Comparison of 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.

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),

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

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

Comparison of Natural and GA chromosomestring genefeature, character allelefeature value locusstring position genotype structure phenotype alternative solution epistasisnonlinearity

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. The Water Allocation Problem

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

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.

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) gene 1gene 2gene 3gene 4

A Simple Test System

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

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).

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

Probability of Selection (P i ) f i = fitness of individual chromosome in that generation n = population size

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

Two Point Crossover

Uniform Crossover

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.

Nodal Water Balance

A Simple System

Objective Function After Wardlaw and Barnes, 1996

Constraints i) Capacity constraint: Q ij <= qmax ij ii) nodal balance constraint: iii ) supply constraint: x i <= d i

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

Penalty Function 1

Penalty Function 2

Penalty Function 3

Schematic Diagram of Song Phi Nong Irrigation System

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

Schematic Diagram

Run Cases Supply / Demand

Water Requirement Cases using WASAM Week 6Initial Stage Week 16Max. Water Requirement Week 22Min. Water Requirement Stage Week 23End Stage

GA result when inflow to the system 60% Weeksupply / demand ratio MinMaxMean

Weeksupply / demand ratio MinMaxMean GA result when inflow to the system 70%

Weeksupply / demand ratio MinMaxMean GA run result when inflow to the system 120%

GA run result when inflow to the system 150% Weeksupply / demand ratio MinMaxMean

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

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.