Solving Many-Objective Optimization Problems Based on PF Shape Classification and Vector Angle Selection

Most many-objective optimization algorithms (MaOEAs) adopt a pre-assumed Pareto front (PF) shape, instead of the true PF shape, to balance convergence and diversity in high-dimensional objective space, resulting in insufficient selection pressure and poor performance. To address these shortcomings, we propose MaOEA-PV based on PF shape classification and vector angle selection. The three innovation points of this paper are as follows: (i) a new method for PF classification; (ii) a new fitness function that combines convergence and diversity indicators, thereby enhancing the quality of parents during mating selection; and (iii) the selection of individuals exhibiting the best convergence to add to the population, overcoming the lack of selection pressure during environmental selection. Subsequently, the max-min vector angle strategy is employed. The solutions with the highest diversity and the least convergence are selected based on the max and min vector angles, respectively, which balances convergence and diversity. The performance of algorithm is compared with those of five state-of-the-art MaOEAs on 41 test problems and 5 real-world problems comprising as many 15 objectives. The experimental results demonstrate the competitive and effective nature of the proposed algorithm.