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The problem dealt with consists of locating a point in a given convex polyhedron which maximizes the minimum Euclidean distance from a given set of convex polyhedra representing protected areas around population points. The paper describes a finite dominating solution set for the optimal solution and develops a geometrical procedure for obtaining the optimal solution comparing a finite number of candidates.
A new and simple methodology is proposed to solve both constrained and unconstrained planar continuous single-facility location problems. As particular instances, the classical location problems with mixed gauges can be solved. Theoretical convergence is proved, and numerical examples are given, showing a fast convergence in a small number of steps.
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