Maximum angle evolutionary selection for many-objective optimization algorithm with adaptive reference vector

How to maintain a good balance between convergence and diversity is particularly important for the performance of the many-objective evolutionary algorithms. Especially, the many-objective optimization problem is a complicated Pareto front, the many-objective evolutionary algorithm can easily converge to a narrow of the Pareto front. An efficient environmental selection and normalization method are proposed to address this issue. The maximum angle selection method based on vector angle is used to enhance the diversity of the population. The maximum angle rule selects the solution as reference vector can work well on complicated Pareto front. A penalty-based adaptive vector distribution selection criterion is adopted to balance convergence and diversity of the solutions. As the evolution process progresses, the new normalization method dynamically adjusts the implementation of the normalization. The experimental results show that new algorithm obtains 30 best results out of 80 test problems compared with other five many-objective evolutionary algorithms. A large number of experiments show that the proposed algorithm has better performance, when dealing with numerous many-objective optimization problems with regular and irregular Pareto Fronts.