  This paper presents two different efficiency-enhancement techniques for
probabilistic model building genetic algorithms. The first technique proposes
the use of a mutation operator which performs local search in the sub-solution
neighborhood identified through the probabilistic model. The second technique
proposes building and using an internal probabilistic model of the fitness
along with the probabilistic model of variable interactions. The fitness values
of some offspring are estimated using the probabilistic model, thereby avoiding
computationally expensive function evaluations. The scalability of the
aforementioned techniques are analyzed using facetwise models for convergence
time and population sizing. The speed-up obtained by each of the methods is
predicted and verified with empirical results. The results show that for
additively separable problems the competent mutation operator requires O(k 0.5
logm)--where k is the building-block size, and m is the number of building
blocks--less function evaluations than its selectorecombinative counterpart.
The results also show that the use of an internal probabilistic fitness model
reduces the required number of function evaluations to as low as 1-10% and
yields a speed-up of 2--50.
