A Reduced Variable Neighbourhood Search for the Beam Angle Optimisation Problem

Abstract

Intensity Modulated Radiation Therapy (IMRT) is a widely used radiation therapy technique to treat cancer. The main goal in IMRT is to obtain a treatment plan that eliminates cancer cells from the tumour and, at the same time, damages as little as possible the Organs at Risk (OAR) around the tumour. To this end, we first need to seek the best possible set of beam angles, called beam angle configuration (BAC), to irradiate from. In this paper, we propose a reduced Variable Neighbourhood Search (rVNS) algorithm that explores the search space employing two different local search movements. Unlike traditional VNS algorithms, the rVNS we implement here does not need any transition rule to be implemented, as it includes both neighbourhoods moves at each iteration the rVNS we implement here does not need any transition rule to be implemented, as it includes two types of movements at each iteration. The first movement replaces each beam angle in the BAC by a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm 5^{\circ }$</tex-math></inline-formula> beam angle, while the second movement replaces each beam angle in the BAC by a randomly chosen beam angle. We try our approach We test our approach on a set of clinical prostate cases from a hospital in Chile. Results show that the rVNS produces better results than both steepest descent and next descent local search algorithms using the same neighbourhood definitions. The rVNS is showed shown to be faster than the Local Search algorithms and quite competitive w.r.t. the obtained treatment plans.