Diversity Loss in General Estimation of Distribution Algorithms

  • Jonathan L. Shapiro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)


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.


Probability Model Diversity Loss Distribution Algorithm Search Variable Bayesian Optimization Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jonathan L. Shapiro
    • 1
  1. 1.University of ManchesterManchesterUK

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