Fast and fuzzy multi-objective radiotherapy treatment plan generation for head and neck cancer patients with the lexicographic reference point method (LRPM).

Previously, we have proposed Erasmus-iCycle, an algorithm for fully automated IMRT plan generation based on prioritised (lexicographic) multi-objective optimisation with the 2-phase ϵ-constraint (2pϵc) method. For each patient, the output of Erasmus-iCycle is a clinically favourable, Pareto optimal plan. The 2pϵc method uses a list of objective functions that are consecutively optimised, following a strict, user-defined prioritisation. The novel lexicographic reference point method (LRPM) is capable of solving multi-objective problems in a single optimisation, using a fuzzy prioritisation of the objectives. Trade-offs are made globally, aiming for large favourable gains for lower prioritised objectives at the cost of only slight degradations for higher prioritised objectives, or vice versa. In this study, the LRPM is validated for 15 head and neck cancer patients receiving bilateral neck irradiation. The generated plans using the LRPM are compared with the plans resulting from the 2pϵc method. Both methods were capable of automatically generating clinically relevant treatment plans for all patients. For some patients, the LRPM allowed large favourable gains in some treatment plan objectives at the cost of only small degradations for the others. Moreover, because of the applied single optimisation instead of multiple optimisations, the LRPM reduced the average computation time from 209.2 to 9.5 min, a speed-up factor of 22 relative to the 2pϵc method.