Multiobjective Combinatorial Optimization with Interactive Evolutionary Algorithms: the case of facility location problems

We consider multiobjective combinatorial optimization problems handled by preference-driven efficient heuristics. They look for the most preferred part of the Pareto front based on some preferences expressed by the user during the process. In general, the Pareto set of efficient solutions is searched for in this case. However, obtaining the Pareto set does not solve the decision problem since one or more solutions, being the most preferred for the user, have to be selected. Therefore, it is necessary to elicit their preferences. What we are proposing can be seen as one of the first structured methodologies in facility location problems to search for optimal solutions taking into account the preferences of the user. To this aim, we use an interactive evolutionary multiobjective optimization procedure called NEMO-II-Ch. It is applied to a real-world multiobjective location problem with many users and many facilities to be located. Several simulations have been performed. The results obtained by NEMO-II-Ch are compared with those obtained by three algorithms knowing 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 the whole user’s true preferences.