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COMPARISON BETWEEN A SIMPLE GA AND AN ANT SYSTEM FOR THE CALIBRATION OF A RAINFALL-RUNOFF MODEL

COMPARISON BETWEEN A SIMPLE GA AND AN ANT SYSTEM FOR THE CALIBRATION OF A RAINFALL-RUNOFF MODEL. NELSON OBREGÓN RAFAEL E. OLARTE. 6th International Conference on Hydroinformatics Singapore, June 2004. OBJECTIVES. To propose an Ant System for solving continuous functions.

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COMPARISON BETWEEN A SIMPLE GA AND AN ANT SYSTEM FOR THE CALIBRATION OF A RAINFALL-RUNOFF MODEL

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  1. COMPARISON BETWEEN ASIMPLE GA AND AN ANT SYSTEM FOR THE CALIBRATION OF A RAINFALL-RUNOFF MODEL NELSON OBREGÓN RAFAEL E. OLARTE 6th International Conference on HydroinformaticsSingapore, June 2004

  2. OBJECTIVES To propose an Ant System for solving continuous functions. To compare this AS with a simple GA in terms of their Parsimony, Efficacy and Efficiency (only the calibration problem of the Thomas Model will be considered).

  3. CONTENTS Brief explanation of a simple AS Adapting an AS for the ThomasModel calibration problem Adapting a GA for the ThomasModel calibration problem Comparison between the 2 algorithms Conclusions

  4. BRIEF EXPLANATION OF A SIMPLE AS

  5. ? ? The Traveler Salesman Problem

  6. A Simple Ant System 1)Distribute randomly m ants on m of the n cities. 1) Distribute randomly m ants on m of the n cities.

  7. A Simple Ant System 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and dies. 2) Every ant makes a random tour and dies.

  8. A Simple Ant System 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and dies. 3) Update pheromone trails tij on the segments (ij). 3)Update pheromone trails tijupon segments (ij).

  9. A Simple Ant System 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and then dies. 3)Update pheromone trails tij upo segments (ij). 4) Distribute randomly m ants on m of the n cities. 4) Distribute randomly m ants on m of the n cities.

  10. A Simple Ant System ? ? 1) Distribute randomly m ants on m of the n cities. ? ? 2) Every ant makes a random tour and then dies. 5) Every ant makes a complete tour according to probability pij and the dies. 3)Update pheromone trails tij upo segments (ij). ? 4) Distribute randomly m ants on m of the n cities. ? ? 5) Every ant makes a complete tour according to probability pij and then dies.

  11. A Simple Ant System 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and then dies. 3)Update pheromone trails tij upon segments (ij). 6) Update pheromone trails tij upon segments (ij). 4) DistribUte randomly m ants on m of the n cities. 5) Every ant makes a complete tour according to probability pij and then dies. 6)Update pheromone trails tij upon segments (ij).

  12. 7) Has the # of iterations (maxIter) been completed? 7) Has the # of iterations (maxIter) been reached? A Simple Ant System 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and then dies. 3)Update pheromone trails tij upon segments (ij). 4) Distribute randomly m ants on m of the n cities. 5) Every ant makes a complete tour according to probability pij and then dies. 6)Update pheromone trails tij upon segments (ij).

  13. ADAPTING AN AS FOR THE THOMAS MODEL CALIBRATION PROBLEM

  14. Initial Conditions Parameters Sw0, Sg0 a, b, c, d P ET Initial Conditions Parameters Sw0, Sg0 a, b, c, d Q? The Thomas Model Calibration Problem PRECIPITATION EVAPOTRANSPIRATION CATCHMENT STREAMFLOW

  15. Initial Conditions Parameters Sw0, Sg0 a, b, c, d The Thomas Model Calibration Problem q a b c d Sw0 Sg0

  16. a b c d Sw0 Sg0 Adapting the simple AS The Thomas Model Calibration Problem q a b c d Sw0 Sg0 q b

  17. 1) Distribute randomly m ants on m of the n cities. 2) Every ant makes a random tour and then dies. 3)Update pheromone trails tij upon segments (ij). 4) Distribute randomly m ants on m of the n cities. 5) Every ant makes a complete tour according to probability pij and then dies. a b c d 6)Update pheromone trails tij upon segments (ij). q Sw0 7) Has the # of iterations (maxIter) been completed? Sg0 b Adapting the simple AS

