With fitness

In the presence of fitness the systems with GA perform much better than systems operating with pure chance.

While a system operating with pure chance selects in each cycle the next generation again and again from the set of all possible values 'forgetting' about the past keeps a system with a GA a certain partially successful subset $\cal{G}$$^{i}$ of the set of all possible values $\cal{G}$$^{*}$ as a kind of memory and looks for the next cycle only to a partial improvement of the already partial successful set of values. As the empirical results show leads this strategy very quickly to the theoretical possible maximum. How quickly ('speed', 'velocity') the theoretical maximum can be reached by the genetic function $\gamma$ depends on the operations leading from the given values $\cal{G}$$^{i}$ to the best possible values $\cal{G}$$^{*}$.

The 'speed' can be measured by the number of cycles necessary. This again leads back to the concrete genetic operations used. In the general case these are crossover and mutation.

The general behavior of crossover keeps the given values or causes some partial improvement.

The general behavior of mutation is the change of the given structure. This can lead away from a local maximum or it can lead closer to a local maximum. This can not be known in advance. The mutation operation works completely at random with regard to a given structure. Applying only mutation is comparable to pure chance. The only point is that mutation - usually - is restricted in the 'amount of change' to a minimal change while pure chance is not restricted. Thus mutation-induced-change is in the average smaller than with pure chance.

In this combination of crossover and mutation is crossover the optimization factor and mutation is the opponent to 'free' from possible captures by a suboptimal local maximum.

The overall success and therefore the real speed/ velocity of a genetic process depends then from the interaction of crossover and mutation.