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An Open Source Java Framework for Multiobjective Optimization
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<page>
<title>Key Features of the MOEA Framework</title>
<description>Walk through introductory examples using the MOEA Framework</description>
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<content>
<h2>Features</h2>
<p>
The MOEA Framework aims to provide a comprehensive collection of algorithms and
tools for multiobjective optimization. This page lists the key features of
the MOEA Framework. For more information, see our online documentation.
</p>
<ul>
<li><a href="#algorithms">Algorithms</a></li>
<li><a href="#controllers">Meta-Algorithms</a></li>
<li><a href="#problems">Problem Sets</a></li>
<li><a href="#representations">Representations</a></li>
<li><a href="#other">Additional Features</a></li>
</ul>
<div class="section">
<a name="algorithms" />
<h3>Algorithms</h3>
<p>The MOEA Framework has the largest collection of MOEAs of any library. In
addition to these pre-defined algorithms, new algorithms can be easily constructed
using existing components.</p>
<table>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
<tr>
<td style="font-weight: bold">AbYSS</td>
<td>Multiobjective Scatter Search<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">Borg MOEA</td>
<td>Adaptive Multioperator Search with ε-Dominance and ε-Progress Triggered Restarts<sup>3</sup></td>
</tr>
<tr>
<td style="font-weight: bold">CellDE</td>
<td>Cellular Genetic Algorithm with Differential Evolution<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">CMA-ES</td>
<td>Covariance Matrix Adaption Evolution Strategy</td>
</tr>
<tr>
<td style="font-weight: bold">DBEA</td>
<td>Improved Decomposition-Based Evolutionary Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">DENSEA</td>
<td>Duplicate Elimination Nondominated Sorting Evolutionary Algorithm<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">ECEA</td>
<td>Epsilon-Constraint Evolutionary Algorithm<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold;">ε-MOEA</td>
<td>ε-Dominance-based Evolutionary Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">ε-NSGA-II</td>
<td>NSGA-II with ε-Dominance, Randomized Restarts, and Adaptive Population Sizing</td>
</tr>
<tr>
<td style="font-weight: bold">FastPGA</td>
<td>Fast Pareto Genetic Algorithm<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">FEMO</td>
<td>Fair Evolutionary Multiobjective Optimizer<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">GDE3</td>
<td>Generalized Differential Evolution</td>
</tr>
<tr>
<td style="font-weight: bold">HypE</td>
<td>Hypervolume Estimation Algorithm for Multiobjective Optimization<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">IBEA</td>
<td>Indicator-Based Evolutionary Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">MOCell</td>
<td>Multiobjective Cellular Genetic Algorithm<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">MOCHC</td>
<td>Multiobjective CHC Algorithm<sup>1</sup></td>
</tr>
<tr>
<td style="font-weight: bold">MOEA/D</td>
<td>Multiobjective Evolutionary Algorithm with Decomposition</td>
</tr>
<tr>
<td style="font-weight: bold">NSGA-II</td>
<td>Non-dominated Sorting Genetic Algorithm II</td>
</tr>
<tr>
<td style="font-weight: bold">NSGA-III</td>
<td>Reference-Point Based Non-dominated Sorting Genetic Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">OMOPSO</td>
<td>Multiobjective Particle Swarm Optimization</td>
</tr>
<tr>
<td style="font-weight: bold">PAES</td>
<td>Pareto Archived Evolution Strategy</td>
</tr>
<tr>
<td style="font-weight: bold">PESA2</td>
<td>Pareto Envelope-based Selection Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">Random</td>
<td>Random Search</td>
</tr>
<tr>
<td style="font-weight: bold">RVEA</td>
<td>Reference Vector Guided Evolutionary Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">SEMO2</td>
<td>Simple Evolutionary Multiobjective Optmimizer<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">SHV</td>
<td>Sampling-Based Hypervolume-Oriented Algorithm<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">SIBEA</td>
<td>Simple Indicator Based Evolutionary Algorithm<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">SMPSO</td>
<td>Speed-Constrained Multiobjective Particle Swarm Optimization</td>
</tr>
<tr>
<td style="font-weight: bold">SMS-EMOA</td>
<td>S-Metric Selection MOEA</td>
</tr>
<tr>
<td style="font-weight: bold">SPAM</td>
<td>Set Preference Algorithm for Multiobjective Optimization<sup>2</sup></td>
</tr>
<tr>
<td style="font-weight: bold">SPEA2</td>
<td>Strength-based Evolutionary Algorithm</td>
</tr>
<tr>
<td style="font-weight: bold">VEGA</td>
<td>Vector Evaluated Genetic Algorithm</td>
</tr>
</table>
<p>
<sup>1</sup> - Algorithms provided by the <a href="http://jmetal.sourceforge.net/">JMetal</a> library (included with the MOEA Framework).<br />
<sup>2</sup> - Algorithms provided by the <a href="http://www.tik.ee.ethz.ch/sop/pisa/">PISA</a> library.<br />
<sup>3</sup> - Available as a JAR plugin from <a href="http://borgmoea.org">borgmoea.org</a>.
