  The utilization of populations is one of the most important features of
evolutionary algorithms (EAs). There have been many studies analyzing the
impact of different population sizes on the performance of EAs. However, most
of such studies are based computational experiments, except for a few cases.
The common wisdom so far appears to be that a large population would increase
the population diversity and thus help an EA. Indeed, increasing the population
size has been a commonly used strategy in tuning an EA when it did not perform
as well as expected for a given problem. He and Yao (2002) showed theoretically
that for some problem instance classes, a population can help to reduce the
runtime of an EA from exponential to polynomial time. This paper analyzes the
role of population further in EAs and shows rigorously that large populations
may not always be useful. Conditions, under which large populations can be
harmful, are discussed in this paper. Although the theoretical analysis was
carried out on one multi-modal problem using a specific type of EAs, it has
much wider implications. The analysis has revealed certain problem
characteristics, which can be either the problem considered here or other
problems, that lead to the disadvantages of large population sizes. The
analytical approach developed in this paper can also be applied to analyzing
EAs on other problems.
