A new penalty/stochastic approach to an application of the covering problem: The gamma knife treatment
RAIRO. Operations Research, Tome 55 (2021), pp. S787-S810

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.

DOI : 10.1051/ro/2020016
Classification : 90C90, 52C17, 90C26, 90C27
Keywords: Covering problem, global optimization, Gamma Knife radiosurgery 
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     title = {A new penalty/stochastic approach to an application of the covering problem: {The} gamma knife treatment},
     journal = {RAIRO. Operations Research},
     pages = {S787--S810},
     year = {2021},
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Venceslau, Marilis Bahr Karam; Venceslau, Helder Manoel; Pinto, Renan Vicente; Dias, Gustavo; Maculan, Nelson. A new penalty/stochastic approach to an application of the covering problem: The gamma knife treatment. RAIRO. Operations Research, Tome 55 (2021), pp. S787-S810. doi: 10.1051/ro/2020016

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