Using An Open Source Interior Point Optimization Solver for Intensity Modulated Radiotherapy Treatment Planning
P Tiwari1*, Y Chen2, Y Xie3, J Deasy4, (1) Washington University in Saint Louis, Saint Louis, Missouri, (2) Washington University in Saint Louis, Saint Louis, Missouri, (3) Washington University in Saint Louis, Saint Louis, Missouri, (4) Memorial Sloan Kettering Cancer Center, New York, NYSU-E-T-640 Sunday 3:00PM - 6:00PM Room: Exhibit Hall
To support IMRT research, we developed an open-source, computationally efficient, and flexible optimization solver that can solve a wide range of problem formulations, including constrained optimization, convex and non-convex polynomial functions, and hierarchical optimization formulations.
The solver is an adaptation and modification of the open-source Interior Point Optimization Solver (IPOPT), with some performance enhancements. Previously, we implemented the IMRT optimization based on the commercial Mosek solver. Mosek can solve convex linear and quadratic problems but cannot solve convex or non-convex polynomials of higher orders. This limits the ability to model IMRT optimization using more appropriate metrics like gEUD. Therefore, we implemented the optimization problem using C++ interface of IPOPT. IPOPT can use the Newton or Quasi-Newton method to solve the optimization problem. In the Newton method, the exact Hessian matrix provided by the user is used to find the direction in each iteration while in the Quasi-Newton method the Hessian matrix is approximated from the Jacobian matrix. After integrating IPOPT with CERR, we found that the Newton method converges more quickly than the Quasi-Newton method. To increase the computational efficiency, we incorporated the uBLAS matrix library.
Few compared the modified IPOPT code to Mosek for a set of convex quadratic problems using realistic, anonymized treatment planning data and dose data accessed using CERR. These problems have a unique global minimum and both solvers were observed to give the same results for eight head and neck planning datasets. The median speedup of IPOPT compared to Mosek was a factor of 3.5.
Our IPOPT implementation provides an open-source framework to model the IMRT optimization using complex objective functions; is integrated with CERR; and our C++ implementation of the optimization problem gives increased control over the optimization process. This tool provides a basis for future IMRT treatment planning research.
Funding Support, Disclosures, and Conflict of Interest: Memorial Sloan-Kettering Cancer Center