Journal of Heuristics

, Volume 7, Issue 1, pp 23-36

First online:

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

  • Rahul SimhaAffiliated withDepartment of Computer Science, The George Washington University
  • , Weidong CaiAffiliated withOpen System Software Division, Hewlett-Packard
  • , Valentin SpitkovskyAffiliated withElectrical Engg. and Computer Science Dept., Massachusetts Institute of Technology

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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