## 2 Materials and Methods
### Personalized Planning and Feasibility Module  
All plans were generated with the personalized planning engine in the Pinnacle3 Evolution (v. 16.4.3) TPS for an Elekta VersaHD LINAC (Elekta Ltd., Crawley, UK) equipped with the high-definition Agility multilevel collimator (160 leaves with 0.5 cm length at isocenter). Personalized planning is the evolution of the previous \"autoplanning\" module, incorporating advanced optimization algorithms [26]: the Broyden-Fletcher-Goldfarb and the Layered Graph algorithms. From a mathematical point of view, this new optimization strategy is highly different from the previous autoplanning module, in which the initial guess proceeded to iteratively modify the parameters for each MLC aperture via a customized gradient formulation to determine an updated configuration, which represents an improvement of the optimization goal in a \"local approach\" setting. In contrast to the autoplanning module, which appeared as a \"black-box\" fully integrated optimizer, the new optimization module is built with a transparent architecture, allowing the planner to modify all the functions involved in the optimization process. In addition, the personalized planning engine in Pinnacle Evolution integrates the feasibility module, a model-based calculation engine [27] that uses the patient CT images, the prescription doses, and the geometric relationship between PTVs and OARs to create the so-called feasibility DVH (fDVH) for each involved OAR; at the end of the calculation, it provides the best-case scenario dose distribution for each treatment planning goal. A comprehensive mathematical description of the feasibility calculation module has been reported in [17]. Briefly, the feasibility is based on a three-step process, as already reported in [23]: (1) The tool loads the planning CT scan with the contouring as input parameters, together with the prescription dose levels for the targets and fundamental calculation variables (such as beam energy and dose grid spatial resolution). (2) A reference dose distribution is calculated assuming 100% coverage of each target with 100% of the prescribed dose (i.e., each voxel inside the PTV volume receives at least the prescribed dose). (3) It estimates the minimal dose received by any voxel outside the targets. For this calculation, an energy-specific high gradient dose spread (HGDS) kernel is used under the assumption that the entire PTV is receiving the prescription dose. Then, two low-dose spread (LDS) kernels are used to convolve the original dose distribution, obtaining two low-dose grids to estimate a minimal dose that must occur at any given voxel outside the targets. Finally, the reference dose is obtained by assigning each voxel the highest value from each calculated grid. The module generates an fDVH \"space\" [28] for each investigated OAR by computing a feasibility level (f), ranging between 0 (unachievable goal) and 1 (easily achievable goal). The ideal plan corresponds to a curve where all the DVH points have f = 0, providing optimal coverage and the best OAR sparing (unachievable by design). The feasibility \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Site** & **OAR** & \begin{tabular}{c} **Overlapping** \\ **Target** \\ \end{tabular} & \
\begin{tabular}{c} **Overlapping** \\ **Volume (\%)** \\ \end{tabular} &
\begin{tabular}{c} **Total Overlap** \\ **Volume (\%)** \\ \end{tabular} \\ \hline PCa & Bladder & PTV56\(\rightarrow\)PTV68 & 1.869 & 17.636 \\  & Bladder & PTV68 & 15.818 & 17.636 \\  & Rectum & PTV56\(\rightarrow\)PTV68 & 0.572 & 8.943 \\  & Rectum & PTV68 & 8.371 & 8.943 \\ \hline HNCa & Larynx & PTV56-PTV63 & 8.349 & 9.085 \\  & Larynx & PTV63-PTV70 & 0.736 & 9.085 \\  & Mandible & PTV56-PTV63 & 2.632 & 28.625 \\  & Mandible & PTV63-PTV70 & 11.595 & 28.625 \\  & Mandible & PTV70 & 14.398 & 28.625 \\  & Rt Parotid & PTV56-PTV63 & 14.005 & 14.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The total overlapping volume of each OAR and the overlapping volume of each OAR and target for each site.