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In this paper, a novel particle swarm optimization (PSO) algorithm is proposed in order to improve the accuracy of traditional clustering approaches with applications in analyzing real-time patient attendance data from an accident & emergency (A&E) department in a local U.K. hospital. In the proposed randomly occurring distributedly delayed PSO (RODDPSO) algorithm, the evolutionary state is determined by evaluating the evolutionary factor in each iteration, based on whether the velocity updating model switches from one mode to another. With the purpose of reducing the possibility of getting trapped in the local optima and also expanding the search space, randomly occurring time-delays that reflect the history of previous personal best and global best particles are introduced in the velocity updating model in a distributed manner. Eight well-known benchmark functions are employed to evaluate the proposed RODDPSO algorithm which is shown via extensive comparisons to outperform some currently popular PSO algorithms. To further illustrate the application potential, the RODDPSO algorithm is successfully exploited in the patient clustering problem for data analysis with respect to a local A&E department in West London. Experiment results demonstrate that the RODDPSO-based clustering method is superior over two other well-known clustering algorithms. [ABSTRACT FROM AUTHOR]