CMA-ES with Two-Point Step-Size Adaptation

We combine a refined version of two-point step-size adaptation with the covariance matrix adaptation evolution strategy (CMA-ES). Additionally, we suggest polished formulae for the learning rate of the covariance matrix and the recombination weights. In contrast to cumulative step-size adaptation or to the 1/5-th success rule, the refined two-point adaptation (TPA) does not rely on any internal model of optimality. In contrast to conventional self-adaptation, the TPA will achieve a better target step-size in particular with large populations. The disadvantage of TPA is that it relies on two additional objective function

[1]  Ralf Salomon,et al.  Evolutionary algorithms and gradient search: similarities and differences , 1998, IEEE Trans. Evol. Comput..

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

[3]  Petros Koumoutsakos,et al.  A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion , 2009, IEEE Transactions on Evolutionary Computation.

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

[5]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

[6]  Dirk V. Arnold,et al.  Weighted multirecombination evolution strategies , 2006, Theor. Comput. Sci..

[7]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[8]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[9]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[10]  Hans-Georg Beyer,et al.  Qualms Regarding the Optimality of Cumulative Path Length Control in CSA/CMA-Evolution Strategies , 2003, Evolutionary Computation.

[11]  J. Leo van Hemmen,et al.  Accelerating backpropagation through dynamic self-adaptation , 1996, Neural Networks.