Table 1 Representative many-objective evolutionary algorithms.

Pareto-based approaches

Pareto-dominance

GA

NSGAII²¹

2, 3

Deb et al.²¹

Random Frog Hopping Algorithm

MOSFLA¹⁶

2, 3, 5

Guo et al.¹⁶

Chimpanzee Algorithm

MOBO²²

2, 3

Amit Kumar Das et al.²²

Grid-dominance

GA

GRID⁶

4, 5, 6, 8, 10

Yang et al.⁶

r-Dominance

PSO

r-MOPSO⁸

3, 5, 10

Zhang et al.⁸

theta-Dominance

SBX operator and variation

\(\theta\)-DEA⁷

3, 5, 8, 10, 15

Yuan et al.⁷

LWM-dominance

GA

LWM-NSGAII¹⁰

5, 10, 15, 20

Zhu et al.¹⁰

Decomposition-based approaches

Weighted sum approach, Weighted Tchebycheff approach, Penalty-based boundary intersection

GA

MOEA/D²³

2, 3, 4

Zhang et al.²³

APD Function

GA

RVEA⁹

3, 6, 8, 10

Cheng et al.⁹

Weighted sum approach

Artificial Fish Swarms Algorithm (AFSA)

MOAFS¹²

5, 6

Ali Dabba et al.¹²

Butterfly Optimization Algorithm (BOA)

MOABO¹⁹

2, 3, 10

Rodrigues et al.¹⁹

Reference point-based method

Artificial Bee Colony Algorithm (ABC)

MaOABC/D-LA¹³

3, 5, 10, 15

Zhao et al.¹³

Bat Algorithm (BA)

MaOBAT¹⁸

2, 3, 5, 7, 10

Perwaiz et al.¹⁸

Penalty-based boundary intersection

Brain Storm Optimization Algorithm (BSO)

MaOBSO¹⁴

5, 10

Wu et al.¹⁴

Reference point + Pareto-dominance

Cuckoo Search (CS)

HMaOCS²⁴

2, 3, 4, 6, 8, 10

Cui²⁴

Indicator-based approaches

HV indicator

GA

HypE⁵

2, 3, 5, 7, 10, 25, 50

Bader et al.⁵

IGD indicator

GA

MaOEA/IGD¹¹

8, 15, 20

Sun et al.¹¹

IGD indicator

collaborative optimization control

MoMCO¹⁵

3, 5, 8, 10

Zhang et al.¹⁵

\(\varepsilon +\) indicator

Bacterial Foraging Algorithm

HMOBFA¹⁷

3, 5, 8

Liu et al.¹⁷

R2 indicator

PSO

R2-MOPSO-II²⁰

3, 5, 8, 10, 15

Li et al.²⁰