<p>This study addresses the dynamic outpatient sequencing (DPS) problem on a single medical examination equipment considering late arrivals to reduce the weighted waiting time of outpatients. Our DPS problem distinguishes punctual patients and late patients by giving them different weights of waiting time to favor the on-time arrivals. To handle this problem, we propose a genetic programming (GP) algorithm combined with feature selection and niching technique to tackle the stochastic factors such as outpatient tardiness and examination duration. The feature selection helps to improve the learning performance and the interpretability of the generated dispatching rule. The niching technique is able to maintain a good population diversity to prevent the search premature convergence. Our GP algorithm generates a combined dispatching rule (CDR-GP) that dynamically selects the next outpatient to take examination based on an integrated measure of the number of examination items, late arrival time, waiting time and appointment time. We generate different scenarios to simulate patient tardiness and medical examination resource availability and compare CDR-GP with widely used dispatching rules. The experimental results demonstrate that CDR-GP consistently outperforms all benchmark methods, achieving improvements ranging from 0.04% to 50.69% across all scenarios. Moreover, a case study conducted at a 3A hospital in China reveals that, under comparable parameter conditions, CDR-GP reduces outpatient waiting times by 38.20% compared to real-world practices.</p>