2. S J van Vuuren The application of Genetic Algorithms (GAs) Planning Design and Management of Water Supply Systems

3. GA’s - not a solution to all problems !

4. Layout What is a GAs?What is a GAs? An Example of a GAAn Example of a GA Programming of network problemsProgramming of network problems GAs in the Planning Design and Management of Water Supply Systems The road ahead What is a GAs?What is a GAs? An Example of a GAAn Example of a GA Programming of network problemsProgramming of network problems GAs in the Planning Design and Management of Water Supply Systems The road ahead

5. What is a GA? GA = Search procedure based on the mechanics of natural selection and natural genetics – survival of the fittests. GA = Search procedure based on the mechanics of natural selection and natural genetics – survival of the fittests.

6. Human Evolution

7. Natural Evolution A different view

8. Processes of a GA Production Select randomly Crossover Pairs change (Random process) Mutation Protects against loss of useful genetic material (secondary mechanisms to prevent local optimum) Reproduction Select according to objective function (Best remain) Production Select randomly Crossover Pairs change (Random process) Mutation Protects against loss of useful genetic material (secondary mechanisms to prevent local optimum) Reproduction Select according to objective function (Best remain)

9. How do GAs differ from traditional methods (Goldberg) Coding of the parameter set, not the parameters themselves. Search for a population of points, not a single point. Use objective functions (payoff) information, not derivatives or other auxiliary knowledge, to determine the fitness of the solution. GAs use probabilistic transition rules not deterministic rules Coding of the parameter set, not the parameters themselves. Search for a population of points, not a single point. Use objective functions (payoff) information, not derivatives or other auxiliary knowledge, to determine the fitness of the solution. GAs use probabilistic transition rules not deterministic rules

10. 3 Main types of search methods Calculus - Enumerative Random Genetic algorithm Calculus - Enumerative Random Genetic algorithm

11. Comparison of Optimization Methods

12. Example

13. Example of a chromosome string

14. Basics of a GA

15. An Example of a GA MAXIMIZE f(x) = x 2 (0 < x < = 31) CODE x as a finite-length string Length = 5 in the binary basis (1x2 4 + 1x2 3 + 1x2 2 + 1x2 1 + 1x2 0 = 31) Select population size - say 4 strings MAXIMIZE f(x) = x 2 (0 < x < = 31) CODE x as a finite-length string Length = 5 in the binary basis (1x2 4 + 1x2 3 + 1x2 2 + 1x2 1 + 1x2 0 = 31) Select population size - say 4 strings

16. Crossover and mating Crossover Mating string 1 with 2, and 3 with 4 and crossover at positions 4 and 3 results in: Crossover Mating string 1 with 2, and 3 with 4 and crossover at positions 4 and 3 results in:

17. Mutation PROBABILITY OF MUTATION = 0,001 BITS TO MUTATE IN A GENERATION = 20 X 0,001 = 0,02 No mutation ! Summary after one generation Note:*Values after one generation and one crossover

18. Programming procedure of Genetic Algorithms (GAs) An Example Programming procedure of Genetic Algorithms (GAs) An Example 1.Problem for the application of Genetic Algorithms in water supply systems 2. Computer Program

19. Processes of a GA - Previously  Selection  Reproduction  Copy according to objective function (bias roulette wheel)  Crossover  Pairs change  Mutation  Protects against loss of useful genetic material (secondary mechanisms)  Selection  Reproduction  Copy according to objective function (bias roulette wheel)  Crossover  Pairs change  Mutation  Protects against loss of useful genetic material (secondary mechanisms)

20. Example Problem - Genetic Algorithms in water supply systems: Layout

21. Solution objective For a given demand it is required that we have to: Determine the pipe diameters that will result in the minimum life cycle cost. For a given demand it is required that we have to: Determine the pipe diameters that will result in the minimum life cycle cost.

22. Calculations procedures Optimum solution through the use of the GA, while the pressure/energy requirements be determined through the use of hydraulic relationships.

23. Flow diagram Start Possible solution Hydraulic solution Cost Calculation Fitness test Crossover mutation New Results Report Reproduction

24. Computer program Two problems can be analyzed : Gravity line Pump line Determine the optimal diameter and pumping time Overview of input screens Results

25. Gravitation and Pumping Systems – Selection Screen

26. Pumping System – Screen P1

27. Pump line details – Screen P2

28. Pump line energy cost – Screen P3

29. Pump line economic analysis Capital data - Screen P4

30. Pump line design parameters Screen P5

31. Results from the GA analysis Pumping Pipeline – Results 1

32. Results from the GA analysis Pumping Pipeline – Results 2

33. Results from the GA analysis Pumping Pipeline – Results 3

34. Results from the GA analysis Pumping Pipeline – Results 4

35. Network Optimization Use EPANET to set-up system Define pipes that can be changed Define a penalty structure/cost on routes which are difficult to change Conceptually develop procedure

36. EPANET to set-up system

37. The application of Genetic Algorithms in the Planning Design and Management of Water Supply Systems WRSM 2000 Water Resources

38. The application of Genetic Algorithms WRSM 2000 Automate calibration of WRSM 2000 parameters

39. WRSM 2000 – Current process

40. The application of Genetic Algorithms WRSM 2000 Optimise calibration on selected monthly flood size Procedure will select monthly flood size based on exceedance probability Obtain from this, a parameter set that will represent the calibrated flow record Develop criteria applicable for this optimisation

41. The application of Genetic Algorithms WRYM Optimize water Resources Analyses Procedures

43. How the GA can be implemented

44. WRC has funded the conceptual assessment of the application of GAs The application of Genetic Algorithms in the Planning Design and Management of Water Supply Systems – December 2004

45. Gas = Where from here ? Development of routines to be included in existing modeling procedures

46. Thank You

47. Programs are available from : Water Research Commission http:\\www.wrc.org.za/software/GAPO P University of Pretoria’s http:\\www.up.ac.za/academic/civil/divi sions/water.html