In radiation therapy treatment planning, generating a treatment plan is a multi-objective optimisation problem. The decision-making strategy is uniform for each group of cancer patients, e.g. prostate cancer, and can thus be automated. Predefined priorities and aspiration levels are assigned to each objective, and the strategy is to attain these levels in order of priority. Therefore, a straightforward lexicographic approach is sequential ϵ-constraint programming where objectives are sequentially optimised and constrained according to predefined rules, mimicking human decision-making. The clinically applied 2-phase ϵ-constraint (2pϵc) method captures this approach and generates clinically acceptable treatment plans. However, the number of optimisation problems to be solved for the 2pϵc method, and hence the computation time, scales linearly with the number of objectives. To improve the daily planning workload and to further enhance radiation therapy, it is extremely important to reduce this time. Therefore, we developed the lexicographic reference point method (LRPM), a lexicographic extension of the reference point method, for generating a treatment plan by solving a single optimisation problem. The LRPM processes multiple a priori defined reference points into modified partial achievement functions. In addition, a priori bounds on a subset of the partial trade-offs can be imposed using a weighted sum component. The LRPM was validated for 30 randomly selected prostate cancer patients. While the treatment plans generated using the LRPM were of similar clinical quality to those generated using the 2pϵc method, the LRPM decreased the average computation time from 12.4 to 1.2 minutes, a speed-up factor of 10.

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 -constraint (2pc) method. For each patient, the output of Erasmus-iCycle is a clinically favourable, Pareto optimal plan. The 2pc 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 2pc 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 2pc method.

In multi-objective optimisation problems, various conflicting objectives need to be optimised simultaneously. When dealing with similarly structured problems, automated decision making may be considered. In this case, the decision making structure needs to be formalised so that the actions of the decision maker (DM) can be replicated using a suitable algorithm. We recently developed the lexicographic reference point method (LRPM) for automated multi-objective optimisation. The LRPM is a generalisation of the reference point method, where multiple reference points are used to process the predefined lexicographic ordering of the objectives with their corresponding aspiration levels. Additionally, trade-off tuning can be implemented into the LRPM to obtain a better balanced solution. The reference points and tradeoff configuration are processed into a single optimisation problem which guarantees to generate a Pareto optimal solution. One of the applications of multi-objective optimisation where we attempt to automate the decision making is radiotherapy. For patients diagnosed with cancer and selected for radiotherapy as treatment, a CT scan is made to localise the tumour and surrounding healthy tissue. For a successful treatment, a sufficient dose has to be delivered to the tumour. Inevitably, the surrounding tissue is also exposed to the radiation. This needs to be minimised as much as possible. Typically, a treatment plan is obtained by minimising suitable treatment objectives (ranging between 10-25) towards aspiration levels in a prioritised order. Our current automated method solves a sequence of -constraint problems to find an optimal balance between tumour irradiation and tissue sparing. This strategy can be approximated using the LRPM, but then in a single optimization. The methods were tested on two sites: 30 prostate and 15 head-and-neck cancer patients. On each site, the aim is to configure the LRPM with a uniform set of input parameters, allowing fully automated treatment plan generation. For both sites, we automatically generated the treatment plans using a uniform set of input parameters for the LRPM. All plans were found clinically acceptable meaning that for each patient, the tumour irradiation was sufficient while keeping the doses on the surrounding healthy tissue at reasonable levels. The prostate plans obtained with the LRPM and with our current method were almost identical. However, the LRPM plans for the head-and-neck site frequently showed strong improvements for lower prioritised objectives at the cost of a small deterioration of higher prioritised ones. The LRPM plans were preferred clinically. The LRPM includes lexicographic ordering of the objectives and allows a flexible trade-off con- figuration, while the computation time is relatively short compared to our current method. For the prostate patients, the average runtime decreased from 34.3 to 3.0 minutes using the LRPM. The LRPM was proven suited for fully automated treatment planning for prostate cancer and head-and-neck cancer patients.