Genetic Algotitm in Water Management

8/3/2019 Genetic Algotitm in Water Management

1/19

Optimal Reservoir Release Policy Considering

Heterogeneity of Command Area by ElitistGenetic Algorithm

A. S. Garudkar & A. K. Rastogi & T. I. Eldho &

S. D. Gorantiwar

Received: 17 September 2010 /Accepted: 25 July 2011# Springer Science+Business Media B.V. 2011

Abstract A number of models with conventional optimization techniques have been

developed for optimization of reservoir water release policies. However these models are

not able to consider the heterogeneity in the command area of the reservoir appropriately,

due to non linear nature of the processes involved. The optimization model based on

genetic algorithm (GA) can deal with the non linearity due to its inherent ability to consider

complex simulation model as evaluation function for optimization. GA based models

available in literature generally minimize the water deficits and do not optimize the total netbenefits through optimal reservoir release policies. The present study focuses on optimum

releases from the reservoir considering heterogeneity of the command area and responses of

the command area to the releases instead of minimizing only the reservoir storage volumes.

An optimization model has been developed for the reservoir releases based on elitist GA

approach considering the heterogeneity of the command area. The developed model was

applied to Waghad irrigation project in upper Godavari basin of Maharashtra, India. The

results showed that 19% increase in the total net benefits could be possible by adopting the

proposed water release policy over the present practice keeping same distribution of area

under different crops. The model presented in this study can also optimize the crop area

under irrigation. It is found that irrigated area can be increased to 50% of ICA (Irrigable

Command Area) from the existing 23% with resulting addition to total net benefits by 31%.

The effect of adopting the proposed irrigation schedule and increased irrigation areas would

be to increase the net benefits to existing farmers.

Keywords Elitist genetic algorithm . Reservoir operating policies . Heterogeneity of

command area. Crop growth model . Waghad irrigation project

Water Resour Manage

DOI 10.1007/s11269-011-9892-0

A. S. Garudkar: A. K. Rastogi : T. I. Eldho (*)Department of Civil Engg., IIT Bombay, Powai, Mumbai 400076, India

e-mail: [email protected]

S. D. Gorantiwar

Department of Irrigation and Drainage Engg, MPKV, Rahuri, Ahmadnagar, Maharashtra, India


2/19

1 Introduction

The share of water for irrigation is continuously decreasing in many parts of the world

including India as more and more water needs to be made available for industrial and

domestic water uses. Food requirement for the growing population makes it imperative toincrease the area under planned irrigation, as the productivity of irrigated agriculture is

certainly more than the productivity of rain fed agriculture. Hence it is extremely important

to enhance the efficiency of irrigation water to bring more cultivable land under planned

irrigation. There are several ways to increase water use efficiency. These include improved

irrigation scheduling, adoption of water saving irrigation methods and optimum allocation

of water. This paper particularly focuses on optimum releases from the storage reservoir to

obtain maximum water use efficiency.

Conventional optimization techniques viz. linear programming, non linear programming

and dynamic programming have been extensively used for the optimization of the water

resources for irrigation. Vedula and Majumdar (1992), Karamouz et al. (1992), Crawley and

Dandy (1993), Lund and Ferreira (1996), Dandy et al. (1997), Wardlaw and Barnes (1999),

Loucks et al. (2000), Paul Sabu et al. (2000) and Gorantiwar and Smout (2005) presented

the detailed methodologies and algorithms using conventional methods for optimum

utilization of water resources for irrigation. However the non linearity associated with the

complex reservoir systems is inadequately addressed by these optimization techniques. This

is due to the fact that conventional techniques require an optimization process to be

formulated in a particular format. For example: linear programming needs the objective

function and the constraints to be formulated as a set of linear equations that is not often a

case with the water resources system. Dynamic programming needs the problem to beseparated into number of states and stages. The optimality may be lost if certain states are

ignored and number of stages are minimized. On the other hand number of stages and states

need to be limited due to computational requirement that increases exponentially with

number of stages and states. Non linear programming has approximation problems dealing

with non-differentiable, non-convex and multi-modal objective functions. Thus due to

difficulties in considering non linearity appropriately by conventional optimization

techniques, the possibility of obtaining the realistic solution is adversely affected.

Genetic algorithm is a search method that mimics natural biological evolution process to

find out near optimal solutions and operates on a population of potential solutions that

satisfy a specified set of constraints. The solution space is continuously updated by anevolution process till the solution is obtained based on satisfaction of a specified criteria.

