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Applying genetic algorithms to the location allocation of shelter sites

Applying genetic algorithms to the location allocation of shelter sites. Xiang Li, Hsiang-te Kung, Jerry Bartholomew, and Esra Ozdenerol Dept. of Earth Sciences The University of Memphis. Outline. Introduction Problem formulation Methodology Experiments Conclusions. Introduction.

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Applying genetic algorithms to the location allocation of shelter sites

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  1. Applying genetic algorithms to the location allocation of shelter sites Xiang Li, Hsiang-te Kung, Jerry Bartholomew, and Esra Ozdenerol Dept. of Earth SciencesThe University of Memphis

  2. Outline • Introduction • Problem formulation • Methodology • Experiments • Conclusions

  3. Introduction • Location-allocation problems • P-median problem • Capacity constraints • Capacitated p-median problem

  4. Problem formulation • Objective function Minimize

  5. Problem formulation • Notation N the number of units P the number of facilities M the number of candidate facilitate sites Ci the maximum capacity of the facility on candidate site in unit i Ai the actually-employed capacity of the facility on candidate site in unit i Dj the total demand volume in unit j xij 1 if demand from unit j is satisfied by the facility in unit i, 0 otherwise. si 1 if unit i is selected to locate a facility, 0 otherwise. tij the total travel cost of satisfying demand from unit j by the facility in unit i fq 1 if unit q has a candidate site, 0 otherwise.

  6. Problem formulation • Subject to

  7. Methodology • Lagrangean relaxation (Mulvey and Beck 1984, Koskosidis and Powell 1992, Murray and Gerrard 1997) • Simulated annealing and tabu search (Osmanl and Christodes 1994, Franca et al. 1999) • Genetic algorithms (Correa et al. 2001) • Column generation approaches (Lorena and Senne 2004, Ceselli and Righini 2005) • etc.

  8. Genetic algorithms • Suitable for large-scale problems in geography • Stemming from Darwin's theory of evolution, i.e. survival of the fittest. • Chromosome: encoded solution • A population: a group of chromosome • Reproduction: crossover, mutation, etc. • Fitness function: evaluate solutions • Find the most optimal solution after a number of generations.

  9. Encoding strategies • Define a chromosome • Consist of genes • Each gene represents a possible location • Employ Hilbert curve to the encoding of possible locations in order to improve the independency of each gene.

  10. Hilbert curve

  11. Encoded solution based on Hilbert curve

  12. Fitness functions • Instead of the objective function • Calculate the number of the spatial units which can be assigned to their nearest facilities with respect to capacity constraints of facilities.

  13. Fitness functions

  14. Reproduction • Randomly generate the first generation • Apply the proposed genetic operator, unique-value operator, to reproduce

  15. Reproduction

  16. Experiments: Data

  17. Experiments: Three scenarios for comparison

  18. Results Scenario 1 Scenario 2 Scenario 3

  19. Shelter sites and service areas

  20. Thank you!

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