Efficient operator-splitting minimax algorithm for robust optimization

Background

The treatment uncertainties such as patient positioning can significantly affect the accuracy of proton radiation therapy (RT). Robust optimization can account for these uncertainties during treatment planning, for which the minimax approach optimizes the worst-case plan quality.

Purpose

This work will develop an efficient minimax robust optimization algorithm for improving plan quality and computational efficiency.

Methods

The proposed method reformulates the minimax problem so that it can be conveniently solved by the first-order operator-splitting algorithm (OS). That is, the reformulated problem is split into several subproblems, which either admit a closed-form solution or can be efficiently solved as a linear system.

Results

The proposed method OS was demonstrated with improved plan quality, robustness, and computational efficiency, compared to robust optimization via stochastic programming (SP) and current minimax robust method via minimax stochastic programming (MSP). For example, in a prostate case, compared to MSP and SP, OS decreased the max target dose from 140% and 121% to 118%, and the mean femoral head dose from 28.6% and 26.3% to 24.8%. In terms of robustness, OS reduced the robustness variance (RV₁₂₀) of the target from 56.07 and 0.30 to 0.04. Compared to MSP, OS decreased the computational time from 16.4 min to 1.7 min.

Conclusions

A novel operator-splitting minimax robust optimization is proposed with improved plan quality and computational efficiency, compared to conventional minimax robust optimization method MSP and probabilistic robust optimization method SP.