Conic formulation of fluence map optimization problems

Area of Science:

• Medical Physics
• Optimization Theory
• Computational Science

Background:

• Convexity of objectives and constraints in fluence map optimization (FMO) is well-studied.
• Conic representation, a powerful optimization characteristic, has not been explored in FMO.

Purpose of the Study:

• To introduce conic representations for FMO objectives and constraints.
• To demonstrate that FMO problems with multiple biological criteria can be solved in polynomial time.

Main Methods:

• Constructing conic representations for FMO objectives and constraints using quadratic, exponential, and power cones.
• Developing conically representable approximations for fractionation-corrected functions.
• Applying primal-dual interior-point algorithms for solving conically represented FMO problems.

Main Results:

• Most FMO objectives and constraints were successfully represented conically.
• The study demonstrated polynomial-time solvability for FMO problems with multiple biological evaluation criteria.
• Numerical results on the TROTS dataset showed stable performance for FMO problems in conic form.

Conclusions:

• Conic optimization offers a promising approach for solving complex FMO problems.
• This work establishes the potential for efficient and optimal solutions in radiation therapy planning.
• Future research in optimization algorithms may further enhance the speed and applicability of conic FMO.