A lexicographic optimiser for fully automated multi-objective optimisation in radiotherapy

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.