The integration of renewable energies into the electricity grid increases the importance of flexible storage systems and short-term trading. This study examines how intelligent storage management systems can be profitably integrated into short-term market and identifies suitable capacities for these operations. Using a genetic algorithm, we optimize buy and sell decisions of 15-min products in the German Continuous Intraday Market for different battery storages over the year 2021. Our results show that a storage management strategy generated by the genetic algorithm enables significant arbitrage revenues with increasing storage capacity. However, with an increasing battery size, decreasing marginal profits are to be expected. In addition, we were able to show that it is possible to generate positive revenues without the need of a storage system by utilizing intra-product price differences. The genetic algorithm we used provides an intelligent strategy for optimizing storage usage and is capable of integrating forecasts into its decision making process.