An Introduction to Genetic Algorithms - Boente

Chapter 4: Theoretical Foundations of Genetic Algorithms
chosen value for locus 4 in the first chromosome is 1.) Once overspecification has been taken care of, the
specified bits in the chromosome can be thought of as a "candidate schema" rather than as a candidate
solution. For example, the first chromosome above is the schema 00*1. The purpose of messy GAs is to
evolve such candidate schemas, gradually building up longer and longer ones until a solution is formed. This
requires a way to evaluate a candidate schema under a given fitness function. However, under most fitness
functions of interest, it is difficult if not impossible to compute the "fitness" of a partial string. Many loci
typically interact non−independently to determine a string's fitness, and in an underspecified string the
missing loci might be crucial. Goldberg and his colleagues first proposed and then rejected an "averaging"
method: for agiven underspecified string, randomly generate values for the missing loci over a number of
trials and take the average fitness computed with these random samples. The idea is to estimate the average
fitness of the candidate schema. But, as was pointed out earlier, the variance of this average fitness will often
be too high for a meaningful average to be gained from such sampling. Instead, Goldberg and his colleagues
used a method they called "competitive templates." The idea was not to estimate the average fitness of the
candidate schema but to see if the candidate schema yields an improvement over a local optimum. The
method works by finding a local optimum at the beginning of a run by a hill−climbing technique, and then,
when running the messy GA, evaluating underspecified strings by filling in missing bits from the local
optimum and then applying the fitness function. A local optimum is, by definition, a string that cannot be
improved by a single−bit change; thus, if a candidate schema's defined bits improve the local optimum, it is
worth further exploration.
The messy GA proceeds in two phases: the "primordial phase" and the "juxtapositional phase." The purpose
of the primordial phase is to enrich the population with small, promising candidate schemas, and the purpose
of the juxtapositional phase is to put them together in useful ways. Goldberg and his colleagues' first method
was to guess at the order k of the smallest relevant schemas and to form the initial population by completely
enumerating all schemas of that order. For example, if the size of solutions is l = 8 and the guessed k is 3, the
initial population will be
After the initial population has been formed and the initial fitnesses evaluated (using competitive templates),
the primordial phase continues by selection only (making copies of strings in proportion to their fitnesses with
no crossover or mutation) and by culling the population by half at regular intervals. At some generation (a
parameter of the algorithm), the primordial phase comes to an end and the juxtapositional phase is invoked.
The population size stays fixed, selection continues, and two juxtapositional operators—"cut" and
"splice"—are introduced. The cut operator cuts a string at a random point. For example,
122