Time Complexity of genetic algorithms on exponentially scaled problems

This paper gives a theoretical and empirical analysis of the time complexity of genetic algorithms (GAs) on problems with exponentially scaled building blocks. It is important to study GA performance on this type of problems because one of the difficulties that GAs are generally faced with is due to the low scaling or low salience of some building blocks. The paper is an extension of the model introduced by Thierens, Goldberg, and Pereira (1998) for the case of building blocks rather than single genes, and the main result is that under the assumption of perfect building block mixing, both population size and time to convergence grow linearly with the problem length, giving an overall quadratic time complexity in terms of fitness function evaluations. With traditional simple GAs, the assumption of perfect mixing only occurs when the user has knowledge about the structure of the problem (which is usually not true). However, the assumption is well approximated for advanced GAs that are able to automatically learn gene linkage.

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