Although there is no guarantee of optimality, we are assured of exponential convergence. If we run the GA several times, it will converge each time, possibly at different optimal chromosomes. The schemata which promise convergence are actually indicative of the regions in the search space where good chromosomes may be found. Typically, the GA is coupled with a local search mechanism to find the optimal chromosome in a region. So, if we use a hybrid algorithm, the problem reduces to ensuring that we run the GA as many times as is needed to pick out all the good regions. If we know before hand the shape of the search space, we can estimate the number of regions we expect to find. We can then repeatedly run the GA until these regions have been found. In most practical problems, however, the shape of the search space is not known before hand. The systematic approach is then to repeat GA runs until the best chromosomes that are found start to repeat with some regularity.
GAs are not good at identifying the optimal value of a chromosome for a problem but do very well in identifying the regions where those optima lie. Therefore, we use a hybrid GA - every ten generations, we anneal the best 10% of the population. This has the effect of moving the top chromosomes in that generation (which are the result of exponential convergence toward the best regions) to the local maximum in their region. A discussion of simulated annealing is beyond the scope of this paper; the interested reader is directed to Metropolis et al. (1953) and Press et al. (1988).