Solving a maximin location problem on the plane with given accuracy

Abstract

We consider the optimal placement problem in a bounded region on a plane with fixed objects. We specify minimal admissible distances between placed and fixed objects. The optimization criterion is to maximize the minimal weighted distances from placed objects to fixed ones. We propose a quasipolynomial combinatorial algorithm to solve this problem with a given accuracy. We show the results of a computational experiment with the integer programming model and the IBM ILOG CPLEX suite.