Simulated N-Body: New Particle Physics-Based Heuristics for a Euclidean Location-Allocation Problem Article DOI:
Cite this article as: Simha, R., Cai, W. & Spitkovsky, V. Journal of Heuristics (2001) 7: 23. doi:10.1023/A:1026561511574 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 References
Appel, A.W. (1985). “An Efficient Program for Many-Body Simulation.”
SIAM J. Sci. Stat. Comput.
Batta, R. and O. Berman. (1989). “A Location Model for a Facility Operating as an M/G/k Queue.”
Berman, O. and R.C. Larson. (1982). “Optimal 2-facility Network Districting in the Presence of Queueing.”
Berman, O. and R.R. Mandowsky (1986). “Location-Allocation on Congested Networks.”
Euro. J. Oper. Res
. 26(2), 238–250.
Burkard, R.E. and R. Rendl. (1984). “A Thermodynamically Motivated Simulation Procedure for Combinatorial Optimization Problems.”
Euro. J. Oper. Res
. 17, 169–174.
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.
Cooper, L. (1964). “Heuristic Methods for Location-Allocation Problems.”
Daskin, M.S. (1995).
Network and Discrete Location: Models, Algorithms and Applications
. New York: JohnWiley & Sons, Inc.
Francis, R.L. and J.M. Goldstein. (1974). “Location Theory: A Selective Bibliography.”
Hockney, R.W. and J.W. Eastwood. (1981).
Computer Simulation Using Particles
. NY: McGraw-Hill.
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
Jacobsen, S.K. (1982). “Heuristics for the Capacitated Plant Location Model.”
European Journal of Operational Research
Keeney, R.L. (1972). “A Method of Districting Among Facilities.”
Kernighan, B.W. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.”
Bell Sys. Tech. J.
Khuller, S. and Y. Sussman. (1996). “The Capacitated k-Center Problem.” Berlin: Springer-Verlag. Lecture Notes in Computer Science, Vol. 1136.
Love, R.L., J.G. Morris, and G.O. Wesolowsky. (1988).
Facilities Location: Models and Methods
. Amsterdam: North-Holland.
Maffioli, F. and G. Righini. (1994). “An Annealing Approach to Multi-Facility Location Problems in Euclidean Space.”
Mirchandani, P.B. and R.L. Francis. (1990).
Discrete Location Theory
. New York: John Wiley & Sons, Inc.
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 SPITKOVSKY
Rosing, K.E. (1991). “Towards the Solution of the (Generalized) Multi-Weber Problem.”
Environment and Planning, Series B
Sharpe, R. and B.S. Marksjo (1985). “Facility Layout Optimization Using the Metropolis Algorithm.”
Environment and Planning B
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
Tansel, B.C., R.L. Francis, and T.J. Lowe. (1983). “Location on Networks: A Survey.”
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.
Wilson, J.D. (1994).
. NJ: Prentice-Hall, 1994.
Wong, R.T. (1985). “Location and Network Design.” In O'Eigeartaigh et al. (eds),
Combinatorial Optimization: Annotated Bibliographies
. New York: John Wiley and Sons.
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