Learning probability distributions in continuous evolutionary algorithms – a comparative review

We present a comparative review of Evolutionary Algorithms that generate new population members by sampling a probability distributionconstructed during the optimization process. We present a unifying formulation for five such algorithms that enables us to characterize them based on the parametrization of the probability distribution, the learning methodology, and the use of historical information.The algorithms are evaluated on a number of test functions in order to assess their relative strengths and weaknesses. This comparative reviewhelps to identify areas of applicability for the algorithms and to guidefuture algorithmic developments.

[1]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[2]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[3]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[4]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[5]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[6]  Rich Caruana,et al.  Removing the Genetics from the Standard Genetic Algorithm , 1995, ICML.

[7]  Nikolaus Hansen,et al.  On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation , 1995, ICGA.

[8]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[9]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[10]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[11]  Dirk Thierens,et al.  Expanding from Discrete to Continuous Estimation of Distribution Algorithms: The IDEA , 2000, PPSN.

[12]  Kalyanmoy Deb,et al.  On self-adaptive features in real-parameter evolutionary algorithms , 2001, IEEE Trans. Evol. Comput..

[13]  David E. Goldberg,et al.  Bayesian optimization algorithm, decision graphs, and Occam's razor , 2001 .

[14]  D. Goldberg,et al.  Escaping hierarchical traps with competent genetic algorithms , 2001 .

[15]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[16]  Dirk Thierens,et al.  Advancing continuous IDEAs with mixture distributions and factorization selection metrics , 2001 .

[17]  Josef Schwarz,et al.  Estimation Distribution Algorithm for mixed continuous-discrete optimization problems , 2002 .

[18]  Pedro Larrañaga,et al.  A Review on Estimation of Distribution Algorithms , 2002, Estimation of Distribution Algorithms.

[19]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[20]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.