In evolutionary computation, systematically structuring the population is used to manage the evolution process. Thus controlling the amount of diversity during the algorithm search. Island-based, hierarchical-based, and cellular automata are the most popular structured population models utilized for evolutionary algorithms to improve their diversity and convergence. Specifically, the cellular automata model arranges the population of individuals in a 2D grid spatial structure where the concepts of cells and their neighbors are considered to drive the evolution step. A recent population-based algorithm is proposed called the crow search algorithm (CSA). It stimulates the behavior of crows in keeping their food in hidden places to be retrieved when needed. Like other population-based algorithms, CSA endures from slow convergence because of inadequate diversity. In this paper, the cellular automata model is incorporated with the optimization framework of CSA to control its diversity during the search, thus boosts its efficiency. The proposed method is abbreviated as CCSA. In CCSA, the population is structured as a 2D grid where the active population is iteratively determined. At each iteration, each individual is updated based on current neighboring individuals determined by the topological neighborhood shapes and follows the best neighboring individual in its active population. The CCSA is evaluated using 23 standard benchmark functions well-circulated in the literature. Initially, six cellular topological neighborhood shapes (i.e., L5, L9, C9, C13, C21, and C25) are studied with various problem sizes to investigate their impact on the CCSA convergence. Comparative evaluations against twelve state-of-the-art methods, including four CSA versions, are conducted. The comparative results prove the effectiveness of the proposed CCSA. The diversity of the proposed CCSA has also been stressed using convergence analysis and hamming distance. For further validations, the proposed algorithm is evaluated using three real-world problems published in IEEE-CEC2011 and welded beam design problems. Again, the proposed CCSA yields more fruitful results than other well-established methods using real-world problems. In conclusion, this paper provides an efficient alternative of CSA to perfectly maintain the diversity of the search, which can be further tested using other optimization problems.