33 lines
1.5 KiB
HTML
33 lines
1.5 KiB
HTML
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<title>Covariance Matrix Adaptation with Rank-Mu-Update</title>
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<h1 align="center">Covariance Matrix Adaptation with rank-mu update after Hansen & Kern 2004</h1>
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Implementing CMA ES with rank-mu-update and weighted recombination. This operator won the CEC 2005
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challenge employed with a restart scheme with increasing population size.
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Basically, in each generation the population is resampled around the weighted center of the
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last population using the adapted covariance matrix C. In contrast to earlier CMA versions,
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this implementation only holds one single covariance matrix for the whole population, making
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it much more memory efficient and useful for high dimensional problems as well.
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<br>
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While C is adapted based on a cumulated evolution path, the step size sigma is adapted based
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on path length control.
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Due to the repeated resampling starting from a single "center", the CMA version can
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be interpreted as a sophisticated local search, if the initial solution set is sampled
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close to an initial guess. In this case, a small initial sigma is favourable.
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<br>
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For multimodal problems, the initial population can be sampled randomly in the search space
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and the initial sigma must be rather high.
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To meet both conditions, the initial sigma may be set to half the average problem range
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or to the average distance in the initial population.
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<br>
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<p>
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* N.Hansen & S.Kern 2004: <i>Evaluating the CMA Evolution Strategy on Multimodal Test Functions.</i>
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Parallel Problem Solving from Nature 2004.
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