Black box maximization of circular coverage

Abstract

The principal problem co nsidered is that of determinin g which p iacem ent of n di s ks of equ al radius will cover as mu ch as poss ible of a circular a rea A . Extensive computer experimen ts wer e performed to find the optimal a rra ngem ents and to co mpare t he performances of sever al " black box" m ax imi zation methods as a pplied to t hi s problem . A second version, in which A is di vided in to s ubregions and eac h di sk is regar<ied as contributing to the coverage of on ly one subregion , is also treated. R elated mat hematical r es ults a nd questions a re discussed .