Comparison of Genetic Algorithm and WASAM Model for Real Time Water Allocation:

1. Comparisonof Genetic Algorithm and WASAM Model for Real Time Water Allocation: A Case Study of Song Phi Nong Irrigation Project Bhaktikul, K, Mahidol Univ. Soiprasert, S., Irrigation College Sombunying, W., Chulalongkorn Univ.

2. References • Davis,L. (1991). Handbook of Genetic Algorithms. Van Nostrand Renhold, New York. • Goldberg, D.E.(1989). Genetic Algorithms in search optimisation&machine learning. Addison-Wesley Publishing Company Inc,USA. • Michalewicz, Z. (1992). Genetic algorithms + data structures = evolution programs. Springer-Verlag, New York, Inc., New York. • Wardlaw, R.B., and Sharif, M. (1999). “Evaluation of genetic algorithms for optimal reservoir system operation”. J. Water Resour. Plng. and Mgmt., ASCE 125(1), 25-33.

3. Presentation Outline • What is GA and Why GA? • Application to the water allocation test system • Application to an irrigation system in • Conclusion

4. Optimisation Approaches • linear Programming • dynamic programming (DP) • non-linear programming (quadratic, QP) • simulated annealing (SA) • evolutionary algorithms (genetic algorithms, GAs) • artificial neural networks (ANNs)

5. Comparison of Natural and GA • chromosome string • gene feature, character • allele feature value • locus string position • genotype structure • phenotype alternative solution • epistasis nonlinearity

6. The Water Allocation Problem • To ensure the equitable distribution of water supplies within an irrigation system. • It is not a planning problem in the crops are assumed to be in the ground. • It is not a scheduling problem in that irrigation supplies are assumed to be run of river.

7. Objective of The Study • To determine optimal and equitable water allocation in various water supply situations (deficit, normal, surplus) using GA. • Study Area Song Phi Nong Irrigation Project which covers area of 300,000 rai and 32 irrigation schemes

8. Why GA ? • GA is flexible and easily set up for • a wide range of linear and non-linear objective functions. • GA is an alternative approach.

9. 0 0 1 1 1 0 1 0 1 1 1 1 gene 1 gene 2 gene 3 gene 4 How the GAs work? • work with a coding of parameter set • search from a population of points • use objective function information • use probabilistic transition rules, Goldberg (1989).

10. A SimpleTest System

11. An Example of a Chromosome Represents the Flows(qi) in Each Canal

12. GA process 1.Initialize a population of chromosome. 2.Evaluate each chromosome in the population. 3.Create new chromosomes by mating current chromosome; apply mutation and recombination as the parent chromosomes mate. 4.Delete members of the population to make room for the new chromosomes. 5.Evaluate the new chromosomes and insert them into the population. 6. Stop and return the best chromosome if time is up ; otherwise go to 3. Davis(1991).

13. Three Operators of Genetic Algorithm Selection Operator string are selected for inclusion in the reproduction process - Crossover Operator - permits the exchange of genes between pairs of chromosomes in a population Mutation Operator - permits new genetic material to be introduced to a population

14. Probability of Selection (Pi) fi= fitness of individual chromosome in that generation n = population size

15. One Point Crossover Approaches to crossover (after Wardlaw and Sharif, 1999)

16. Two Point Crossover

17. Uniform Crossover

18. Mutation Schemes • In binary coding, individual of alleles changed from 0 to 1 or vice versa. • Uniform mutation, the value of a gene can be mutated randomly within its feasible range of values. • Modified uniform mutation permits modifications of a gene by a specified amount • Non-uniform mutation, gene can be mutated by the reduced amount as the run progresses.

19. Nodal Water Balance

20. A Simple System

21. Objective Function After Wardlaw and Barnes, 1996

22. Constraints • i) Capacity constraint: Qij <= qmaxij • ii) nodal balance constraint: • iii ) supply constraint: xi <= di

23. where; Q(N) = flow in reach N S(N) = water requirement within reach N Q(I) = discharge from reachN to connecting reach I til reach M LOSS(N)= Loss in canal within reach N

24. Penalty Function 1

25. Penalty Function 2

26. Penalty Function 3

27. Schematic Diagram of Song Phi Nong Irrigation System

28. Song Phi Nong Irrigation System • Seasonal water requirement is in range 0.0 – 5.65 m3/s • Max. canal capacity 0.42 – 82.98 m3/s

29. Schematic Diagram

31. Water Requirement Cases using WASAM

32. GA result when inflow to the system 60%

33. GA result when inflow to the system 70%

34. GA run result when inflow to the system 120%

35. GA run result when inflow to the system 150%

39. Best fitness obtained when using; Pc = 0.7, Pm = 0.1, R1 = 10, R2 = 4

40. Conclusions • The advantage of GA is that it could solve the problem with any type of objective function and could be easily set up. • In water allocation problem the appropriate decision variables are the flows that vary as max. and min.capacity of the canals. • GA has been improved to water allocation problem if the violation of nodal balance constraints decreased. • In the deficit case GA can provide an equitable allocation among nodes while WASAM couldn’t. • GA is able to solve the water allocation problem, reach the optimum and achieves near equity.