On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis

Quality evaluations in optimization processes are frequently noisy. In particular evolutionary algorithms have been shown to cope with such stochastic variations better than other optimization algorithms. So far mostly additive noise models have been assumed for the analysis. However, we will argue in this paper that this restriction must be relaxed for a large class of applied optimization problems. We suggest “systematic noise” as an alternative scenario, where the noise term is added to the objective parameters or to environmental parameters inside the fitness function. We thoroughly analyze the sphere function with systematic noise for the evolution strategy with global intermediate recombination. The progress rate formula and a measure for the efficiency of the evolutionary progress lead to a recommended ratio between μ and λ. Furthermore, analysis of the dynamics identifies limited regions of convergence dependent on the normalized noise strength and the normalized mutation strength. A residual localization error R∞ can be quantified and a second μ to λ ratio is derived by minimizing R∞.

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