Fabian Becker
b1553f3088
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41 lines
2.5 KiB
HTML
41 lines
2.5 KiB
HTML
<html>
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<title>Particle Swarm Optimization - PSO</title>
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</head>
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<body>
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<h1 align="center">Particle Swarm Optimization - PSO</h1>
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<center>
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</center><br>
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The Particle Swarm Optimization by Kennedy and Eberhardt is inspired by swarm intelligent
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behaviour seen in animals like birds or ants. A swarm of particles is a set of individual agents
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"flying" across the search space with individual velocity vectors. There is no selection as in
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classic Evolutionary Algorithms. Instead, the individuals exchange knowledge about the space they
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have come across. Each one is attracted to the best position the individual has seen so far (cognitive
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component) and to the best position known by its neighbors (social component).
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<p>
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The neighborhood is defined by the swarm velocity, which may be a linear ordering, a grid and some others.
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The influence of the velocity of the last time-step is taken into account using an inertness/
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constriction parameter, which controls the convergence behaviour of the swarm.
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</p>
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The influence of social and cognitive attraction are weighed using the <i>phi</i> parameters. In the
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constriction variant there is a dependence enforced between constriction and the phi, making sure that
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the swarm converges slowly but steadily, see the publications of M.Clerc, e.g.
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Typical values for the attractor weights are phi1=phi2=2.05.
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<p>
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The topology defines the communication structure of the swarm. In linear topology, each particle has contact
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to n others in two directions, so there is a linear overlay structure. The grid topology connects a particle
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in 4 directions, while the star variant is completely connected. The random variant just connects each
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particle to k others by random and anew in every generation cycle.
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Basically, the more connections are available, the quicker will information about good areas spread through
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the swarm and lead to quicker convergence, thereby increasing the risk of converging prematurely.
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By default, the random (e.g. with range=4) or grid structure (e.g. with range=2) are good choices.
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</p>
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<p>
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The multi-swarm approach splits the main swarm in sub-swarms defined by the distance to a local "leader",
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as in the dynamic multi-swarm approaches by Shi and Branke, for example. The tree structure orders the
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swarm to a tree of degree k, where the fittest individuals are on top and inform all their children nodes.
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In this case, the higher the degree, the quicker will information spread. HPSO is a hierarchical tree variant
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by Janson and Middendorf, 2005.
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</body>
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