A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance

The p-center location problem is concerned with determining the location of p centers in a plane/space to serve n demand points having fixed locations. The continuous absolute p-center location problem attempts to locate facilities anywhere in a space/plane with Euclidean distance. The continuous Euclidean p-center location problem seeks to locate p facilities so that the maximum Euclidean distance to a set of n demand points is minimized. A particle swarm optimization (PSO) algorithm previously advised for the solution of the absolute p-center problem on a network has been extended to solve the absolute p-center problem on space/plan with Euclidean distance. In this paper we develop a PSO algorithm for the continuous absolute p-center location problem to minimize the maximum Euclidean distance from each customer to his/her nearest facility, called “PSO-ED”. This problem is proven to be NP-hard. We tested the proposed algorithm “PSO-ED” on a set of 2D and 3D problems and compared the results with a branch and bound algorithm. The numerical experiments show that PSO-ED algorithm can solve optimally location problems with Euclidean distance including up to 1,904,711 points.

@article{Rabie2013,
  title     = {A particle swarm optimization algorithm for the continuous absolute p-center location problem with Euclidean distance},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {4},
  number    = {12},
  year      = {2013},
  publisher = {The Science and Information Organization},
  author    = {Hassan M. Rabie and Dr. Ihab A. El-Khodary and Prof. Assem A. Tharwat},
  doi       = {10.14569/IJACSA.2013.041215},
  url       = {https://doi.org/10.14569/IJACSA.2013.041215}
}