In order to enhance the speed and accuracy of cluster scheduling for mobile robots in the medication management system, a cluster scheduling model is established using mobile robots as carriers. The scheduling coding adopts a discrete-continuous dual-mapping encoding method. In order to enhance the computational performance of the scheduling algorithm, an improved Harmony Search algorithm (IKHS) is proposed, which integrates the optimal estimation optimization method. The algorithm combines optimal iteration and directed search for optimal scheduling search, thereby improving the computational speed and accuracy of the algorithm. Adaptive bandwidth adjustment and global random crossover mutation are performed based on the global optimum and harmony, expanding the algorithm's search range and sample diversity, thereby enhancing the algorithm's ability to search and compute the global optimal solution. Furthermore, the improved algorithm is validated on continuous intervals using standard test functions, yielding favorable results. Through comparative experiments, it is demonstrated that, under identical test conditions, the improved algorithm in this paper exhibits superior capability in searching for optimal solutions compared to the control algorithm, resulting in varying degrees of improvement in the accuracy of scheduling results. It is evident that the improved Harmony Algorithm (IKHS) effectively optimizes the performance of the automatic medication system scheduling system.