Variable Metrics in Evolutionary Computation
Nikolaus Hansen · 2009
This thesis considers variable metrics in the context of stochastic, function-value free optimization in continuous search spaces. We argue that the choice of a (variable) metric or equivalently the choice of a coordinate system can be decoupled from the underlying optimization procedure. An adaptive encoding procedure is presented, that is in principle applicable to any optimization procedure, and is proved to recover the covariance matrix adaptation evolution strategy (CMA-ES) when applied to a simple isotropic evolution strategy with step-size adaptation. The proof suggests that adaptive encoding should be able to improve the performance of many stochastic optimization algorithms in particular on ill-conditioned, non-separable objective functions.