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

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Multi-objective Optimization

Background:

• Many-objective optimization algorithms (MaOEAs) struggle with convergence and diversity in high-dimensional spaces.
• Existing MaOEAs often rely on pre-assumed Pareto front (PF) shapes, leading to suboptimal performance.
• Insufficient selection pressure is a key challenge in many-objective optimization.

Purpose of the Study:

• To propose a novel many-objective optimization algorithm, MaOEA-PV, that addresses limitations of existing methods.
• To enhance the balance between convergence and diversity in high-dimensional objective spaces.
• To improve the selection pressure within optimization algorithms.

Main Methods:

• Developed a new method for Pareto front (PF) shape classification.
• Introduced a novel fitness function integrating convergence and diversity indicators for improved parent selection.
• Implemented a strategy to select highly convergent individuals to bolster population quality.
• Employed a max-min vector angle strategy to balance convergence and diversity in solution selection.

Main Results:

• MaOEA-PV demonstrated competitive and effective performance compared to five state-of-the-art MaOEAs.
• Evaluated on 41 test problems and 5 real-world problems with up to 15 objectives.
• The proposed algorithm successfully overcomes the lack of selection pressure in environmental selection.

Conclusions:

• The proposed MaOEA-PV effectively balances convergence and diversity through PF shape classification and vector angle selection.
• The algorithm shows significant improvements in performance for many-objective optimization problems.
• MaOEA-PV offers a promising approach for tackling complex high-dimensional optimization challenges.