Proton therapy with continuous scanning is a radiotherapy technique for cancer treatment that is faster than the conventional discrete scanning approach, as the beam remains on while moving between spots. Since the beam deposits additional, unplanned dose to the tissue during this movement, the goal is to minimize the beam's cumulative travel time across all spots. Algorithms for the travelling salesman problem, which is closely related to our problem, are well optimized but too slow. In the search for a faster algorithm, we exploit the specific geometric structure of spot placements in two-dimensional layers and also accept suboptimal solutions. We analyze optimal solutions for selected layers as well as theoretically and experimentally evaluate several scan path optimization methods: default serpentine method, greedy methods, simulated annealing, and clustering-based methods. The best results are produced by a combined method, which first clusters spots along the faster axis and then connects the clusters using simulated annealing. This combination returns solutions within a fraction of a second that are only a few percentage points worse than the optimum. While discussing the results, we also highlight practical considerations in scan path optimization and suggest ideas for future work.
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