Integration of Preferences in Decomposition Multiobjective Optimization

Rather than a whole Pareto-optimal front, which demands too many points (especially in a high-dimensional space), the decision maker (DM) may only be interested in a partial region, called the region of interest (ROI). 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 many objectives. In this paper, we develop a systematic way to incorporate the DM's preference information into the decomposition-based evolutionary multiobjective optimization methods. Generally speaking, our basic idea is a nonuniform mapping scheme by which the originally evenly distributed reference points on a canonical simplex can be mapped to new positions close to the aspiration-level vector supplied by the DM. By this means, we are able to steer the search process toward the ROI either directly or interactively and also handle many objectives. Meanwhile, solutions lying on the boundary can be approximated as well given the DM's requirements. Furthermore, the extent of the ROI is intuitively understandable and controllable in a closed form. Extensive experiments on a variety of benchmark problems with 2 to 10 objectives, fully demonstrate the effectiveness of our proposed method for approximating the preferred solutions in the ROI.