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New portable consumer embedded devices must execute multimedia applications (e.g., 3D games, video players and signal processing software, etc.) that demand extensive memory accesses and memory usage at a low energy consumption. Moreover, they must heavily rely on Dynamic Memory (DM) due to the unpredictability of the input data and system behavior. Within this context, consistent design methodologies that can tackle effciently the complex DM behavior of these multimedia applications are in great need. In this article, we present a novel design framework, based on genetic programming, which allows us to design custom DM management mechanisms, optimizing memory accesses, memory use and energy consumption for the target embedded system. First, we describe the large design space of DM management decisions for multimedia embedded applications. Then, we propose a suitable way to traverse this design space using grammatical evolution and construct custom DM managers that minimize the DM used by these highly dynamic applications. As a result, our methodology achieves significant improvements in memory accesses (23% less on average), memory usage (38% less on average) and energy consumption (reductions of 21% on average) in real case studies over the current state-of-the-art DM managers used for these types of dynamic applications. To the best of our knowledge, this is the first approach to efficiently design DM managers for embedded systems using evolutionary computation and grammar evolution.