An Efficient Genetic Algorithm for the p-Median Problem

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.

[1]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[2]  E. Hillsman.  The p-Median Structure as a Unified Linear Model for Location—Allocation Analysis , 1984 .

[3]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[4]  M. Goodchild,et al.  Discrete space location-allocation solutions from genetic algorithms , 1986 .

[5]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[6]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[7]  Antonio Sassano,et al.  On the p-Median polytope , 2001, Math. Program..

[8]  Erhan Erkut,et al.  TransAlta Redesigns Its Service-Delivery Network , 2000, Interfaces.

[9]  Nelio Domingues Pizzolato,et al.  A heuristic for large-sizep-median location problems with application to school location , 1994, Ann. Oper. Res..

[10]  J. Current,et al.  An efficient tabu search procedure for the p-Median Problem , 1997 .

[11]  L. Cooper.  Location-Allocation Problems , 1963 .

[12]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[13]  Manfred Körkel.  On the exact solution of large-scale simple plant location problems , 1989 .

[14]  James A. Fitzsimmons,et al.  A Warehouse Location Model Helps Texas Comptroller Select Out-of-State Audit Offices , 1983 .

[15]  Roberto D. Galvão,et al.  A Dual-Bounded Algorithm for the p-Median Problem , 1980, Oper. Res..

[16]  Subhash C. Narula,et al.  Technical Note - An Algorithm for the p-Median Problem , 1977, Oper. Res..

[17]  Kathryn A. Dowsland,et al.  Genetic Algorithms-a Tool for OR? , 1996 .

[18]  C. Revelle,et al.  Heuristic concentration: Two stage solution construction , 1997 .

[19]  Charles S. Revelle,et al.  A gamma heuristic for the p-median problem , 1999, Eur. J. Oper. Res..

[20]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[21]  R. D. Galvão,et al.  A tabu search heuristic for the concentrator location problem , 1998 .

[22]  Richard L. Church,et al.  Applying simulated annealing to location-planning models , 1996, J. Heuristics.

[23]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .

[24]  Pj Densham,et al.  GENERATING INTERESTING ALTERNATIVES IN GIS AND SDSS USING GENETIC ALGORITHMS , 1993 .

[25]  E. Correa,et al.  A genetic algorithm for the P-median problem , 2001 .

[26]  Paul J. Densham,et al.  A more efficient heuristic for solving largep-median problems , 1992 .

[27]  C. Revelle,et al.  A Lagrangean heuristic for the maximal covering location problem , 1996 .

[28]  R. D. Galvão,et al.  A method for solving to optimality uncapacitated location problems , 1990 .

[29]  Fernando Y. Chiyoshi,et al.  A statistical analysis of simulated annealing applied to the p-median problem , 2000, Ann. Oper. Res..