From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms

Research output: Contribution to journalArticle


Colleges, School and Institutes


Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1 + 1) EAs only. Theoretical results on the average computation time of population-based EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The use of population has been regarded as one of the key features of EAs. It is important to understand in depth what the real utility of population is in terms of the time complexity of EAs, when EAs are applied to combinatorial optimization problems. This paper compares (1 + 1) EAs and ( V + N) EAs theoretically by deriving their first hitting time on the same problems. It is shown that a population can have a drastic impact on an EA's average computation time, changing an exponential time to a polynomial time (in the input size) in some cases. It is also shown that the first hitting probability can be improved by introducing a population. However, the results presented in this paper do not imply that population-based EAs will always be better than (1 + 1) EAs for all possible problems.


Original languageEnglish
Pages (from-to)495-511
Number of pages17
JournalIEEE Transactions on Evolutionary Computation
Issue number5
Publication statusPublished - 1 Oct 2002


  • evolutionary algorithms, first hitting time, time complexity, population