Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S787 - S810|
|Published online||02 March 2021|
A new penalty/stochastic approach to an application of the covering problem: The gamma knife treatment
COPPE – PESC, Federal University of Rio de Janeiro, Cidade Universitária, Centro de Tecnologia, Bloco H, 21941-972 Rio de Janeiro, RJ, Brazil.
2 Colégio Pedro II, Campo de São Cristóvão, 177, São Cristóvão, 20921-903 Rio de Janeiro, RJ, Brazil.
3 CEFET/RJ – Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Av. Maracanã, 229, Maracanã, 20271-110 Rio de Janeiro, RJ, Brazil.
4 Universidade Federal Rural do Rio de Janeiro, BR-465, Km 7, 23897-000 Seropédica, RJ, Brazil.
5 LIX, École Polytechnique, 91128 Palaiseau, France.
Accepted: 19 February 2020
The covering problem of a three dimensional body using different radii spheres is considered. The motivating application – the treatment planning of Gamma Knife radiosurgery – is briefly discussed. We approach the problem only by the geometric covering point of view, that is, given a set of spheres and a body, the objective is to cover the body using the smallest possible number of spheres, regardless of the dosage issue. In order to solve this mathematical programming problem, we consider an approach based on the application of penalty and stochastic local search techniques. Finally, some illustrative results and comparisons are presented.
Mathematics Subject Classification: 90C90 / 52C17 / 90C26 / 90C27
Key words: Covering problem / global optimization / Gamma Knife radiosurgery
© EDP Sciences, ROADEF, SMAI 2021
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