We consider a class of problems with a small number of critical
variables and many normal variables.  The normal variables are easy to
optimise, but their optimum value depend on the critical variables.  The
critical variables are only weakly coupled to each other, but strongly
coupled with the normal variables.  This leads to a set of problems with
many local minima which are hard to solve with a hill-climbing
algorithm.  We show that a hybrid genetic algorithm can solve this class
of problems vary efficiently.  Furthermore, we will argue that many of
the classic hard optimisation problems may have a structure which, at
least approximately, is similar to the critical variable problems.  We
finally discuss some recent observation on the Max-Sat problem and argue
that it may be possible to exploit information from a population to more
effectively find good solutions.