High utility itemsets (HUIs) are items in the dynamically streaming transaction list that generate a high‐profit margin. Many of the real‐time applications depend on finding HUIs from the transaction list. However, HUI mining is time‐consuming and results in high complexity due to memory requirements, a large search space, and the cost of HUI estimation. To overcome these issues we have proposed a novel High Median Utility Itemset Mining (HMUIM) approach. This approach utilizes the HMUI‐Miner which effectively ignores the unnecessary itemsets, that is, items with less profit, and mines the HUIs from the database. Furthermore, it has the limitation of deleting the transaction list based on the sliding window size used while conducting a dynamic streaming dataset. To tackle this issue we proposed a novel Modified Heap‐based Optimizer (MHBO) algorithm which effectively copies the HUIs transaction list and preserves it for further process. The MHBO is the combination of Heap Based Optimizer and nine fuzzy rules. The fuzzy rules are used to analyze the priority of the transaction list and based on that it ignores the transaction list with low priorities. Experimental analysis is performed for the proposed method on the real‐time dataset and compared with HUI and HAUIM approaches. The proposed method reduces the execution time and memory usage based on the minimum threshold. Meanwhile, the proposed MHBO approach is compared with iMEFIM, REX, and FCHUIM state‐of‐art works based on the sliding window concept. The execution time to store the replicated copies of original data is less for our proposed method.