A preference-based multi-objective evolutionary algorithm using preference selection radius

In traditional preference-based multi-objective optimization, the reference points in different regions often impact the performance of the algorithms so that the region of interest (ROI) cannot easily be obtained by the decision maker (DM). In dealing with many-objective optimization problems, the objective space is filled with non-dominated solutions in terms of the Pareto dominance relationship, since the dominance relationship cannot differentiate the mutual relationship between the solutions. To solve the above problems, this paper proposes a new selection mechanism with two main steps. First, we construct a preference radius to divide the whole population into two distinct parts: a dispreferred solution set and a preferred solution set. Second, the algorithm selects the optimal solutions in the preferred solution set by means of the Pareto dominance relationship. If the number of the obtained solutions does not satisfy the quantity’s upper limit, it selects those dispreferred solutions which have smaller distances to the reference direction until the number matches the size of the population. Experimental results show that the algorithm applying the mechanism is able to adapt to different reference points in varying regions in objective space. Moreover, it assists the DM in obtaining different sizes of ROI by adjusting the length of the radius of ROI. In dealing with many-objective problems, the mechanism can dramatically contribute to the convergence of an algorithm proposed in this paper, in comparison with other two state-of-the-art algorithms: g-dominance and r-dominance. Thus, this paper provides a new way to deal with user preference-based multi-objective optimization problems.