A comparison of an algorithm for automated sequential beam orientation selection (Cycle) with simulated annealing.

Some time ago we developed and published a new deterministic algorithm (called Cycle) for automatic selection of beam orientations in radiotherapy. This algorithm is a plan generation process aiming at the prescribed PTV dose within hard dose and dose-volume constraints. The algorithm allows a large number of input orientations to be used and selects only the most efficient orientations, surviving the selection process. Efficiency is determined by a score function and is more or less equal to the extent of uninhibited access to the PTV for a specific beam during the selection process. In this paper we compare the capabilities of fast-simulated annealing (FSA) and Cycle for cases where local optima are supposed to be present. Five pancreas and five oesophagus cases previously treated in our institute were selected for this comparison. Plans were generated for FSA and Cycle, using the same hard dose and dose-volume constraints, and the largest possible achieved PTV doses as obtained from these algorithms were compared. The largest achieved PTV dose values were generally very similar for the two algorithms. In some cases FSA resulted in a slightly higher PTV dose than Cycle, at the cost of switching on substantially more beam orientations than Cycle. In other cases, when Cycle generated the solution with the highest PTV dose using only a limited number of non-zero weight beams, FSA seemed to have some difficulty in switching off the unfavourable directions. Cycle was faster than FSA, especially for large-dimensional feasible spaces. In conclusion, for the cases studied in this paper, we have found that despite the inherent drawback of sequential search as used by Cycle (where Cycle could probably get trapped in a local optimum), Cycle is nevertheless able to find comparable or sometimes slightly better treatment plans in comparison with FSA (which in theory finds the global optimum) especially in large-dimensional beam weight spaces.