Development and evaluation of a matheuristic for the combined beam angle and dose distribution problem in radiotherapy planning

Abstract

Radiotherapy planning is vital for ensuring the maximum level of effectiveness of treatment. In the planning task, there are at least two connected decision problems that can be modelled and solved using operational research techniques: determining the best position of the radiotherapy machine (beam angle problem) and the optimal dose delivered through each beam (dose distribution problem). This paper presents a mathematical optimization model for solving the combined beam angle and dose distribution problems in the presence of multiple objectives. A matheuristic based on Tabu Search (called TSrad) is developed to solve realistic large-scale instances. The performance of the proposed method is assessed on two prostate cancer instances, namely a single computed tomography (CT) slice and a set of CT slices (three-dimensional problem). For the single-slice problem, the results of TSrad are compared to the optimal solutions obtained by an exact method. Our experiments show that TSrad is able to achieve optimality for some instances. For the multi-slice problem, our experiments show that TSrad produces viable solutions that can be attained in a reasonable computational time.

An automated bi‐level optimization approach for IMRT

“…(2005), a particle swarm algorithm is proposed to select a beam ensemble with five beams, obtained from a $$10^{\circ }$$ gantry angle spacing set. Other approaches include matheuristics based on tabu search (Obal et al., 2018), hybrid approaches (Bertsimas et al., 2013), branch and prune (Lim and Cao, 2012), neighborhood search (Aleman et al., 2008), and gradient search (Craft, 2007). In our previous works, the optimal value of the FMO function has been used to guide the highly non‐convex BAO problem, which is addressed using derivative‐free algorithms (Rocha et al., 2013a, 2013b, 2013c; Dias et al., 2014, 2015; Rocha et al., 2016, 2019; Carrasqueira et al., 2023).…”