Simulation and optimization of treatment schedule for multi-gantry heavy ion therapy.

Background: Carbon ion radiotherapy (CIRT) facilities face scheduling challenges due to multiple treatment rooms sharing a single synchrotron, leading to extended patient wait times and reduced efficiency. This study developed and evaluated an optimization tool for patient scheduling in multi-gantry CIRT facilities to minimize in-room patient wait time and maximize patient throughput. Methods: A simulation-optimization model was created to emulate patient flow in a facility with one fixed-beam and three gantry rooms. We developed a genetic algorithm (GA) to balance competing objectives like wait times, room utilization, and treatment priority. Its performance was evaluated against baseline scheduling and a Bayesian optimization (BO) approach, using metrics of average in-room wait time and algorithm execution speed. Robustness was tested across various scenarios, including equipment downtime. Results: The GA reduced average patient wait times by 17% (from 0.47 to 0.39 min) compared to baseline. BO performed significantly better, achieving a 92% reduction (to 0.04 min). While GA converged faster (3 min), BO required more iterations to converge, thereby taking longer (7 min), but achieving much greater reduction in average patient wait times. In 100 independent test scenarios, the BO approach significantly reduced wait times in 100% of the simulations, compared to 19% for the GA. Both algorithms maintained robust performance across diverse conditions, demonstrating their reliability. Analysis of outliers (N = 100) showed that BO significantly reduced the maximum patient wait time from 3.52 to 1.33 min (p < 0.001), minimizing clinically relevant extremes. Conclusion: This application of scheduling optimization to the unique constraints of CIRT shows potential for improving efficiency at CIRT facilities. While requiring minutes rather than seconds to converge, the BO algorithm effectively eliminates immobilized wait times, making it a powerful tool for daily schedule optimization. Future research will focus on validation with empirical data from operational CIRT centers.