1769 A Restart CMA Evolution Strategy With Increasing Population Size Anne Auger Nikolaus Hansen CoLab Computational Laboratory, CSE Lab, ETH Zurich, Switzerland ETH Zurich, Switzerland
[email protected] [email protected] Abstract- In this paper we introduce a restart-CMA- 2 The restart CMA-ES evolution strategy, where the population size is increased for each restart (IPOP). By increasing the population The (,uw, )-CMA-ES In this paper we use the (,uw, )- size the search characteristic becomes more global af- CMA-ES thoroughly described in [3]. We sum up the gen- ter each restart. The IPOP-CMA-ES is evaluated on the eral principle of the algorithm in the following and refer to test suit of 25 functions designed for the special session [3] for the details. on real-parameter optimization of CEC 2005. Its perfor- For generation g + 1, offspring are sampled indepen- mance is compared to a local restart strategy with con- dently according to a multi-variate normal distribution stant small population size. On unimodal functions the ) fork=1,... performance is similar. On multi-modal functions the -(9+1) A-()(K ( (9))2C(g)) local restart strategy significantly outperforms IPOP in where denotes a normally distributed random 4 test cases whereas IPOP performs significantly better N(mr, C) in 29 out of 60 tested cases. vector with mean m' and covariance matrix C. The , best offspring are recombined into the new mean value (Y)(0+1) = Z wix(-+w), where the positive weights 1 Introduction w E JR sum to one. The equations for updating the re- The Covariance Matrix Adaptation Evolution Strategy maining parameters of the normal distribution are given in (CMA-ES) [5, 7, 4] is an evolution strategy that adapts [3]: Eqs.