A successive LP approach with C-VaR type constraints for IMRT optimization

Publication date: June 2018Source: Operations Research for Health Care, Volume 17Author(s): Shogo Kishimoto, Makoto YamashitaAbstractIn this paper, we propose a successive linear programming (LP) approach for an intensity-modulated radiotherapy treatment (IMRT) optimization. The use of IMRT enables to control the beam intensities accurately and gives more flexibility for cancer treatment plans, but finding a feasible plan that satisfies all dose-volume constraints (DVCs) requires expensive computation cost. Romeijn et al. (2003) replaced the DVCs with C-VaR (conditional Value-at-Risk) type constraints, and successfully reduced this computation cost. However, the feasible region of the LP problem was small compared to the original DVCs, therefore, their approach often failed to find a feasible plan even when the DVCs were not so stringent.In the proposed method, we integrate the C-VaR type constraints with a successive LP approach. Exploiting the solution of LP problems, we automatically detect outliers and remove them from the domain of the C-VaR type constraints. This reduces the sensitivity of the C-VaR type constraints to outliers, therefore, we can search feasible plans in a wider region than the C-VaR type constraints. We give a mathematical proof that if the optimal value of an LP problem in the proposed method is non-positive, the corresponding optimal solution satisfies all the DVCs. From a numerical experiment on test data sets, we observed that the proposed method f...
Source: Operations Research for Health Care - Category: Hospital Management Source Type: research