Abstract
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.
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Abbreviations
- Abbreviations:
-
Full name
- MOP:
-
Multi-objective optimizaiton problem
- MaOP:
-
Many-objective optimizaiton problem
- PF:
-
Pareto-optimal front
- MOEA:
-
Multi-objective evolutionary algorithm
- MaOEA:
-
Many-objective evolutionary algorithm
- HV:
-
Hypervolume
- APD:
-
Angle-penalized distance
- PBI:
-
Penalty-based boundary intersection
- PVD:
-
Angle-based adaptive penalty-based vector distribution
- SBX:
-
Simulated binary crossover
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Funding
This work was supported by Natural Science Foundation-Steel and Iron Foundation of Hebei Province [Grant Nos. E2019105123], the Department of Education of Hebei Province [Grant Nos. ZD2019311].
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Xiong, Z., Yang, J., Zhao, Z. et al. Maximum angle evolutionary selection for many-objective optimization algorithm with adaptive reference vector. J Intell Manuf 34, 961–984 (2023). https://doi.org/10.1007/s10845-021-01865-1
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DOI: https://doi.org/10.1007/s10845-021-01865-1