  We consider multiobjective combinatorial optimization problems handled by
means of preference driven efficient heuristics. They look for the most
preferred part of the Pareto front on the basis of some preferences expressed
by the Decision Maker during the process. In general, what is searched for in
this case is the Pareto set of efficient solutions. This is a problem much more
difficult than optimizing a single objective function. Moreover, obtaining the
Pareto set does not mean that the decision problem is solved since one or some
of the solutions have to be chosen. Indeed, to make a decision, it is necessary
to determine the most preferred solution in the Pareto set, so that it is also
necessary to elicit the preferences of the user. In this perspective, what we
are proposing can be seen as the first structured methodology in facility
location problems to search optimal solutions taking into account preferences
of the user. With this aim, we approach facility location problems using a
recently proposed interactive evolutionary multiobjective optimization
procedure called NEMO-II-Ch. NEMO-II-Ch is applied to a real world
multiobjective location problem with many users and many facilities to be
located. Several simulations considering different fictitious users have been
performed. The results obtained by NEMO-II-Ch are compared with those got by
three algorithms which know the user's true value function that is, instead,
unknown to NEMO-II-Ch. They show that in many cases NEMO-II-Ch finds the best
subset of locations more quickly than the methods knowing, exactly, the whole
user's true preferences.
