MOEAFramework-3.7.website.xslt.examples.xml Maven / Gradle / Ivy
<?xml version="1.0"?>
<!DOCTYPE some_name [
<!ENTITY nbsp " ">
<!ENTITY copy "©">
<!ENTITY epsilon "ε">
]>
<page>
<title>Examples using the MOEA Framework</title>
<description>Walk through introductory examples using the MOEA Framework</description>
<header>
<script type="text/javascript" src="scripts/shCore.js"></script>
<script type="text/javascript" src="scripts/shBrushJava.js"></script>
<script type="text/javascript" src="scripts/shBrushCpp.js"></script>
<script type="text/javascript" src="scripts/shBrushPlain.js"></script>
<link type="text/css" rel="stylesheet" href="styles/shCoreEclipse.css" />
<script type="text/javascript">SyntaxHighlighter.all();</script>
</header>
<content>
<h2>Examples</h2>
<p>
The following examples demonstrate the basic functionality provided by the
MOEA Framework. Links to the full source code are provided alongside each
code snippet. You may also find these and more examples in the demo
application on the <a href="downloads.html">downloads</a> page.
</p>
<ul>
<li><a href="#setup">Setup</a></li>
<li><a href="#example1">Example 1: Simple Run</a></li>
<li><a href="#example2">Example 2: Quality Indicators</a></li>
<li><a href="#example3">Example 3: Customizing Algorithms</a></li>
<li><a href="#example4">Example 4: Statistical Comparison of Algorithms</a></li>
<li><a href="#example5">Example 5: Collecting Runtime Dynamics</a></li>
<li><a href="#example6">Example 6: Defining New Problems</a></li>
</ul>
<div class="section">
<a name="setup" />
<h3>Setup</h3>
<p>
In order to run these examples or use the MOEA Framework, Java 8 (or a later
version) must be installed on your computer. The Java 8 development kit (JDK)
for Windows and Linux can be downloaded
<a href="https://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html">here</a>.
</p>
<p>
To run these examples, first download and extract the latest compiled
binaries from the <a href="downloads.html">downloads</a> page. Windows users
may extract the downloaded file using
<a href="http://www.7-zip.org/">7-zip</a>. The files will extract to a
folder called MOEAFramework-%VERSION%. This folder will look similar to:
</p>
<div class="files">
<ul>
<li class="folder">MOEAFramework-%VERSION%/</li>
<li class="empty">
<ul>
<li class="folder">docs/</li>
<li class="folder">examples/</li>
<li class="folder">javadoc/</li>
<li class="folder">lib/</li>
<li class="folder">licenses/</li>
<li class="folder">pf/</li>
<li>COPYING</li>
<li>launch-diagnostic-tool.bat</li>
<li>moeaframework.properties</li>
<li>README.md</li>
</ul>
</li>
</ul>
</div>
<p>
All of the examples below are in the examples/ folder. You may compile and
run an example using the following commands. Run these commands in the
Command Prompt from the MOEAFramework-%VERSION% folder.
</p>
<pre>
javac -cp "examples;lib/*" examples/Example1.java
java -cp "examples;lib/*" Example1</pre>
<p>
If you receive the message <i>'javac' is not recognized as an internal or
external command, operable program or batch file</i>, try the following steps
to setup your environment on
<a href="http://vietpad.sourceforge.net/javaonwindows.html">Windows</a> or
<a href="http://vietpad.sourceforge.net/javaonlinux.html">Linux</a>.
Unix/Linux users should replace the semicolons (;) with colons (:).
</p>
</div>
<div class="section">
<a name="example1" />
<h3>Example 1: Simple Run</h3>
<div class="files">
<ul>
<li><a href="Example1.java">Example1.java</a></li>
</ul>
</div>
<p>
Create and solve the bi-objective DTLZ2 test problem using NSGA-II. At the end,
we display the Pareto front.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
Problem problem = new DTLZ2(2);
NSGAII algorithm = new NSGAII(problem);
algorithm.run(10000);
algorithm.getResult().display();
]]>
</pre>
</div>
<p>
Displaying the Pareto front will print all the decision variables, objectives, an
constraints (if any).
