Abstract
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.
Highlights
M ANY REAL-LIFE applications usually consider optimizing multiple conflicting objectives simultaneously
Over the past two decades and beyond, many efforts have been devoted to developing Evolutionary multiobjective optimization (EMO) algorithms (e.g., elitist nondominated sorting genetic algorithm (NSGA-II) [1], indicator-based EA [2], multiobjective EA based on decomposition (MOEA/D) [3], and their variants [4]–[10]) to find a set of efficient solutions that well approximate the whole Pareto-optimal front (PF) in terms of convergence and diversity
4) Given the decision maker (DM)’s requirements, the proposed NUMS is able to obtain a set of biased reference points toward the region of interest (ROI), and preserve the ones located on the boundary
Summary
M ANY REAL-LIFE applications usually consider optimizing multiple conflicting objectives simultaneously. To integrate the DM’s preference information into the decomposition-based EMO methods, a natural idea is to make the distribution of the reference points be biased toward the ROI. 3) Different from the existing preference-based EMO algorithms, where the extent of the approximated ROI is controlled in an ad-hoc manner, this paper provides an intuitively understandable manner to quantify this extent in a closed form It is the ratio of the biased reference points proportional to the simplex. 4) Given the DM’s requirements, the proposed NUMS is able to obtain a set of biased reference points toward the ROI, and preserve the ones located on the boundary This latter characteristic enables a decomposition-based EMO method to find the preferred solutions and provide the global information about the PF to the DM.
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