This document is the API specification for the MOEA Framework. The MOEA Framework is a free and open source Java library for developing and experimenting with multiobjective evolutionary algorithms (MOEAs) and other general-purpose optimization algorithms and metaheuristics. It supports genetic algorithms, differential evolution, particle swarm optimization, genetic programming, grammatical evolution, and more. Problems can be defined using real or integer-valued decision variables, permutations, binary arrays (bit strings), expression trees (programs), grammars, and any combination thereof. This makes the MOEA Framework one of the most comprehensive evolutionary algorithm libraries available.

For most users, the {@link org.moeaframework.Executor} and {@link org.moeaframework.Analyzer} classes provide sufficient functionality to execute and analyze MOEAs. The following table lists the algorithms provided by the MOEA Framework and supported third-party libraries.

Algorithm Type Real Binary Permutation Subset Grammar Program Constraints Provider

AbYSS Scatter Search Yes No No No No No Yes JMetal

CellDE Differential Evolution Yes No No No No No Yes JMetal

CMA-ES Evolutionary Strategy Yes No No No No No Yes Native

DBEA Decomposition Yes Yes Yes Yes Yes Yes Yes Native

DENSEA Genetic Algorithm Yes Yes Yes No No No Yes JMetal

ECEA Genetic Algorithm Yes Yes Yes Yes Yes Yes No PISA

eMOEA ε-Dominance Yes Yes Yes Yes Yes Yes Yes Native

eNSGAII ε-Dominance Yes Yes Yes Yes Yes Yes Yes Native

FastPGA Genetic Algorithm Yes Yes Yes No No No Yes JMetal

FEMO Genetic Algorithm Yes Yes Yes Yes Yes Yes No PISA

GDE3 Differential Evolution Yes No No No No No Yes Native

HypE Indicator-Based Yes Yes Yes Yes Yes Yes No PISA

IBEA Indicator-Based Yes Yes Yes Yes Yes Yes No Native

MOCell Cellular Yes Yes Yes No No No Yes JMetal

MOCHC CHC Algorithm No Yes No No No No Yes JMetal

MOEAD Decomposition Yes No No No No No Yes Native

NSGAII Genetic Algorithm Yes Yes Yes Yes Yes Yes Yes Native

NSGAIII Reference Points Yes Yes Yes Yes Yes Yes Yes Native

OMOPSO Particle Swarm Yes No No No No No Yes Native

PAES Evolutionary Strategy Yes Yes Yes Yes Yes Yes Yes Native

PESA2 Genetic Algorithm Yes Yes Yes Yes Yes Yes Yes Native

RVEA Reference Vectors Yes Yes Yes Yes Yes Yes Yes Native

SEMO2 Genetic Algorithm Yes Yes Yes Yes Yes Yes No PISA

SHV Indicator-Based Yes Yes Yes Yes Yes Yes No PISA

SIBEA Indicator-Based Yes Yes Yes Yes Yes Yes No PISA

SMPSO Particle Swarm Yes No No No No No Yes Native

SMSEMOA Indicator-Based Yes Yes Yes Yes Yes Yes Yes Native

SPAM Indicator-Based Yes Yes Yes Yes Yes Yes No PISA

SPEA2 Genetic Algorithm Yes Yes Yes Yes Yes Yes Yes Native

VEGA Genetic Algorithm Yes Yes Yes Yes Yes Yes No Native

Algorithm	Type	Real	Binary	Permutation	Subset	Grammar	Program	Constraints	Provider
AbYSS	Scatter Search	Yes	No	No	No	No	No	Yes	JMetal
CellDE	Differential Evolution	Yes	No	No	No	No	No	Yes	JMetal
CMA-ES	Evolutionary Strategy	Yes	No	No	No	No	No	Yes	Native
DBEA	Decomposition	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
DENSEA	Genetic Algorithm	Yes	Yes	Yes	No	No	No	Yes	JMetal
ECEA	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
eMOEA	ε-Dominance	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
eNSGAII	ε-Dominance	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
FastPGA	Genetic Algorithm	Yes	Yes	Yes	No	No	No	Yes	JMetal
FEMO	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
GDE3	Differential Evolution	Yes	No	No	No	No	No	Yes	Native
HypE	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
IBEA	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	No	Native
MOCell	Cellular	Yes	Yes	Yes	No	No	No	Yes	JMetal
MOCHC	CHC Algorithm	No	Yes	No	No	No	No	Yes	JMetal
MOEAD	Decomposition	Yes	No	No	No	No	No	Yes	Native
NSGAII	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
NSGAIII	Reference Points	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
OMOPSO	Particle Swarm	Yes	No	No	No	No	No	Yes	Native
PAES	Evolutionary Strategy	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
PESA2	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
RVEA	Reference Vectors	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
SEMO2	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
SHV	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
SIBEA	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
SMPSO	Particle Swarm	Yes	No	No	No	No	No	Yes	Native
SMSEMOA	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
SPAM	Indicator-Based	Yes	Yes	Yes	Yes	Yes	Yes	No	PISA
SPEA2	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Native
VEGA	Genetic Algorithm	Yes	Yes	Yes	Yes	Yes	Yes	No	Native

While the MOEA Framework provides a large collection of built-in algorithms, operators and problems, advanced users can take advantage of its object-oriented design to extend existing features or add new functionality. In addition, the service provider interface allows extending the software with algorithms and problems provided by third-party libraries. Any algorithms and problems working within the MOEA Framework can take advantage of its suite of diagnostic and statistical testing tools. As this project is academic in nature, every effort is taken to ensure the correctness, quality and openness of the codes.