A distance and cosine similarity-based fitness evaluation mechanism for large-scale many-objective optimization

The fitness evaluation mechanism (FEM) based on nondominated sorting may lead to slow convergence when solving large-scale many -objective optimization problems (LSMaOPs), because the number of comparisons will become extremely large with the increase of optimization objectives and iterations. To solve this problem, a novel FEM based on distance and cosine similarity (DCS) is proposed in this paper. In each iteration, DCS needs to generate an ideal point after normalizing all objective functions. DCS consists of two important components, i.e., the distance and cosine similarity. The distance similarity that mines the similar relationship between solutions and ideal point is calculated as the convergence measure, and the cosine similarity that reflects the uniformity of solution distribution is calculated as the diversity measure. Furthermore, DCS fuses the distance and cosine similarity into a comprehensive similarity to fully evaluate the quality of solutions. Both theoretical analysis and empirical results indicate that DCS has lower computational complexity than other state-of-the-art FEMs. To verify the performance of DCS in solving LSMaOPs, DCS and the competitors are respectively embedded in genetic algorithm, and then compared on 56 test instances with 5-15 objectives and 100-1000 decision variables. The experimental results show the effectiveness and superiority of DCS.