Journal of Heuristics

, Volume 7, Issue 1, pp 23–36

Simulated N-Body: New Particle Physics-Based Heuristics for a Euclidean Location-Allocation Problem

  • Rahul Simha
  • Weidong Cai
  • Valentin Spitkovsky
Article

Abstract

The general facility location problem and its variants, including most location-allocation and P-median problems, are known to be NP-hard combinatorial optimization problems. Consequently, there is now a substantial body of literature on heuristic algorithms for a variety of location problems, among which can be found several versions of the well-known simulated annealing algorithm. This paper presents an optimization paradigm that, like simulated annealing, is based on a particle physics analogy but is markedly different from simulated annealing. Two heuristics based on this paradigm are presented and compared to simulated annealing for a capacitated facility location problem on Euclidean graphs. Experimental results based on randomly generated graphs suggest that one of the heuristics outperforms simulated annealing both in cost minimization as well as execution time. The particular version of location problem considered here, a location-allocation problem, involves determining locations and associated regions for a fixed number of facilities when the region sizes are given. Intended applications of this work include location problems with congestion costs as well as graph and network partitioning problems.

facility location P-median location-allocation simulated annealing graph partitioning 

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References

  1. Appel, A.W. (1985). “An Efficient Program for Many-Body Simulation.” SIAM J. Sci. Stat. Comput. 6, 85–103.Google Scholar
  2. Batta, R. and O. Berman. (1989). “A Location Model for a Facility Operating as an M/G/k Queue.” Networks 19, 717–728.Google Scholar
  3. Berman, O. and R.C. Larson. (1982). “Optimal 2-facility Network Districting in the Presence of Queueing.” Transportation Science 19(3), 207–216.Google Scholar
  4. Berman, O. and R.R. Mandowsky (1986). “Location-Allocation on Congested Networks.” Euro. J. Oper. Res. 26(2), 238–250.Google Scholar
  5. Burkard, R.E. and R. Rendl. (1984). “A Thermodynamically Motivated Simulation Procedure for Combinatorial Optimization Problems.” Euro. J. Oper. Res. 17, 169–174.Google Scholar
  6. Choi, H.-A., B. Narahari, and R. Simha. (1997). “Algorithms for Mapping Task Graphs to a Network of Hetergeneous Workstations.” In Proc. ADCOMP 97, 1997.Google Scholar
  7. Cooper, L. (1964). “Heuristic Methods for Location-Allocation Problems.” SIAM Review 6, 37–53.Google Scholar
  8. Daskin, M.S. (1995). Network and Discrete Location: Models, Algorithms and Applications. New York: JohnWiley & Sons, Inc.Google Scholar
  9. Francis, R.L. and J.M. Goldstein. (1974). “Location Theory: A Selective Bibliography.” Operations Research 22, 400–410.Google Scholar
  10. Hockney, R.W. and J.W. Eastwood. (1981). Computer Simulation Using Particles. NY: McGraw-Hill.Google Scholar
  11. Houck, C.R., J.A. Joines, and M.G. Kay. (1996). “Comparison of Genetic Algorithms, Random Restart and Two-Opt Switching for Solving Large Location-Allocation Problems.” Computers & Operations Research 23(6),587.Google Scholar
  12. Jacobsen, S.K. (1982). “Heuristics for the Capacitated Plant Location Model.” European Journal of Operational Research 12, 253–261.Google Scholar
  13. Keeney, R.L. (1972). “A Method of Districting Among Facilities.” Operations Research 20(3), 613–618.Google Scholar
  14. Kernighan, B.W. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.” Bell Sys. Tech. J. 49, 291–307.Google Scholar
  15. Khuller, S. and Y. Sussman. (1996). “The Capacitated k-Center Problem.” Berlin: Springer-Verlag. Lecture Notes in Computer Science, Vol. 1136.Google Scholar
  16. Love, R.L., J.G. Morris, and G.O. Wesolowsky. (1988). Facilities Location: Models and Methods. Amsterdam: North-Holland.Google Scholar
  17. Maffioli, F. and G. Righini. (1994). “An Annealing Approach to Multi-Facility Location Problems in Euclidean Space.” Location Science 2(4), 205–222.Google Scholar
  18. Mirchandani, P.B. and R.L. Francis. (1990). Discrete Location Theory. New York: John Wiley & Sons, Inc.Google Scholar
  19. Rolland, E., D.A. Schilling, and J.R. Current. (1996). “An Efficient Tabu Search Procedure for the p-Median Problem.” Euro. J. Op. Res. 96, 329–342. 36 SIMHA, CAI AND SPITKOVSKYGoogle Scholar
  20. Rosing, K.E. (1991). “Towards the Solution of the (Generalized) Multi-Weber Problem.” Environment and Planning, Series B 18, 347–360.Google Scholar
  21. Sharpe, R. and B.S. Marksjo (1985). “Facility Layout Optimization Using the Metropolis Algorithm.” Environment and Planning B 12, 443–453.Google Scholar
  22. Sharpe, R., B.S. Marksjo, J.R. Mitchell, and J.R. Crawford. (1985). “An Interactive Model for the Layout of Buildings.” Applied Mathematics and Modelling 9, 207–214.Google Scholar
  23. Tansel, B.C., R.L. Francis, and T.J. Lowe. (1983). “Location on Networks: A Survey.” Management Science 29,482–511.Google Scholar
  24. Warren, M.S. and J.K. Salmon. (1992). “Astrophysical N-body Simulation Using Hierarchical Tree Data Structures.” In Proc. Supercomputing 92, 1992, pp. 570–576.Google Scholar
  25. Wilson, J.D. (1994). College Physics. NJ: Prentice-Hall, 1994.Google Scholar
  26. Wong, R.T. (1985). “Location and Network Design.” In O'Eigeartaigh et al. (eds), Combinatorial Optimization: Annotated Bibliographies. New York: John Wiley and Sons.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Rahul Simha
    • 1
  • Weidong Cai
    • 2
  • Valentin Spitkovsky
    • 3
  1. 1.Department of Computer ScienceThe George Washington UniversityWashington
  2. 2.Open System Software DivisionHewlett-PackardCupertinoUSA
  3. 3.Electrical Engg. and Computer Science Dept.Massachusetts Institute of TechnologyBostonUSA

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