Calibration and Validation Optimisation

Optimisation method

The optimisation method used for the OSMOSE calibration is the "Adaptative Hierarchical Recombination - Evolutionary strategies" (AHR-ES), i.e. the default method of the package. This method is an Evolutionary algorithm which reproduces the biological evolution principles: (i) selection of the best individuals (i.e. the individuals for which the fitness is the best), (ii) recombination between the best individuals and (iii) mutation applied to the recombined parents. Contrary to traditional genetic algorithms, AHR-ES is more likely to converge to the global minimum of the objective function thanks to its "self-adaptation" which avoids a premature convergence to local minima. This supplementary process allows to make meta-parameters of the algorithm vary to improve their performance over the evolutionary process.

Functioning of the algorithm

Selection

At each generation (g), a partial fitness value (f) is calculated for each of the K components of the objective function (K=44 in this particular case). For each of these components, a selection of the µ individuals with the lowest partial fitness is done. The selected individuals represent the parents of the next generation.

First recombination

The parents are then sorted according to their partial fitness values and a weight (w) is assigned to each of them. The smaller the fitness value is, the higher the weight assigned will be. A weighted sum is then applied to the parents in order to create the recombined parent of the generation g.

Second recombination

The past of the recombined parent is then exploited by a supplementary recombination with the recombined parent of the last generation (g-1). $\alpha$ is the meta-parameter which manages the exploitation rate of the past, hence the exploratory nature of the algorithm.

Third recombination

Then, a weighted mean of all the recombined parents, i.e. for all the K components, is done to create the parental genotype. Weights (w) allow to assess the relative importance of each parameter (q) to the partial fitness (f).

Mutation

Finally, individuals of the next generation (g+1) are produced by mutating the parental genotype using a multivariate normal distribution with $\sigma_{size}$ and $C$ as parameters. The covariance matrix $CC$ and the step size control $\sigma_{size}$ are both derived from Hansen et al. (2001) and vary at each generation g.

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N. Hansen and A. Ostermeier, "Completely Derandomized Self-Adaptation in Evolution Strategies," in Evolutionary Computation, vol. 9, no. 2, pp. 159-195, June 2001, doi: 10.1162/106365601750190398. keywords: {Evolution strategy;self-adaptation;strategy parameter control;step size control;de-randomization;derandomized self-adaptation;covariance matrix adaptation;evolution path;cumulation;cumulative path length control},