A multi/many-objective evolutionary algorithm based on normal-boundary intersection direction

Predefined reference vectors decomposition-based evolutionary algorithms have demonstrated excellent performance in many-objective optimization problems (MaOPs). The performance of the algorithm may decrease when it encounters various issues, including degenerate, strongly convex, and discontinuous Pareto fronts (PFs). The predefined reference vectors may not intersect or even intersect uniformly with the PF, leading to poor solution uniformity. This paper proposes a mirror advantage decomposition-based algorithm (MADEA), which integrates mirror point distance and NBI direction to ensure convergence while improving the diversity of solutions. MADEA employs 8 of the most representative algorithms to test on a total of 16 benchmark test problems including DTLZ1-7 and WFG1-9, ranging from objectives 2 to 10. The experimental results demonstrate the strong competitiveness of MADEA in handling both regular and irregular PFs in MaOPs.