A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning

Abstract

Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated.

Directional Emission from Photonic Crystal Waveguide Output by Terminating with CROW and Employing the PSO Algorithm

“…ω is the inertial weight, a constant acting as the inertia of the particle, which determines that how the velocity of particles in (k+1) th iteration are affected by the velocities in k th iteration. The inertial weight improves the performance of the PSO algorithm [41,49]. As the iteration count increases, each particle in the swarm will progressively be guided to the position where the fitness function has its desired value.…”

“…One of the powerful algorithms that can be employed for optimization of the multidimensional problems of this kind, especially in the domain of computational electromagnetism, is the particle swarm optimization (PSO) method [37][38][39][40][41][42][43][44][45][46][47]. Recently, some different PC structures have been optimized by using the PSO algorithm to evaluate a fitness function [48,49].…”

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

“…In most of the previous works on BAO, the entire range, [0 • , 360 • ] in the coplanar case, of gantry angles is discretized into equally spaced beam directions with a given angle increment, such as 5 or 10 degrees, where exhaustive searches are performed directly or guided by a variety of different heuristics including simulated annealing [7], genetic algorithms [19], particle swarm optimization [24] or other heuristics incorporating a priori knowledge of the problem [20]. Although those global heuristics can theoretically avoid local optima, globally optimal or even clinically better solutions cannot be obtained without a large number of objective function evaluations.…”

IMRT Beam Angle Optimization Using Non-descent Pattern Search Methods

“…1. In most of the previous works on BAO, the entire range [0 • , 360 • ] of gantry angles is discretized into equally spaced beam directions with a given angle increment, such as 5 or 10 degrees, where exhaustive searches are performed directly or guided by a variety of different heuristics including simulated annealing [3], genetic algorithms [10], particle swarm optimization [12] or other heuristics incorporating a priori knowledge of the problem [15]. Although those global heuristics can theoretically avoid local optima, globally optimal or even clinically better solutions can not be obtained without a large number of objective function evaluations.…”