Comparing variable neighbourhood search algorithms for the direct aperture optimisation in radiotherapy

Intensity modulated radiation therapy (IMRT) is a prevalent approach for administering radiation therapy in cancer treatment. The primary objective of IMRT is to devise a treatment strategy that eradicates cancer cells from the tumour while minimising damage to the surrounding organs at risk. Conventional IMRT planning entails a sequential procedure: optimising beam intensity for a certain set of angles, followed by sequencing. Unfortunately, treatment plans obtained in the optimisation stage are severely impaired after the sequencing stage due to physical and delivery constraints that are not considered during the optimisation stage. One method that tackles the issues above is the direct aperture optimisation (DAO) technique. The DAO problem seeks to generate a set of deliverable aperture configurations and a corresponding set of radiation intensities. This method accounts for physical and delivery time limitations, facilitating the creation of clinically appropriate treatment programs. In this article, we propose and compare two variable neighbourhood search (VNS) based algorithms, called variable neighbourhood descent (VND) and reduced variable neighbourhood search (rVNS). The VND algorithm is a deterministic variant of VNS that systematically explores different neighbourhood structures. This approach allows for a more thorough solution for space exploration while maintaining computational efficiency. The rVNS, unlike traditional VNS algorithms, does not require any transition rule, as it integrates a set of predefined neighbourhood moves at each iteration. We apply our proposed algorithms to prostate cancer cases, achieving highly competitive results for both algorithms. In particular, the proposed rVNS requires 62.75% fewer apertures and achieved a 63.93% reduction in beam-on time compared to the sequential approach's best case, which means treatment plans that can be delivered in less time. Additionally, we evaluate the clinical quality of the treatment plans using established dosimetric indicators, comparing our results against those produced by matRad's tool for DAO to assess target coverage and organ-at-risk sparing.