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<!DOCTYPE html>
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<head>
<meta charset="utf-8" />
<title>jMetal Web site</title>
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<header id="header">
<h1 id="logo"><a href="index.html" title="index"><img src="images/jMetalLogo.png" alt="jMetal Logo" /></a></h1>
<p>
A Framework for Multi-Objective Optimization
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<a href="smpso.html" id="active">Our Techniques <span>▼</span></a>
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<article class="columms_container">
<header id="articleHeader">
<h1><strong>SMPSO</strong> Speed-constrained Multiobjective PSO</h1>
</header>
<!--<hr>-->
<aside>
<header>
</header>
<section>
<h2 class=invert>Pseudo-code</h2>
<br />
<img src="resources/smpso_code.png" alt="smpso pseudocode" class="asideImage expand">
</section>
<hr>
<section>
<h2 class=invert>Swarm explosion control in SMPSO</h2>
<br />
<p>
Behavior of a particle with OMOPSO (problem ZDT4)
</p>
<img src="resources/omopso.png" alt="omopso" class="asideImage expand">
<p>
Behavior of a particle with SMPSO (problem ZDT4)
</p>
<img src="resources/smpso.png" alt="smpso" class="asideImage expand">
</section>
</aside>
<section class="col3">
<header>
<h1>Description</h1>
</header>
<p>
<strong>SMPSO</strong> (Speed constrained Multi-objective PSO) is a metaheuristic based on the OMOPSO algorithm (<a href="references/RC05.bib">BIBTEX</a>)
that was designed to cope with difficulties of this technique when solving multi-modal problems. The SMPSO approach is to apply a <strong>constraint
velocity scheme</strong> to control the so-called <strong>swarm explosion</strong>
</p>
<header>
<h1>Main features</h1>
</header>
<ul>
<li>
Velocity constriction mechanism
</li>
<li>
External archive to store the non-dominated solutions
(leaders)
<ul>
<li>
Density estimator: crowding distance
</li>
</ul>
</li>
<li>
Leader selection: binary tournament from the leaders archive taking into account the crowding distance
</li>
<li>
Mutation (turbulence) operator: polynomial mutation
</li>
</ul>
<header>
<h1>Variants</h1>
</header>
<p>
The SMPSOhv variant, presented in CEC 2013, has the following features:</p>
<ul>
<li>
Density estimator: hypervolume contribution
</li>
<li>
Leader selection: binary tournament from the leaders archive taking into account the hypervolume contribution
</li>
</ul>
<!--
<header>
<h1>References</h1>
</header>
<ul>
<li>
A.J. Nebro, J.J. Durillo, J. García-Nieto, C.A. Coello Coello, F. Luna and E. Alba. <a href="resources/MCDM2009.pdf">SMPSO: A New PSO-based Metaheuristic for Multi-objective Optimization.</a>
IEEE Symposium on Computational Intelligence in Multicriteria Decision-Making (MCDM 2009), pp: 66-73. March 2009. <a href="references/MCDM2009.bib">BIBTEX</a>
</li>
<li>
J.J. Durillo, J. García-Nieto, A.J. Nebro, C.A. Coello Coello, F. Luna and E. Alba. <a href="resources/EMO2009a.pdf">Multi-Objective Particle Swarm Optimizers: An Experimental Comparison</a>.
5th International Conference, EMO 2009, pp: 495-509. April 2009. <a href="references/EMO2009a.bib">BIBTEX</a>
</li>
<li>
J.J. Durillo, A.J. Nebro, C.A. Coello Coello, J. García-Nieto, F. Luna, E. Alba. A Study of Multi-Objective Metaheuristics when Solving Parameter Scalable Problems.
IEEE Transactions on Evolutionary Computation. Vol. 14, No. 4 (August 2010), pp. 618-635. <a href="resources/DNC10.bib">BIBTEX</a>
<a href="http://dx.doi.org/10.1109/TEVC.2009.2034647">DOI</a>
</li>
</ul>
-->
</section>
<section class="col3">
<header>
<h1>Leader management</h1>
</header>
<img src="resources/smpso_picture.png" alt="smpso" class="asideImage">
<h2>Leader selection:</h2>
<ul>
<li>SMPSO: the particles in the archive having larger crowding distance have more chances to be choosen as a leader</li>
<li>SMPSOhv: the particles in the archive contributing the most to the hypevolume have more chances to be choosen as a leader</li>
</ul>
<h2>Leader replacement:</h2>
<ul>
<li>SMPSO: the particle in the archive having the smallest crowding distance is removed</li>
<li>SMPSOhv: the particle in the archive contributing the least to the hypevolume is removed</li>
</ul>
</section>
<section class="col1">
<header>
<h1>References</h1>
</header>
<ul>
<li>
A.J. Nebro, J.J. Durillo, J. García-Nieto, C.A. Coello Coello, F. Luna and E. Alba. <a href="resources/MCDM2009.pdf">SMPSO: A New PSO-based Metaheuristic for Multi-objective Optimization.</a>
IEEE Symposium on Computational Intelligence in Multicriteria Decision-Making (MCDM 2009), pp: 66-73. March 2009. <a href="references/MCDM2009.bib">BIBTEX</a>
</li>
<li>
J.J. Durillo, J. García-Nieto, A.J. Nebro, C.A. Coello Coello, F. Luna and E. Alba. <a href="resources/EMO2009a.pdf">Multi-Objective Particle Swarm Optimizers: An Experimental Comparison</a>.
5th International Conference, EMO 2009, pp: 495-509. April 2009. <a href="references/EMO2009a.bib">BIBTEX</a>
</li>
<li>
J.J. Durillo, A.J. Nebro, C.A. Coello Coello, J. García-Nieto, F. Luna, E. Alba. A Study of Multi-Objective Metaheuristics when Solving Parameter Scalable Problems.
IEEE Transactions on Evolutionary Computation. Vol. 14, No. 4 (August 2010), pp. 618-635. <a href="resources/DNC10.bib">BIBTEX</a>
<a href="http://dx.doi.org/10.1109/TEVC.2009.2034647">DOI</a>
</li>
<li>
A.J Nebro, J.J. Durillo, C.A. Coello Coello. Analysis of Leader Selection Strategies in a Multi-Objective Particle Swarm Optimizer.
2013 IEEE Congress on Evolutionary Computation. June 2013. <!--<a href="resources/DNC10.bib">BIBTEX</a>-->
</li>
</ul>
</section>
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