  18. 1) Distribute randomly m ants on m of the n cities. 2) Let each ant make a random tour and die. 3) Calculate tmax and set all segments with that pheromone. 1) Distribute randomly m ants on m of the n cities. 4)Update pheromone trails tij upon segments (ij) within tmax and tmin. 2) Every ant makes a random tour and then dies. Parameters’ Sensibility 3)Update pheromone trails tij upon segments (ij). 5)If an interval of globUpdate iterations has been made, reinforce pheromone trail of the global best found solution. 4) Distribute randomly m ants on m of the n cities. 6) Distribute randomly m ants on m of the n cities. 5) Every ant makes a complete tour according to probability pij and then dies. + a d c b a c b d 7) Let each ant make a complete tour (according to probability pij) and die. Update the limit tmax. 6)Update pheromone trails tij upon segments (ij). – Sw0 8) Has the # of iterations (maxIter) been completed? 7) Has the # of iterations (maxIter) been completed? Sg0 Adapting the MAX-MIN AS Adapting the simple AS At each iteration, set limits for the values oftij, that is, tmin and tmax. At each iteration, only update tij of the iteration best found solution. Every globUpdate iterations, update the tijof the global best found. q b

  19. ADAPTING A GA FOR THE THOMASMODEL CALIBRATION PROBLEM

  20. 1) Generate population of popSize chromosomes. 2) Evaluate the objective function in each chromosome. 3) Select the fittest chromosomes using normalization. 4) Generate next population using double point crossover (with pc probability) and mutation (with pm probability). 5) Get rid of the e worst chromosomes and replace them with the e best from the previous population.. (6) Number of generations maxGen reached? A Simple GA

  21. Chromosomes q a b c d Sw0 Sg0

  22. Generation t-1 Generation t e best e worst Elitism

  23. Other Algorithm’s Properties Double-Point Crossover Roulette-Wheel selection with previous normalization according to the following equation.

  24. COMPARISON BETWEEN THE 2 ALGORITHMS

  25. Area of Study used for the Comparison

  26. Search Spaces MAX-MIN Ant System 201 x 1000 x 900 x 341 x 501 x 501 = 3.6x106 Simple Genetic Algorithm 2(8+10+10+9+9+9)= 3.6x106

  27. Efficacy • Parameters used • MM AS • m = 150 • globUpdate = 10 • r = 0.95 • tmin = 0.1 • GA • popSize = 75 • elite = 1 • pm = 0.1 • pc =0.7 • Parameters used • MM AS • m = 150 • globUpdate = 10 • r = 0.95 • tmin = 0.1 • GA • popSize = 75 • elite = 1 • pm = 0.01 • pc =0.6 • Parameters used • MM AS • m = 150 • globUpdate = 10 • r = 0.95 • tmin = 0.1 • GA • popSize = 75 • elite = 1 • pm = 0.1 • pc =0.6

  28. Efficiency • Parameters used • MM AS • m = 50 • globUpdate = 10 • r = 0.95 • tmin = 0.1 • GA • popSize = 50 • elite = 1 • pm = 0.1 • pc =0.6

  29. 1) Distribute randomly m ants on m of the n cities. 2) Let each ant make a random tour and die. Simple GA MAX-MIN AS 1) Generate population of popSize chromosomes. 3) Calculate tmax and set all segments with that pheromone. 2) Evaluate the objective function in each chromosome. 4)Update pheromone trails tij upon segments (ij) within tmax and tmin. maxGen maxIter 3) Select the fittest chromosomes using normalization. 5)If an interval of globUpdate iterations has been made, reinforce pheromone trail of the global best found solution. 4) Generate next population using double point crossover (with pc probability) and mutation (with pm probability). popSize m 6) Distribute randomly m ants on m of the n cities. 5) Get rid of the e worst chromosomes and replace them with the e best from the previous population.. 7) Let each ant make a complete tour (according to probability pij) and die. Update the limit tmax. elite globUpdate (6) Number of generations maxGen reached? 8) Has the # of iterations (maxIter) been completed? r pm tmin pc Parsimony

  30. Parsimony pm globUpdate r tmin elite ExploitationExploration

  31. maxGen maxIter popSize m

  32. elite Other Parameters: maxGen=750 popSize=75 pm=0.2 pc =0.6 globUpdate Other Parameters: maxIter= 300 m = 50 r = 0.97 tmin = 0.1

  33. pc r :maxIter= 300 m = 50 globUpdate = 10 tmin = 0.1 maxIter= 300 m = 50 globUpdate = 10 tmin = 0.1 pm tmin maxGen = 750 popSize= 75 elite = 1 pc = 0.6 maxIter= 300 m = 50 globUpdate = 10 r = 0.95

  34. CONCLUSIONS

  35. Some parameter values can now been taken from the present work for the application of both algorithms to the Thomas Model Calibration Problem The GA showed a much better efficiency than the AS. Research must continue in order to improve the implementation of AS for solving continuous functions.

  36. THANK-YOU

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