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Real-time anomaly detection of massive data streams is one of the important research topics nowadays due to the fact that the most of the world data is generated in continuous temporal processes. It addresses various problems in a lot of domains such as health, education, finance, government, etc. In this work, we propose an enhancement of this approach implemented in HW and TDHW forecasting models. The Genetic Algorithm (GA) is applied to periodically optimize HW and TDHW smoothing parameters in addition to the two sliding windows parameters that improve Hyndman's MASE measure of deviation and value of the threshold parameter that defines no anomaly confidence interval. We also propose a new optimization function based on the input training datasets with the annotated anomaly intervals to detect the right anomalies and reduce the number of false ones.