Dose–volume objectives in multi-criteria optimization

Unlike conventional optimization with dose-volume (DV) constraints, multi-criteria optimization (MCO) with DV objectives provides tradeoff information which we believe is necessary for choosing better treatment plans. We show that the MCO formulation with DV objectives is better suited to convex approximation than conventional formulations with DV constraints. We provide a relaxation of the integer programming formulation which reduces the computation time for a single plan from over 5 h to about 2 min, without significantly compromising the results. We also derive a heuristic to improve on the relaxed solutions, adding only a few additional minutes of computation time. We apply these techniques to a skull based tumour case and a paraspinal tumour case. Based on a careful examination of the driving terms in the relaxed formulation and the heuristic, we argue that our techniques should apply more generally for DV objectives in multi-objective IMRT treatment planning.