Decomposition and Metaoptimization of Mutation Operator in Differential Evolution

Metaoptimization is a way of tuning parameters of an optimization algorithm with use of a higher-level optimizer. In this paper it is applied to the problem of choosing among possible mutation range adaptation schemes in Differential Evolution (DE). We consider a new version of DE, called DE/rand/∞. In this algorithm, differential mutation is replaced by a Gaussian one, where the covariance matrix is determined from the contents of the current population. We exploit this property to separate the adaption of search directions from the adaptation of mutation range. The former is characterized by a norm of the covariance matrix while the latter can be expressed as a normed covariance matrix multiplied by the scaling factor. Such separation allows us to introduce a few schemes of direct, explicit control of the mutation range and to compare them with the basic, implicit scheme present in DE/rand/∞. To ensure fair comparisons all versions of DE/rand/∞ are first metaoptimized and then assessed on the CEC’05 benchmark.