Abstract
In the last two decades significant progress has been made
in the theory and design of competent genetic algorithms--
genetic algorithms (GAs) that solve hard problems quickly,
reliably, and accurately (Goldberg, 2002). In contrast to
the first generation GAs which use fixed recombination
operators, competent GAs employ recombination operators
that adapt linkages. Competent GAs have been shown to
solve problems of bounded difficulty in polynomial (usually
subquadratic) time.
Parallel to the progress in the theory of competent GAs,
there has been a growing interest in multiobjective optimization
in general and multiobjective genetic algorithms (MOGAs)
in particular. However, similar to the first generation GAs,
existing MOGAs use fixed genetic operators and there is a
need to develop competent MOGAs---GAs that solve hard
multiobjective problems quickly, reliably, and accurately.
This study combines the selection scheme of NSGA-II (Deb,
Agrawal, Pratap & Meyarivan, 2000), a multiobjective GA,
with the linkage learning capabilities of two powerful
single objective competent GAs, BOA (Pelikan, Goldberg
& Cantú-Paz, 1999) and hBOA (Pelikan & Goldberg, 2000), to
form two component MOGAs called multiobjective Bayesian
optimization algorithm (mBOA) and multiobjective hierarchical
Bayesian optimization algorithm (mhBOA), respectively. A
test suite of additively decomposable problems with
controllable difficulty has also been developed in a
principled manner to test both mBOA and mhBOA. Results
show that while mBOA is capable of finding boundedly
difficult problems with variable interactions at a single
level, mhBOA is also able to solve hierarchically difficult
problems.