Evolution Strategies (ES) are a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection. Gaussian mutation captures pair-wise dependencies between the variables through a covariance matrix. Covariance Matrix Adaptation (CMA) is a method to update this covariance matrix. In this paper, the CMA-ES, which has found many applications in solving continuous optimizatio...

The cloud computing is considered as a computational model which provides the uses requests with resources upon any demand and needs.The need for planning the scheduling of the user's jobs has emerged as an important challenge in the field of cloud computing. It is mainly due to several reasons, including ever-increasing advancements of information technology and an increase of applications and...

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a popular method to deal with nonconvex and/or stochastic optimization problems when the gradient information is not available. Being based on the CMA-ES, the recently proposed Matrix Adaptation Evolution Strategy (MA-ES) provides a rather surprising result that the covariance matrix and all associated operations (e.g., potentially...

In this paper, we propose an efficient approximated rank one update for covariance matrix adaptation evolution strategy (CMA-ES). It makes use of two evolution paths as simple as that of CMA-ES, while avoiding the computational matrix decomposition. We analyze the algorithms’ properties and behaviors. We experimentally study the proposed algorithm’s performances. It generally outperforms or per...

We combine a refined version of two-point step-size adaptation with the covariance matrix adaptation evolution strategy (CMA-ES). Additionally, we suggest polished formulae for the learning rate of the covariance matrix and the recombination weights. In contrast to cumulative step-size adaptation or to the 1/5-th success rule, the refined two-point adaptation (TPA) does not rely on any internal...

The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) combines a mutation operator that adapts its search distribution to the underlying optimization problem with multicriteria selection. Here, a generational and two steady-state selection schemes for the MO-CMA-ES are compared. Further, a recently proposed method for computationally efficient adaptation of the search ...

The covariance matrix adaptation evolution strategy (CMA-ES) rates among the most successful evolutionary algorithms for continuous parameter optimization. Nevertheless, it is plagued with some drawbacks like the complexity of the adaptation process and the reliance on a number of sophisticatedly constructed strategy parameter formulae for which no or little theoretical substantiation is availa...

This report proposes a simple modification of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for high dimensional objective functions, that reduces the internal time and space complexity from quadratic to linear. The covariance matrix is constrained to be diagonal and the resulting algorithm, sep-CMA-ES, samples each coordinate independently. Because the model complexity is reduce...

The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) is a variable-metric algorithm for real-valued vector optimization. It maintains a parent population of candidate solutions, which are varied by additive, zero-mean Gaussian mutations. Each individual learns its own covariance matrix for the mutation distribution considering only its parent and offspring. However, t...

The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a nonelitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist CovarianceMatrix Adaptation Evolution Strategy (CMA-ES). In the original CMA...