  The Bayesian Optimisation Algorithm (BOA) is an Estimation of Distribution
Algorithm (EDA) that uses a Bayesian network as probabilistic graphical model
(PGM). Determining the optimal Bayesian network structure given a solution
sample is an NP-hard problem. This step should be completed at each iteration
of BOA, resulting in a very time-consuming process. For this reason most
implementations use greedy estimation algorithms such as K2. However, we show
in this paper that significant changes in PGM structure do not occur so
frequently, and can be particularly sparse at the end of evolution. A
statistical study of BOA is thus presented to characterise a pattern of PGM
adjustments that can be used as a guide to reduce the frequency of PGM updates
during the evolutionary process. This is accomplished by proposing a new
BOA-based optimisation approach (FBOA) whose PGM is not updated at each
iteration. This new approach avoids the computational burden usually found in
the standard BOA. The results compare the performances of both algorithms on an
NK-landscape optimisation problem using the correlation between the ruggedness
and the expected runtime over enumerated instances. The experiments show that
FBOA presents competitive results while significantly saving computational
time.
