A Self-Guided Reference Vector Strategy for Many-Objective Optimization

Generally, decomposition-based evolutionary algorithms in many-objective optimization (MaOEA/Ds) have widely used reference vectors (RVs) to provide search directions and maintain diversity. However, their performance is highly affected by the matching degree on the shapes of the RVs and the Pareto front (PF). To address this problem, this article proposes a self-guided RV (SRV) strategy for MaOEA/Ds, aiming to extract RVs from the population using a modified
${k}$
-means clustering method. To give a promising clustering result, an angle-based density measurement strategy is used to initialize the centroids, which are then adjusted to obtain the final clusters, aiming to properly reflect the population’s distribution. Afterward, these centroids are extracted to obtain adaptive RVs for self-guiding the search process. To verify the effectiveness of this SRV strategy, it is embedded into three well-known MaOEA/Ds that originally use the fixed RVs. Moreover, a new strategy of embedding SRV into MaOEA/Ds is discussed when the RVs are adjusted at each generation. The simulation results validate the superiority of our SRV strategy, when tackling numerous many-objective optimization problems with regular and irregular PFs.