Multi-Criteria Inverse Robustness in Radiotherapy Planning Using Semidefinite Programming
Jan Schröeder, Yair Censor, Philipp Süss, Karl-Heinz Küfer
TL;DR
This work reframes radiotherapy planning as a multi-criteria optimization under interval uncertainty, introducing inverse robustness to balance robustness against other objectives. By modeling uncertainty with interval matrices and relaxing the resulting QCQP to a convex SDP, it enables efficient exploration of robust Pareto fronts, with a reconstruction method to recover QCQP-feasible solutions. Clustering reduces problem size, making large-scale problems tractable, and a new Pareto-front navigation approach provides real-time feedback to decision-makers. The method is demonstrated on a liver-case, showing competitive robustness-quality trade-offs compared with established approaches and offering a practical interactive tool for clinicians.
Abstract
Radiotherapy planning naturally leads to a multi-criteria optimization problem which is subject to different sources of uncertainty. In order to find the desired treatment plan, a decision maker must balance these objectives as well as the level of robustness towards uncertainty against each other. This paper showcases a quantitative approach to do so, which combines the theoretical model with the ability to deal with practical challenges. To this end, the uncertainty, which can be expressed via the so-called dose-influence matrix, is modelled using interval matrices. We use inverse robustness to introduce an additional objective, which aims to maximize the volume of the uncertainty set. A multi-criteria approach allows to handle the uncertainty while keeping appropriate values of the other objective functions. We solve the resulting quadratically constrained quadratic optimization problem (QCQP) by first relaxing it to a convex semidefinite problem (SDP) and then reconstructing optimal solutions of the QCQP from solutions of the SDP.