  Decomposition has become an increasingly popular technique for evolutionary
multi-objective optimization (EMO). A decomposition-based EMO algorithm is
usually designed to approximate a whole Pareto-optimal front (PF). However, in
practice, the decision maker (DM) might only be interested in her/his region of
interest (ROI), i.e., a part of the PF. Solutions outside that might be useless
or even noisy to the decision-making procedure. Furthermore, there is no
guarantee to find the preferred solutions when tackling many-objective
problems. This paper develops an interactive framework for the
decomposition-based EMO algorithm to lead a DM to the preferred solutions of
her/his choice. It consists of three modules, i.e., consultation, preference
elicitation and optimization. Specifically, after every several generations,
the DM is asked to score a few candidate solutions in a consultation session.
Thereafter, an approximated value function, which models the DM's preference
information, is progressively learned from the DM's behavior. In the preference
elicitation session, the preference information learned in the consultation
module is translated into the form that can be used in a decomposition-based
EMO algorithm, i.e., a set of reference points that are biased toward to the
ROI. The optimization module, which can be any decomposition-based EMO
algorithm in principle, utilizes the biased reference points to direct its
search process. Extensive experiments on benchmark problems with three to ten
objectives fully demonstrate the effectiveness of our proposed method for
finding the DM's preferred solutions.
