Real-coded Genetic Algorithms, Virtual Alphabets, and Blocking

This pap er present s a theory of convergence for realcoded genet ic algorit hmsGAs that use float ing-point or oth er highcardinality codings in their chromosomes . The theory is consistent with th e theory of schemata and postulates tha t select ion domin ates early GA perform ance and restri cts subsequent search to int ervals with above-average fun ction values, dimension-by-dimension. These intervals may be further subdivided on the basis of th eir at tract ion under genet ic hillclimbin g. Each of th ese subintervals is called a virtu al char acter, and the collect ion of characters along a given dimension is called a virtu al alphabet. It is the virtual alphabet that is searched during the recombinat ive phase of the genet ic algorit hm, and in many problems thi s is sufficient to ensure that good solut ions are found. Although the theory helps suggest why many problems have been solved using real-coded GAs, it also suggests that real-coded GAs can be blocked from fur ther prog ress in those situa tions when local opt ima separate the virtual characters from the global optimum.