A Restart CMA Evolution Strategy With Increasing Population Size
             Anne Auger and Nikolaus Hansen

In this paper we introduce a restart-CMA-evolution strategy, where
the population size is increased for each restart (IPOP). By
increasing the population size the search characteristic becomes
more global after each restart. The IPOP-CMA-ES is evaluated on
the test suit of 25 functions designed for the special session on
real-parameter optimization of CEC 2005.  Its performance is
compared to a local restart strategy with constant small
population size. On unimodal functions the performance is similar.
On multi-modal functions the local restart strategy significantly
outperforms IPOP in 4 test cases whereas IPOP performs
significantly better in 29 out of 60 tested cases.

ERRATA: 

End of Section 2, stopping criterion "noeffectcoord":

  "Stop if adding 0.2-standard deviation in each coordinate does
  change ..."

should be 

  "Stop if adding 0.2-standard deviation in any coordinate does
  not change ..."


The following has been pointed out by Xiao-Min Hu from the Sun
Yat-sen University: 

1) On function F4 the initial search point was chosen by
  mistake as Xup + (Xup-Xlow)*rand instead of Xlow +
  (Xup-Xlow)*rand The corrected initialization will
  presumably give better result.

2) On some function the boundary setting was omitted, but
  this has most probably no impact on the results.