A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Abstract

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 • , 360 • ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual's fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.

Operational research techniques applied throughout cancer care services: a review

“…Jalalimanesh, Haghighi, Ahmadi, and Soltani (2017) optimise the number of fractions and dose per fraction, rather than assuming constant doses as is commonly the case. Dias, Rocha, and Ferreira (2014) address the beam angle optimisation problem, while Bertsimas, Cacchiani, Craft, and Nohadani (2013) optimise both angles and intensities jointly. The "leaf sequencing" problem is considered by Taşkin and Cevik (2013): which sequence of rectangular aperture shapes and intensities to use so that the total planned intensities are achieved.…”

“…Bertsimas et ail (2013) develop a heuristic combining simulated annealing with gradient descent to solve their linear program. On the other hand, Dias et al (2014) provide a non-linear formulation and find solutions with a genetic algorithm incorporating a neural network to estimate the fitness functions quickly. Jalalimanesh et al (2017) develop an agent-based simulation of tumour growth and use the Q-learning algorithm, a type of reinforcement learning, to optimise.…”

“…Some authors report how their methods improved solutions or computational time compared to other approaches (Aleman et al, 2014;Chan & Mišić, 2013;Dias et al, 2014;Taşkin & Cevik, 2013;Van Haveren et al, 2017). Mahmoudzadeh et al (2016) found that adding one constraint each time their problem was resolved was slowest, and it was fastest to add several constraints each time.…”

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.…”

IMRT Beam Angle Optimization Using Dynamically Dimensioned Search

“…Inverse planning applied to radiotherapy is a fruitful ground of research with several important unresolved issues, but until now most of the efforts have been devoted at solving the FMO, and comparatively fewer research effort has been directed to the BAO problem. The BAO problem has been tackled using several different methodologies like response surface approaches [1], derivative-free approaches [2], mixed integer programming approaches [3], simulated annealing [4], particle swarm optimization [5] or genetic algorithms [6]. In this paper we apply DDS algorithm to the BAO problem.…”