Abstract
A very general class of EDAs is defined, on which universal results on the rate of diversity loss can be derived. This EDA class, denoted SML-EDA, requires two restrictions: 1) in each generation, the new probability model is build using only data sampled from the current probability model; and 2) maximum likelihood is used to set model parameters. This class is very general; it includes simple forms of many well-known EDAs, e.g. BOA, MIMIC, FDA, UMDA, etc. To study the diversity loss in SML-EDAs, the trace of the empirical covariance matrix is the proposed statistic. Two simple results are derived. Let N be the number of data vectors evaluated in each generation. It is shown that on a flat landscape, the expected value of the statistic decreases by a factor 1–1/N in each generation. This result is used to show that for the Needle problem, the algorithm will with a high probability never find the optimum unless the population size grows exponentially in the number of search variables.
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Shapiro, J.L. (2006). Diversity Loss in General Estimation of Distribution Algorithms. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_10
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DOI: https://doi.org/10.1007/11844297_10
Publisher Name: Springer, Berlin, Heidelberg
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