5 - Inverse Fractionation

Summary

This chapter continues with the theme of tackling uncertainty in the LQ dose-response parameters within formulations of the optimal fractionation problem. However, it pursues an approach called inverse optimization, which is quite different from the earlier robust optimization methodology. Unlike in usual (forward) optimization, the goal in inverse optimization is to determine parameters of a model that would render given values of decision variables optimal. In our context, this reduces to finding parameters of the LQ dose-response model that would render a given dosing plan optimal to the fractionation problem. The chapter relies on the structure of optimal dosing plans as derived in earlier chapters to solve this inverse problem in closed-form. In fact, the chapter calculates simple formulas for all possible values of LQ parameters that would make a given dosing plan optimal. The calculation procedure is illustrated through a numerical example.