Robust optimization for temporally feathered radiation therapy under radiobiological uncertainty
A robust scheduling model for head-and-neck radiation therapy that stays feasible when the biology is only known within an interval.
14.6%
price of robustness
35
fractions scheduled
5
organs at risk
3.2%
gain from two-stage adaptive
Problem
Temporally feathered radiation therapy (TFRT) cycles organ-sparing subplans across 35 daily fractions so each organ at risk gets recovery windows. The schedule depends on radiobiological parameters (the linear-quadratic α and β), but those come from population studies and vary from patient to patient. A plan tuned to nominal values can be wrong for the person in front of you.
Approach
The model treats each organ's (α, β) as an uncertain point inside a polyhedral set (a box intersected with α/β ratio bounds) and minimizes worst-case cell kill. Two structural results keep it tractable: under one subplan per fraction the quadratic dose term linearizes exactly, and LP duality collapses the robust counterpart into a single MILP of polynomial size. A Bertsimas-Sim budget adds one knob from nominal to fully robust, with windowed and two-stage adaptive variants on top.
Outcome
On a five-organ, five-subplan, thirty-five-fraction head-and-neck instance solved with Pyomo and Gurobi, the price of robustness was 14.6%. Strong duality was verified against direct vertex enumeration to solver tolerance, and a two-stage adaptive variant recovered 3.2% from a single mid-course re-imaging.