A weight vector generation method based on normal distribution for preference-based multi-objective optimization

In researching multi-objective evolutionary algorithms (MOEAs), the decision-maker (DM) may not need the entire Pareto optimal front searched and may only be interested in the region of interest (ROI). Most existing preference-based research focuses on determining the location of the ROI and controlling its size. Those research typically ignores the preference information provided by the DM when solving problems. Since the convergence region and diversity of the population are determined according to the DM's preference information, so we propose a preference-based MOEA that uses a normal distribution (ND) to generate a weight vector, called MOEA/D-ND. The generation of the weight vector uses the DM's preference information to guide the solution to converge to the vicinity of the preference information. Because the randomness of the normal distribution can lead to a loss of diversity, an angle-based niche selection strategy is adopted. This strategy prevents the population from falling into a local optimum during the search process. Although the reference vector generated by MOEA/D-ND using the normal distribution will make the final solution set no longer uniformly distributed in the ROI, still, the closer region to the reference point, the more solution sets are obtained. The experimental results show that this algorithm has advantages in various benchmark problems with 2 to 15 goals.