</p>
</div>
<div class="section">
<a name="controllers" />
<h3>Meta-Algorithms</h3>
<p>Meta-algorithms are wrappers around existing algorithms to provide additional functionality.</p>
<table>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
<tr>
<td style="font-weight: bold;">Adaptive Time Continuation</td>
<td>Periodically restart the algorithm, possibly adapting parameters</td>
</tr>
<tr>
<td style="font-weight: bold">Epsilon Progress Continuation</td>
<td>Monitor search progress, triggering a restart if search stagnates</td>
</tr>
<tr>
<td style="font-weight: bold">Checkpoints</td>
<td>Periodically save the state of the algorithm to resume interrupted runs</td>
</tr>
</table>
</div>
<div class="section">
<a name="problems" />
<h3>Problem Sets</h3>
<p>Also included are all major test problems from the literature. Additionally,
new problems written in Java or other languages can be easily incorporated.</p>
<table>
<tr>
<th>Name</th>
<th>Description</th>
</tr>
<tr>
<td style="font-weight: bold;">ZDT</td>
<td>6 real-valued problems from Zitzler et al. (2000)</td>
</tr>
<tr>
<td style="font-weight: bold">DTLZ</td>
<td>5 unconstrained, scalable real-valued problems from Deb et al. (2001)</td>
</tr>
<tr>
<td style="font-weight: bold">LZ</td>
<td>9 real-valued problems from Hui Li and Qingfu Zhang (2009)</td>
</tr>
<tr>
<td style="font-weight: bold">CEC2009</td>
<td>13 unconstrained and 10 constrained real-valued problems from the CEC2009 competition</td>
</tr>
<tr>
<td style="font-weight: bold">WFG</td>
<td>9 scalable, real-valued problems by Huband et al. (2005)</td>
</tr>
<tr>
<td style="font-weight: bold">BBOB-2016</td>
<td>55 bi-objective problems from the BBOB workshop hosted at GECCO 2016</td>
</tr>
<tr>
<td style="font-weight: bold">Miscellaneous</td>
<td>28 real-valued, binary, permutation, and program-based test problems from the literature (e.g., knapsack, NK-landscapes)</td>
</tr>
</table>
</div>
<div class="section">
<a name="representations" />
<h3>Representations</h3>
<table>
<tr>
<th>Representation</th>
<th>Operators</th>
</tr>
<tr>
<td style="font-weight: bold;">Real-Valued</td>
<td>Simulated Binary Crossover (SBX)<br />
Polynomial Mutation (PM)<br />
Parent-Centric Crossover (PCX)<br />
Simplex Crossover (SPX)<br />
Unimodal Normal Distribution Crossover (UNDX)<br />
Uniform Mutation (UM)<br />
Differential Evolution (DE)<br />
Adaptive Metropolis (AM)</td>
</tr>
<tr>
<td style="font-weight: bold">Binary</td>
<td>Bit Flip Mutation<br />
Half-Uniform Crossover (HUX)</td>
</tr>
<tr>
<td style="font-weight: bold">Permutation</td>
<td>Insertion<br />
Swap<br />
Partially Mapped Crossover (PMX)</td>
</tr>
<tr>
<td style="font-weight: bold">Subset</td>
<td>Replace<br />
Subset Crossover (SSX)</td>
</tr>
<tr>
<td style="font-weight: bold">Grammars</td>
<td>Single-point Crossover<br />
Uniform Mutation</td>
</tr>
<tr>
<td style="font-weight: bold">Programs</td>
<td>Point Mutation<br />
Subtree Crossover</td>
</tr>
<tr>
<td style="font-weight: bold">Generic</td>
<td>One Point Crossover<br />
Two Point Crossover<br />
Uniform Crossover<br />
Adaptive Multimethod Variation</td>
</tr>
</table>
</div>
<div class="section">
<a name="other" />
<h3>Additional Features</h3>
<p></p>
<table>
<tr>
<th>Feature</th>
<th>Description</th>
</tr>
<tr>
<td style="font-weight: bold;">Performance Indicators</td>
<td>Hypervolume<br />
Generational Distance (GD)<br />
Inverted Generational Distance (IGD)<br />
Additive ε-Indicator<br />
Contribution<br />
Maximum Pareto Front Error<br />
Spacing<br />
R1 Indicator<br />
R2 Indicator<br />
R3 Indicator</td>
</tr>
<tr>
<td style="font-weight: bold">Executor, Analyzer, and Instrumenter</td>
<td>Three simple Java classes for accessing 90% of the functionality of the MOEA Framework:
<ul>
<li>Executor - Construct and execute MOEAs to solve optimization problems</li>
<li>Analyzer - Statistically compare results</li>
<li>Instrumenter - Record runtime dynamics</li>
</ul>
</td>
</tr>
<tr>
<td style="font-weight: bold">Diagnostic Tool</td>
<td>GUI for quickly comparing the performance of algorithms on standard test problems</td>
</tr>
<tr>
<td style="font-weight: bold">Sensitivity Analysis</td>
<td>Sensitivity analysis tools for identifying key parameters for an algorithm (accessible through a command-line interface)</td>
</tr>
<tr>
<td style="font-weight: bold">Parallelization</td>
<td>Automatic parallelization of algorithms across multiple cores, or distribute processing across a network using <a href="http://www.jppf.org/">JPPF</a>, <a href="http://www.gridgain.com/">GridGain</a>, or any other supported grid computing library</td>
</tr>
<tr>
<td style="font-weight: bold">Extensible</td>
<td>Build new algorithms, operators, representations, or problems and integrate them into the MOEA Framework using our Service Provider Interface (SPI)</td>
</tr>
<tr>
<td style="font-weight: bold">Best Practices</td>
<td>Extensively documented and unit tested source code to ensure quality</td>
</tr>
</table>
</div>
</content>
</page>