In the external beam radiotherapy, it is required to optimize the number of beams, the beam angles, and the strength of irradiation, which deliver the lethal dose to the tumor while limiting the dose absorbed in the normal tissue with fewer beams. In this study, we formulate this problem as a multiobjective linear programming, and propose a planning method to balance the dose distribution and the number of beams by using satisficing trade-off method. An aspiration level to each concerning point specifies the planner's direction for each objective. Therefore, we applied cluster analysis to classify the objective functions, enabling the planner to set up aspiration levels for clusters rather than each objective, which significantly ease the planning task. An illustrated plan of a treatment for cerebral tumor is given to demonstrate the effectiveness of the proposed method.
