Mathematical Models and Nonlinear Optimization in Continuous Maximum Coverage Location Problem

This paper considers the maximum coverage location problem (MCLP) in a continuous formulation. It is assumed that domain and family of geometric objects arbitrary shape are specified. necessary to find such cover greatest possible amount domain. A mathematical model MCLP proposed form an unconstrained nonlinear optimization problem. Python computational geometry packages were used calculate area partial Many experiments carried out which made it describe statistical dependence calculation time on number covering objects. To obtain local solution, BFGS method with first-order differences was used. An approach numerical estimation objective function gradient proposed, significantly reduces costs, confirmed experimentally. The shown solve rectangular by ellipses.