Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy

We generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible. In multiobjective linear optimization, given a solution that is not a weakly efficient solution to the forward problem, our method generates objective function weights that make the given solution a near-weakly efficient solution. Our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem. We provide a novel interpretation of our inverse formulation as the dual of the well-known Benson's method and by doing so develop a new connection between inverse optimization and Pareto surface approximation techniques. We apply our method to prostate cancer data obtained from Princess Margaret Cancer Centre in Toronto, Canada. We demonstrate that clinically acceptable treatments can be generated using a small number of objective functions and inversely optimized weights—current treatments are designed using a complex formulation with a large parameter space in a trial-and-error reoptimization process. We also show that our method can identify objective functions that are most influential in treatment plan optimization.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada [Grant #385972-2010]