</p>
<div class="code">
<pre class="brush: plain; toolbar: false;">
Var1 Var2 Var3 Var4 Var5 Var6 Var7 Var8 Var9 Var10 Var11 Obj1 Obj2
-------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- --------
0.000001 0.499800 0.499459 0.493195 0.512840 0.501684 0.496219 0.510478 0.497724 0.490473 0.498708 1.000436 0.000002
1.000000 0.493931 0.496459 0.504963 0.492117 0.487517 0.495901 0.506916 0.498368 0.508016 0.504378 0.000000 1.000443
0.967343 0.500695 0.493870 0.493354 0.496931 0.489186 0.496910 0.489151 0.498778 0.499109 0.496012 0.051294 0.999038
0.570016 0.500760 0.493834 0.485232 0.492111 0.487856 0.498199 0.507383 0.498864 0.502869 0.504378 0.625569 0.780878
...
</pre>
</div>
</div>
<div class="section">
<a name="example2" />
<h3>Example 2: Quality Indicators</h3>
<div class="files">
<ul>
<li><a href="Example2.java">Example2.java</a></li>
</ul>
</div>
<p>
Quality indicators are used to compare results between different algorithms. Here,
we calculate the hypervolume and generational distance relative to a reference set.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
Problem problem = new DTLZ2(2);
NSGAII algorithm = new NSGAII(problem);
algorithm.run(10000);
NondominatedPopulation result = algorithm.getResult();
NondominatedPopulation referenceSet = PopulationIO.readReferenceSet("pf/DTLZ2.2D.pf");
Hypervolume hypervolume = new Hypervolume(problem, referenceSet);
GenerationalDistance gd = new GenerationalDistance(problem, referenceSet);
System.out.println("Hypervolume: " + hypervolume.evaluate(result));
System.out.println("GD: " + gd.evaluate(result));
]]>
</pre>
</div>
<p>
Running this program produces the following output:
</p>
<div class="code">
<pre class="brush: plain; toolbar: false;">
Hypervolume: 0.20834956047273037
GD: 0.001119315294859704
</pre>
</div>
</div>
<div class="section">
<a name="example3" />
<h3>Example 3: Customizing Algorithms</h3>
<div class="files">
<ul>
<li><a href="Example3.java">Example3.java</a></li>
</ul>
</div>
<p>
The examples above used default parameters for each algorithms. But, each algorithms
is customizable! In this example, we setup NSGA-II to use the Parent Centric Crossover (PCX)
operator, use a population size of 250, and include an archive to store the best solutions.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
Problem problem = new DTLZ2(2);
NSGAII algorithm = new NSGAII(problem);
algorithm.setInitialPopulationSize(250);
algorithm.setVariation(new PCX(5, 2));
algorithm.setArchive(new EpsilonBoxDominanceArchive(0.01));
algorithm.run(10000);
algorithm.getResult().display();
]]>
</pre>
</div>
</div>
<div class="section">
<a name="example4" />
<h3>Example 4: Statistical Comparison of Algorithms</h3>
<div class="files">
<ul>
<li><a href="Example4.java">Example4.java</a></li>
</ul>
</div>
<p>
Larger experiments are performed using the Executor and Analyzer. The Executor
is resonsible for configuring and running algorithms. Unlike the previous example
where we solved one problem, the Executor is useful when running multiple seeds,
multiple algorithms, or different configurations. The Analyzer performs the
statistical analysis. It can compute various performance indicators, including
hypervolume, generational distance, inverted generational distance, additive
ε-indicator, spacing and contribution. Additionally, Kruskal-Wallis and
Mann-Whitney U tests measure the statistical significance of results.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
String problem = "UF1";
String[] algorithms = { "NSGAII", "GDE3", "eMOEA" };
//setup the experiment
Executor executor = new Executor()
.withProblem(problem)
.withMaxEvaluations(10000);
Analyzer analyzer = new Analyzer()
.withProblem(problem)
.includeHypervolume()
.showStatisticalSignificance();
//run each algorithm for 50 seeds
for (String algorithm : algorithms) {
analyzer.addAll(algorithm,
executor.withAlgorithm(algorithm).runSeeds(50));
}
//print the results
analyzer.display();
]]>
</pre>
</div>
<p>
Running this script produces the output shown below. We can see that GDE3 and
NSGA-II produce the best (largest) hypervolume values. Furthermore, we have
determined statistically that there is no significant difference in
performance between GDE3 and NSGA-II.
