The manual scheduling of medical treatment in a health centre is a complex, time consuming, and error prone task. Furthermore, there is no guarantee a manually generated schedule maximises the operational efficiency of the centre. Scheduling problems have seen extensive research across several domains. The current work presents a novel genetic algorithm for the scheduling of repetitive Transcranial Magnetic Stimulation (rTMS) appointments. The proposed List Scheduling Wildcard Tournament Genetic Algorithm (LSWT-GA) combines an innovative survivor selection policy with heuristic population initialisation. The algorithm aims to optimise the operational efficiency of a medical centre through efficient rTMS appointment scheduling. Additionally, the algorithm has the capacity to consider patient priority. Empirical experiments were conducted to evaluate the performance of the proposed algorithm, using a synthetic data set specifically developed to simulate the medical treatment scheduling problem. The experimental results showed the LSWT-GA algorithm outperforms other algorithms, obtaining the optimal makespan more frequently than a List Scheduling Genetic Algorithm (LS-GA) using traditional survivor selection policies and a standard genetic algorithm using random population initialisation (Random-GA). In addition to the novel genetic algorithm, LSWT-GA, the paper also makes a theoretical contribution by evaluating the run time of the LSWT-GA for makespan minimisation. The proposed algorithm and related findings can be applied directly to the administration systems in medical and healthcare centres and helps improve the deployment of medical resources for better treatment effect. •A novel genetic algorithm, LSWT-GA, is presented for medical treatment scheduling.•LSWT-GA adopts survivor selection policy with heuristic population initialisation.•The evaluation of the LSWT-GA run time for makespan minimisation is promising.•An original synthetic data set is developed for medical scheduling optimisation.