The use of genetic algorithms (GA) in various applications has been the focus of much research. However, not many have tried to formalize the theory of GAs mathematically. The main purpose of this paper is to offer an understandable theory of GAs, and it also shows several interesting properties about the boundary conditions for its application. Among them are that
- a larger mutation rate at the beginning of the algorithm enhances weak ergodicity;
- crossover alone is not really suitable as random generator phase in GAs since this leads to implementation of genetic drift, which is non-ergodic in nature;
- if a scaled genetic algorithm is used, then the selection pressure should not increase too fast.
The theory includes proof of strong ergodicity for various types of scaled GA using common fitness selection methods, whose contracting properties were also considered.The introduction is excellent, and reports an analysis on the results presented by other authors to justify the results obtained in this work. The conclusion is well organized, and presents a set of cases of asymptotic behavior of GAs, as well as references to other authors’ theorems that prove the statements in this paper.
Summing up, the paper is good from a technical point of view, but in view of the fact that it is an extension of a previous paper [1], it could be considered slightly long.
