Models and Metaheuristic Algorithms for Radiotherapy Planning Problems
Cancer, Radiotherapy, Metaheuristic, Mathematical Programming
Cancer affects millions of people worldwide. Thus, the scientific community has made a great effort to find ways to diagnose, prevent, and treat cancer. Radiotherapy is one of the most widely used treatment methods. Computational methods can improve radiotherapy treatment planning. These radiotherapy plans involve two complex computational problems related to the choice of angles that must irradiate the patient and the intensity that each radiation beam must have so that cancer cells are killed and simultaneously avoid reaching regions with healthy tissue. Five mathematical programming models were used to define the intensity of the radiation beams. Two algorithms were developed to select the angles. The first is an application of the GRASP metaheuristic, and the second is the hybridization of GRASP with the VNS metaheuristic as a local search. The VNS uses mathematical programming models for each neighborhood. To compare the quality of the solutions generated, a quality indicator was proposed that aggregates metrics from the literature on evaluating radiotherapy plans. The algorithms were tested on ten liver cancer instances, collecting timing and quality information. Statistical tests were used to support the conclusions regarding the behavior of the algorithms. The tests showed that the GRASP algorithm hybridized with VNS can find better or at least equal solutions compared to the GRASP algorithm alone.