Problems of varying complexities and dimensions of water resources systems are solved by

GA. Chen Yu-Ming (1997), Wardlaw and Sharif (1999), Sheng-Feng Kuo et al. (2000),

Labadie (2004), Raju and Kumar (2004), Ahmed and Sarma (2005), Jothiprakash and

Shanthi (2006), and Momtahen and Dariane (2007) concluded that though genetic

algorithm does not appear to be providing the global optimal solution but certainly assures

the near global optimal solution and has an inherent ability to consider the complexity of

any degree. Raju and Kumar (2004), Nagesh Kumar et al. (2006), Ahmed and Sarma

(2005) and Sharif and Wardlaw (2000) confirmed that GA compares acceptably withconventional optimization techniques. Hnal et al. (2011) compared results of energy

maximization due to three reservoirs in the Colorado River storage project by GAwith real

operation data and concluded that GA is an alternative technique to other traditional

optimization techniques. Thus GA has an added advantage of representing the complexity

of the system to be optimized adequately over conventional optimization technique due to

its inherent ability of evaluating the function/model that simulates the real system.

A.S. Garudkar et al.


3/19

Most of the previous studies on optimal irrigation water releases by GA considered the

command area of the irrigation project as one unit meaning that the command area is

homogenous in respect of soil, climate and water delivery system (single field typeChen Yu-

Ming 1997; Sheng-Feng Kuo et al. (2000) and Momtahen and Dariane 2007). However the

irrigation water deliveries i.e. water releases from the reservoirs depend on soil, crop and theirgrowth stages, amount and timing of water and farm management practices and hence the

single field type models do not provide the optimum releases of water from the reservoir. Raju

and Kumar (2004) and Nagesh Kumar et al. (2006) considered the parameters that influence

the irrigation water deliveries in the optimization process of genetic algorithm. However these

studies did not particularly consider optimizing water releases from the reservoir, but focused

on minimizing the shortages or deficit in the reservoir due to certain predefined water release

policy. Hence as such they do not propose optimum release policy. According to Gorantiwar

and Smout (2005), optimization of water release schedule by considering the heterogeneity of

command area (multi field type) in terms of soil, climate, irrigation method and water delivery

system is more relevant as these parameters influence crop yield and the subsequent net

benefits. Hence these types of models can provide water release schedules for optimization of

the net benefits. The present study emphasizes on deciding the releases of water from the

storage reservoir for optimum utilization of water for irrigation and presents the methodologies

developed for the formulation of the model and its application to a field problem.

The developed model aims at finding canal water releases during each intra seasonal period

or rotation wise water releases for maximizing the net benefits derived from the command area

in response to these water releases. The rotation wise canal water releases are decision variables.

The net benefits in response to a set of canal water release are simulated by allocating the

releases to different crops grown in different units of the command area according to a prespecified allocation policy with the help of simulation model.

2 Modeling Methodology

The optimization model using genetic algorithm has been developed to obtain optimum

water releases from storage reservoir. The objective function is maximization of the net

benefits in response to water releases during different intraseasonal rotation periods for

irrigation from different canals of a reservoir. The objective function (Z) can be

mathematically represented by Eq. 1 as follow:

Max Z XNi1

BiR0

ip fPnl R0

ip XEptSp

Rit 1

Where, Z = total net benefits, N = number of canals, Bi = net benefits, f(pnl) = penalty

function for violation of the constraints, R0

ip = matrix of releases from the reservoir i.e. Ri 1,

Ri2.Rip for irrigation through ith canal during pth rotation period, p = total number of

rotations/irrigations during irrigation season, Rit = release from the reservoir for irrigation

through i

th

canal on t

th

day, sp = starting day of p

th

irrigation or rotation period Ep = endingday of pth irrigation period.

2.1 Penalty Function

During the successive generations of the population in the process of evolution in GA, it is

possible that certain strings amongst generated population may not satisfy the constraints

Optimal Reservoir Release Policy Considering Heterogeneity


4/19

but tend to produce optimum solution. In order to discourage such strings from entering into the

solution space and at the same time to retain the information contained in the string for

successive generations, it is necessary to penalize them by reducing the value of the function for

the maximization and increasing the value for the minimization problem by way of penalty

function. In this formulation, there is a possibility that certain strings or a set of water releasesmight violate canal capacity and reservoir storage constraints. The string is then penalized by

reducing value of the function by the quantity with which the dead storage is encroached and

canal capacities are exceeded. Mathematically penalty function is given by Eq. 2 as

fpnl XTt1

Maxsmin st; 0 XNt1

XTt1

MaxQi Rit; 0 2

Where, T = number of days, S min = minimum storage or dead storage capacity, St =

storage on tth day, Qi = canal capacity of ith canal.

