular automata, social pedestrians behavior in evacuation, genetic algorithms, inverted pheromone from ant colonies and Tabu search, as hybrid search mechanism. The objective of this new model is to provide an advance of surrogate techniques for swarm robotics as a field of science and engineering and that may be relevant to deal with the robotic surveillance task. The new model is called Genetic Shared Tabu Inverted Ant Cellular Automata, or shortly GSTIACA. Initially, it was made a meta-optimization of the surrogate parameters through a genetic algorithm. Then, we apply these new parameters for hundreds steps in a robot control and navigation algorithm based on cellular automata techniques in different environments types. The system global search takes place at different times, one of which is based on the spread of pheromone in the environment and the other which is based on the memory sharing based on Tabu search. The novelty of this work is precisely the Tabu search application as a local and used as a shared global search algorithm. Besides that, we developed a new algorithm for swarm robotics that integrates different artificial intelligence techniques and natural computing not yet used all together in precursor works. In addition, we reduced the cost of processing the pheromone decline calculation using an asynchronous cellular-automaton. Later, we contrasted the new model in different situations, and saw that the new algorithm proposed here is better than its precursors. Finally, we did a test using the e-Puck architecture within the Webots simulation environment to prove that the mathematical model proposed herein is capable of being applied in the real world application.