J Heuristics https://doi.org/10.1007/s10732-018-9365-1 Pareto local search algorithms for the multi-objective beam angle optimisation problem Guillermo Cabrera-Guerrero 1,2 · Andrew J. Mason 2 · Andrea Raith 2 · Matthias Ehrgott 3 Received: 5 October 2016 / Revised: 17 September 2017 / Accepted: 19 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Due to inherent trade-offs between tumour control and sparing of organs at risk, optimisation problems arising in intensity modulated radiation therapy planning are naturally modelled as multi-objective optimisation problems. Nevertheless, the vast majority of studies in the literature consider single objective approaches to these problems. The beam angle optimisation problem, that we address ion this paper, is one of these problems. It attempts to identify “good” beam angle configurations that allow the delivery of efficient treatment plans. In this paper two bi-objective local search algorithms are developed for the bi-objective beam angle optimisation prob- lem, namely Pareto local search (PLS) and a variation of PLS we call adaptive PLS (aPLS). Both algorithms are able to find a set of (approximately) efficient beam angle configurations. While the PLS algorithm aims to find a set of efficient BACs by per- forming a very focused search over a specific region of the objective space, the aPLS algorithm aims to produce a set of efficient BACs that are well-distributed over the B Guillermo Cabrera-Guerrero guillermo.cabrera@ucv.cl Andrew J. Mason a.mason@auckland.ac.nz Andrea Raith a.raith@auckland.ac.nz Matthias Ehrgott m.ehrgott@lancaster.ac.uk 1 Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Valparaiso, Chile 2 Department of Engineering Science, University of Auckland, Auckland, New Zealand 3 Department of Management Science, Lancaster University Management School, Lancaster, UK 123