Cellular evolutionary algorithms (cEAs) are a particular type of EAs in which a communication structure is imposed to the population and mating restricted to topographically nearby individuals. In general, these algorithms have longer takeover times than panmictic EAs and previous investigations argue that they are more efficient in escaping local optima of multimodal and deceptive functions. However, most of those studies are not primarily concerned with population size, despite being one of the design decisions with a greater impact in the accuracy and convergence speed of population-based metaheuristics. In this paper, optimal population size for cEAs structured by regular and random graphs with different degree is estimated. Selecto-recombinative cEAs and standard cEAs with mutation and different types of crossover were tested on a class of functions with tunable degrees of difficulty. Results and statistical tests demonstrate the importance of setting an appropriate population size. Event Takeover Values (ETV) were also studied and previous assumptions on their distribution were not confirmed: although ETV distributions of panmictic EAs are heavy-tailed, log-log plots of complementary cumulative distribution functions display no linearity. Furthermore, statistical tests on ETVs generated by several instances of the problems conclude that power law models cannot be favored over log-normal. On the other hand, results confirm that cEAs impose deviations to distribution tails and that large ETVs are less probable when the population is structured by graphs with low connectivity degree. Finally, results suggest that for panmictic EAs the ETVs’ upper bounds are approximately equal to the optimal population size.

细胞进化算法（cEAs）是一种特定类型的EA，其中，通信结构被强加于人群，交配仅限于地形附近的个体。通常，这些算法的接收时间比panicmic EA更长，并且先前的研究表明，它们在逃避多模态和欺骗性功能的局部最优方面更有效。但是，尽管这些研究是设计决策之一，但对基于人口的元启发式方法的准确性和收敛速度影响更大，但大多数研究并没有主要涉及人口规模。在本文中，估计了由具有不同程度的规则图和随机图构成的cEA的最佳种群规模。在具有可调难度的一类功能上测试了具有突变和不同交叉类型的选择重组cEA和标准cEA。结果和统计测试证明了设定适当人口规模的重要性。还对事件接管值（ETV）进行了研究，但尚未确认其分布的先前假设：尽管恐慌EA的ETV分布是重尾的，但互补累积分布函数的对数-对数图却没有线性。此外，对由若干问题实例产生的ETV的统计测试得出的结论是，幂律模型不能优于对数正态模型。另一方面，结果证实，当总体由具有低连通度的图构成时，cEA会给分布尾部带来偏差，并且大型ETV的可能性较小。最后，结果表明，对于大规模EA，ETV的上限大约等于最佳种群规模。