BBOB-benchmarking a simple estimation of distribution algorithm with cauchy distribution

The restarted estimation of distribution algorithm (EDA) with Cauchy distribution as the probabilistic model is tested on the BBOB 2009 testbed. These tests prove that when using the Cauchy distribution and suitably chosen variance enlargment factor, the algorithm is usable for broad range of fitness landscapes, which is not the case for EDA with Gaussian distribution which converges prematurely. The results of the algorithm are of mixed quality and its scaling is at least quadratic.

[1]  David E. Goldberg,et al.  Real-Coded Bayesian Optimization Algorithm: Bringing the Strength of BOA into the Continuous World , 2004, GECCO.

[2]  Marcus Gallagher,et al.  On the importance of diversity maintenance in estimation of distribution algorithms , 2005, GECCO '05.

[3]  Petr Pos ´ ik Truncation Selection and Gaussian EDA: Bounds for Sustainable Progress in High-Dimensional Spaces , 2008 .

[4]  Petr Pošı́k Gaussian EDA and Truncation Selection : Setting Limits for Sustainable Progress , 2008 .

[5]  Petros Koumoutsakos,et al.  A Mixed Bayesian Optimization Algorithm with Variance Adaptation , 2004, PPSN.

[6]  Petr Pos ´ ik Preventing Premature Convergence in a Simple EDA Via Global Step Size Setting , 2008 .

[7]  Franz Rothlauf,et al.  SDR: a better trigger for adaptive variance scaling in normal EDAs , 2007, GECCO '07.

[8]  Bo Yuan,et al.  A Mathematical Modelling Technique for the Analysis of the Dynamics of a Simple Continuous EDA , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[9]  Franz Rothlauf,et al.  The correlation-triggered adaptive variance scaling IDEA , 2006, GECCO.

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

[11]  Pedro Larrañaga,et al.  Mathematical modelling of UMDAc algorithm with tournament selection. Behaviour on linear and quadratic functions , 2002, Int. J. Approx. Reason..

[12]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[13]  Jörn Grahl,et al.  Behaviour of UMDAc algorithm with truncation selection on monotonous functions , 2005 .

[14]  Raymond Ros,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Experimental Setup , 2009 .

[15]  Anne Auger,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions , 2009 .