A column generation heuristic for VMAT planning with adaptive CVaR constraints

In this study we develop an efficient computational procedure that generates medically acceptable treatment plans for volumetric modulated arc therapy with constant gantry speed. Our proposed method is a column generation heuristic based on a mixed integer linear programming model, where the objective function contains minimization of total monitor unit of the treatment plan and dose-volume requirements are included as conditional value-at-risk constraints. Our heuristic generates a full treatment arc for the restricted master problem and calibrates the right hand side parameters of the conditional value-at-risk constraints in the first phase. In the second phase, this initial solution is improved by performing column generation. This is a fully automated procedure and produces treatment plans in a single call without any human intervention. We evaluate its performance on real prostate cancer data by comparing the quality of the generated plans with those obtained by a widely used commercial treatment planning system. Our analysis shows that the results are promising, and the generated plans satisfy the prescription restrictions and require fewer monitor units on average compared to the ones obtained using Eclipse.