Rapidly converging solution for p-centers in nonconvex regions

Abstract

This paper aims to locate $p$ resources in a nonconvex demand plane having $n $demand points. The objective of the location problem is to find the location for these $p$ resources so that the distance from each of $n$ demand points to its nearest resource is minimized, thus simulating a $p$-center problem. We employ various geometrical structures for solving this location problem. The suggested approach is also capable of finding the optimal value of $p$ so that all demand points have at least one resource at a distance $\Delta $, where $\Delta $ is the maximum permissible distance for emergency services. Finally, an implementation of the proposed approach is presented and it is observed that the suggested approach rapidly converges towards the optimal location.