A two-phase method for selecting IMRT treatment beam angles: Branch-and-Prune and local neighborhood search

A Global Score-Driven Beam Angle Optimization in IMRT

“…In a first class, BAO is formulated as a combinatorial optimization problem, considering a discrete sample of all continuous beam angle directions. Since exhaustive searches are not feasible in terms of computational time, many different algorithms have been proposed, including gradient search [10], neighborhood search [2], simulated annealing [14], genetic algorithms [13], branch-and-prune [16], hybrid approaches [6] or iterative BAO [9]. Regardless of the algorithm used, it is not possible to calculate, in a polynomial run time, the optimal solution of the combinatorial BAO problem (NP hard problem) [4].…”

Noncoplanar beam angle optimization in IMRT treatment planning using pattern search methods

“…Aleman et al [4] propose a response surface approach and include noncoplanar angles in beam orientation optimization. Lim and Cao [25] propose an approach that consists of two sequential phases: branch-and-prune and local neighborhood search. Schreibmann et al [34] propose a hybrid multiobjective evolutionary optimization algorithm for IMRT treatment planning and apply it to the optimization of the number of incident beams, their orientations and intensity profiles.…”

Comparison of Combinatorial and Continuous Frameworks for the Beam Angle Optimization Problem in IMRT

“…This formulation leads to a NP-hard optimization problem [3]. A large number of different algorithms have been used to speed up the searches, including gradient search [8], neighborhood search [1], simulated annealing [10], response surface approaches [2], branch-and-prune [12] or hybrid approaches [5]. Iterative BAO is a successful combinatorial strategy used in practice that adds one beam at a time, sequentially, to a treatment plan, reducing the total number of possible combinations significantly [3].…”