methods that do not contain any random elements

Thus, the notion of global convergence of the algorithms in this section refers to obtaining a strict local minimum 59#59 from any given starting point 60#60 and not the global minimum of a function.

methods that contain random elements

In this context an homogeneous Markov chain is a series of random changes in the control variables.

In other words, there is an 80 chance that a change which increases the objective function will be accepted.

In fact, Evolution Strategies (see section 4.3 almost always perform better than Genetic Algorithms on optimization problems with continuous control variables and do not incur quantization errors, so there is, in practice, little incentive to use a GA on such problems.