</p>
<div class="code">
<pre class="brush: plain; toolbar: false;">
GDE3:
Hypervolume:
Min: 0.4389785065649592
Median: 0.4974186560778636
Max: 0.535166930530847
Count: 50
Indifferent: [NSGAII]
eMOEA:
Hypervolume:
Min: 0.35003766343295073
Median: 0.47633216464734596
Max: 0.53311360537305
Count: 50
Indifferent: []
NSGAII:
Hypervolume:
Min: 0.38868701091987184
Median: 0.5040946740799506
Max: 0.5371138081508796
Count: 50
Indifferent: [GDE3]
</pre>
</div>
</div>
<div class="section">
<a name="example5" />
<h3>Example 5: Collecting Runtime Dynamics</h3>
<div class="files">
<ul>
<li><a href="Example5.java">Example5.java</a></li>
</ul>
</div>
<p>
Runtime dynamics provide insight into the behavior of an optimization
algorithm throughout a run. For instance, one can observe how solution
quality changes with the number of function evaluations (NFE). The
Instrumenter class records the runtime dynamics.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
Instrumenter instrumenter = new Instrumenter()
.withProblem("UF1")
.withFrequency(100)
.attachElapsedTimeCollector()
.attachGenerationalDistanceCollector();
new Executor()
.withProblem("UF1")
.withAlgorithm("NSGAII")
.withMaxEvaluations(10000)
.withInstrumenter(instrumenter)
.run();
instrumenter.getObservations().display();
]]>
</pre>
</div>
<p>
The output from this script, shown below, shows how the generational
distance metric changes over time. We see that NSGA-II is rapidly converging
to the reference set (the optimal solutions) since its generational
distance is converging to 0.
</p>
<div class="code">
<pre class="brush: plain; toolbar: false">
NFE Elapsed Time GenerationalDistance
----- ------------ --------------------
100 0.048455 0.554547
200 0.068240 0.486866
300 0.076951 0.876918
400 0.082156 0.690796
500 0.087247 0.542534
...
9500 0.351868 0.044477
9600 0.354273 0.037876
9700 0.356552 0.038029
9800 0.358757 0.038815
9900 0.361296 0.032959
10000 0.363735 0.020477
</pre>
</div>
</div>
<div class="section">
<a name="example6" />
<h3>Example 6: Defining New Problems</h3>
<div class="files">
<ul>
<li><a href="Example6.java">Example6.java</a></li>
</ul>
</div>
<p>
While we provide many test problem suites for comparing optimization algorithms,
we can also introduce new problems. As demonstrated below, we need to define
two methods: newSolution and evaluate. The newSolution
method defines the problem representation (the number and types of its
decision variables). The evaluate method takes a solution and computes its
objective function values.
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
public class Srinivas extends AbstractProblem {
public Srinivas() {
super(2, 2, 2);
}
@Override
public void evaluate(Solution solution) {
double[] x = EncodingUtils.getReal(solution);
double f1 = Math.pow(x[0] - 2.0, 2.0) + Math.pow(x[1] - 1.0, 2.0) + 2.0;
double f2 = 9.0*x[0] - Math.pow(x[1] - 1.0, 2.0);
double c1 = Math.pow(x[0], 2.0) + Math.pow(x[1], 2.0) - 225.0;
double c2 = x[0] - 3.0*x[1] + 10.0;
// set the objective values - these are being minimized
solution.setObjective(0, f1);
solution.setObjective(1, f2);
// set the constraint values - we treat any non-zero value as a constraint violation!
solution.setConstraint(0, c1 <= 0.0 ? 0.0 : c1);
solution.setConstraint(1, c2 <= 0.0 ? 0.0 : c2);
}
@Override
public Solution newSolution() {
Solution solution = new Solution(2, 2, 2);
solution.setVariable(0, new RealVariable(-20.0, 20.0));
solution.setVariable(1, new RealVariable(-20.0, 20.0));
return solution;
}
}
]]>
</pre>
</div>
<p>
Then, we can solve this problem using:
</p>
<div class="code">
<pre class="brush: java; toolbar: false;">
<![CDATA[
Problem problem = new Srinivas();
NSGAII algorithm = new NSGAII(problem);
algorithm.run(10000);
algorithm.getResult().display();
]]>
</pre>
</div>
</div>
<div class="section">
<h3>Conclusion</h3>
<p>
In addition to the above examples, we provide many more inside the
<a href="https://github.com/MOEAFramework/MOEAFramework/tree/master/examples">examples</a> folder.
Navigate to the <a href="downloads.html">downloads</a> page to download the MOEA Framework or
visit our <a href="https://github.com/MOEAFramework/MOEAFramework">GitHub page</a> for more information.
</p>
</div>
</content>
</page>
© 2015 - 2025 Weber Informatics LLC | Privacy Policy