  Most existing studies on evolutionary multi-objective optimization focus on
approximating the whole Pareto-optimal front. Nevertheless, rather than the
whole front, which demands for too many points (especially in a
high-dimensional space), the decision maker might only interest in a partial
region, called the region of interest. In this case, solutions outside this
region can be noisy to the decision making procedure. Even worse, there is no
guarantee that we can find the preferred solutions when tackling problems with
complicated properties or a large number of objectives. In this paper, we
develop a systematic way to incorporate the decision maker's preference
information into the decomposition-based evolutionary multi-objective
optimization methods. Generally speaking, our basic idea is a non-uniform
mapping scheme by which the originally uniformly distributed reference points
on a canonical simplex can be mapped to the new positions close to the
aspiration level vector specified by the decision maker. By these means, we are
able to steer the search process towards the region of interest either directly
or in an interactive manner and also handle a large number of objectives. In
the meanwhile, the boundary solutions can be approximated given the decision
maker's requirements. Furthermore, the extent of the region of the interest is
intuitively understandable and controllable in a closed form. Extensive
experiments, both proof-of-principle and on a variety of problems with 3 to 10
objectives, fully demonstrate the effectiveness of our proposed method for
approximating the preferred solutions in the region of interest.
