The MOEAs Included in PlatEMO

Algorithm | Year of Publication | Description |

Multi-Objective Genetic Algorithms | ||

SPEA2 [2] | 2001 | Strength Pareto evolutionary algorithm 2 |

PSEA-II [3] | 2001 | Pareto envelope-based selection algorithm II |

NSGA-II [1] | 2002 | Non-dominated sorting genetic algorithm II |

ϵ-MOEA [8] | 2003 | Multi-objective evolutionary algorithm based on ϵ-dominance |

IBEA [9] | 2004 | Indicator-based evolutionary algorithm |

MOEA/D [4] | 2007 | Multi-objective evolutionary algorithm based on decomposition |

SMS-EMOA [10] | 2007 | S metric selection evolutionary multi-objective optimization algorithm |

MSOPS-II [11] | 2007 | Multiple single objective Pareto sampling algorithm II |

MTS [12] | 2009 | Multiple trajectory search |

AGE-II [13] | 2013 | Approximation-guided evolutionary algorithm II |

NSLS [14] | 2015 | Non-dominated sorting and local search |

BCE-IBEA [15] | 2015 | Bi-criterion evolution for IBEA |

MOEA/IGD-NS [16] | 2016 | Multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric |

Many-Objective Genetic Algorithms | ||

HypE [17] | 2011 | Hypervolume-based estimation algorithm |

PICEA-g [18] | 2013 | Preference-inspired coevolutionary algorithm with goals |

GrEA [19] | 2013 | Grid-based evolutionary algorithm |

NSGA-III [20] | 2014 | Many-objective evolutionary algorithm based on objective space reduction and diversity improvement |

A-NSGA-III [21] | 2014 | Adaptive NSGA-III |

SPEA2+SDE [22] | 2014 | SPEA2 with shift-based density estimation |

BiGE [23] | 2015 | Bi-goal evolution |

EFR-RR [7] | 2015 | Ensemble fitness ranking with ranking restriction |

I-DBEA [24] | 2015 | Improved decomposition based evolutionary algorithm |

KnEA [25] | 2015 | Knee point driven evolutionary algorithm |

MaOEA-DDFC [26] | 2015 | Many-objective evolutionary algorithm based on directional diversity and favorable convergence |

MOEA/DD [27] | 2015 | Multi-objective evolutionary algorithm based on dominance and decomposition |

MOMBI-II [28] | 2015 | Many-objective metaheuristic based on the R2 indicator II |

Two Arch2 [29] | 2015 | Two-archive algorithm 2 |

MaOEA-R&D [30] | 2016 | Many-objective evolutionary algorithm based on objective space reduction and diversity improvement |

RPEA [31] | 2016 | Reference points-based evolutionary algorithm |

RVEA [32] | 2016 | Reference vector guided evolutionary algorithm |

RVEA* [32] | 2016 | RVEA embedded with the reference vector regeneration strategy |

SPEA/R [33] | 2016 | Strength Pareto evolutionary algorithm based on reference direction |

θ-DEA [34] | 2016 | θ-dominance based evolutionary algorithm |

Multi-Objective Genetic Algorithms for Large-Scale Optimization | ||

MOEA/DVA [35] | 2016 | Multi-objective evolutionary algorithm based on decision variable analyses |

LMEA [36] | 2016 | Large-scale many-objective evolutionary algorithm |

Multi-Objective Genetic Algorithms with Preference | ||

g-NSGA-II [37] | 2009 | g-dominance based NSGA-II |

r-NSGA-II [38] | 2010 | r-dominance based NSGA-II |

WV-MOEA-P [39] | 2016 | Weight vector based multi-objective optimization algorithm with preference |

Multi-objective Differential Algorithms | ||

GDE3 [40] | 2005 | Generalized differential evolution 3 |

MOEA/D-DE [5] | 2009 | MOEA/D based on differential evolution |

Multi-objective Particle Swarm Optimization Algorithms | ||

MOPSO [41] | 2002 | Multi-objective particle swarm optimization |

SMPSO [42] | 2009 | Speed-constrained multi-objective particle swarm optimization |

dMOPSO [43] | 2011 | Decomposition-based particle swarm optimization |

Multi-objective Memetic Algorithms | ||

M-PAES [44] | 2000 | Memetic algorithm based on Pareto archived evolution strategy |

Multi-objective Estimation of Distribution Algorithms | ||

MO-CMA [45] | 2007 | Multi-objective covariance matrix adaptation |

RM-MEDA [46] | 2008 | Regularity model-based multi-objective estimation of distribution algorithm |

IM-MOEA [47] | 2015 | Inverse modeling multi-objective evolutionary algorithm |

Surrogate Model Based Multi-objective Algorithms | ||

ParEGO [48] | 2005 | Efficient global optimization for Pareto optimization |

SMS-EGO [49] | 2008 | S-metric-selection-based efficient global optimization |

K-RVEA [50] | 2016 | Kriging assisted RVEA |

The MOPs Included in PlatEMO

Problem | Year of Publication | Description |

MOKP [51] | 1999 | Multi-objective 0/1 knapsack problem and |

ZDT1–ZDT6 [53] | 2000 | Multi-objective test problems |

mQAP [54] | 2003 | Multi-objective quadratic assignment problem |

DTLZ1–DTLZ9 [55] | 2005 | Scalable multi-objective test problems |

WFG1–WFG9 [56] | 2006 | Scalable multi-objective test problems and degenerate problem WFG3 analyzed in [57] |

MONRP [58] | 2007 | Multi-objective next release problem |

MOTSP [59] | 2007 | Multi-objective traveling salesperson problem |

Pareto-Box [60] | 2007 | Pareto-Box problem |

CF1–CF10 [61] | 2008 | Constrained multi-objective test problems for the CEC 2009 special session and competition |

F1–F10 for RM-MEDA [46] | 2008 | The test problems designed for RM-MEDA |

UF1–UF12 [61] | 2008 | Unconstrained multi-objective test problems for the CEC 2009 special session and competition |

F1–F9 for MOEA/D-DE [5] | 2009 | The test problems extended from [62] designed for MOEA/D-DE |

C1_DTLZ1, C2_DTLL2, C3_DTLZ4，IDTLZ1, IDTLZ2 [21] | 2014 | Constrained DTLZ andinverted DTLZ |

F1–F7 for MOEA/D-M2M [6] | 2014 | The test problems designed for MOEA/D-M2M |

F1–F10 for IM-MOEA [47] | 2015 | The test problems designed for IM-MOEA |

BT1–BT9 [63] | 2016 | Multi-objective test problems with bias |

LSMOP1–LSMOP9 [64] | 2016 | Large-scale multi-objective test problems |

REFERENCES