Local-meta-model CMA-ES for partially separable functions

In this paper, we propose a new variant of the covariance matrix adaptation evolution strategy with local meta-models (lmm-CMA) for optimizing partially separable functions. We propose to exploit partial separability by building at each iteration a meta-model for each element function (or sub-function) using a full quadratic local model. After introducing the approach we present some first experiments using element functions with dimensions 2 and 4. Our results demonstrate that, as expected, exploiting partial separability leads to an important speedup compared to the standard CMA-ES. We show on the tested functions that the speedup increases with increasing dimensions for a fixed dimension of the element function. On the standard Rosenbrock function the maximum speedup of λ is reached in dimension 40 using element functions of dimension 2. We show also that higher speedups can be achieved by increasing the population size. The choice of the number of points used to build the meta-model is also described and the computational cost is discussed.