2.2 Constraints

The following constraints need to be satisfied while optimizing the objective function,

1) Reservoir storage constraint

Reservoir storage on any tth day (St) should not exceed gross storage capacity of the

reservoir (Smax) or should not be less than dead storage capacity (Smin) of the reservoir as

given by Eq. 3

smin st smax for t 1; . . . . . . ; T 3

2) Canal capacity constraints

The quantity of water released from a canal on tth day should not exceed its capacity as

given by Eq. 4.

Rit Qi for t 1; . . . ; T and i 1; . . . :;N 4

3) Reservoir mass balance constraint

Reservoir mass balance as given by following continuity equation should not be violated

on any given day

St1 St It Rft XNi1

Rit Ot Oot Et Zt 5

Where, St = storage in the reservoir at the beginning of tth day, It = inflow in the reservoir

on tth day, Rft = rainfall over the submergence area of reservoir on tth day, Ot = spill from the

reservoir on tth day, Oot = other withdrawals of water on tth day, Et = evaporation from the

reservoir water spread area on t

th

day and Zt = seepage from the reservoir on t

th

day.

2.3 Fitness Function

The fitness functionPNi1

BiR0

ip in Eq. 1 is evaluated with the help of the simulation model

which is described in this section. As stated earlier, the total net benefits are derived due to



5/19

allocation of canal water for irrigation to different crops grown on different units of the

command area. The releases from the canal Rip are distributed over different units in the

command area of the project according to a predefined policy e.g. water allocation to a unit

is proportional to irrigable command area of the unit. According to this policy, the water

that is available at the outlet of the unit is obtained by using Eq. 6

r0

kip R

0

ip Akip hcki

TAipTAip

Xnkik1

Akip p 1;p; i 1;N 6

Where, rk i p = water released at the outlet of kth unit of ith canal during pth rotation

period, Akip = total area to be brought under irrigation or irrigation area of kth unit of ith canal

during pth rotation period, nki = number of units in the command area of ith canal and cki =

conveyance efficiency for delivery of water to kth unit of ith canal from the headworks.

The water deliveries to individual crop in a unit command area grown on different soils

are estimated by Eq. 7

rjlpki r

0

kip ajlpkihdki

Akip7

Where, r0

jlpki = water released to the field having jth crop grown on lth soil of kth unit on ith

canal during pth rotation period, ajlpki = area to be brought under irrigation of jth crop grown on

lth soil of kth unit on ith canal during pth rotation period, and hdkl

= the distribution efficiency

within the command area of kth unit on ith canal of delivering water from outlet to field.

The depth of water applied to the field is estimated as given by Eq. 8

djlpki r

0

jlpkihajlki

ajlk i8

Where, djlpki = the depth of water applied during pth

rotation period to a field having jth

crop grown in lth soil of kth unit on ith canal, haj l k i

= the application efficiency of irrigation

system used for jth crop grown in lth soil of kth unit on ith canal.

The yields and net benefits from a particular crop grown on a particular soil of a

particular unit in response to water applied during different rotation periods over its

growing season are estimated by simulating actual evapotransporation by performing the

soil water balance in the root zone of a crop by Eq. 9.

qt qt1 ERt dt st ETat DPt 9

Where, t = volumetric soil moisture content in the root zone at the end of tth day, ERt =

effective rainfall received on tth day; dt = depth of irrigation water applied on tth day, t = the

contribution of water to the root zone from capillary rise of ground water on tth day, ETa t =

water lost from the root zone on tth day and used for the crop growth and DPt = the

application of water in the root zone (by effective rainfall or by irrigation) in excess of the

water holdings capacity of the root zone that is lost as a deep percolation.

ETat ETmt ifqt qw Rzt ! 1 p qf qw Rzt otherwise;

ETat qt qw RZt ETmt = 1 p qf qw RZt10

Where, ETmt = maximum crop evapotranspiration on tth day and is equal to ETrt*kct,

ETrt = reference crop evapotranspiration on tth day (estimated by Penman Monteith



6/19

method), kct = crop coefficient on tth day, p = soil water depletion factor, f = volumetric

soil moisture content in the root zone at field capacity, w = volumetric soil moisture

content in the root zone at wilting point; Rzt = root zone depth on tth day since sowing/

planting of crop in mm and given by Rz 0+ (Rz mRz0) t/tm (Fereres et al. 1981) where,

Rz0 = root zone depth at the time of sowing/planting, Rz m = maximum root zone depth, tmdays required for root depth to reach Rzm

Following stage wise crop growth model (Eq. 11) proposed by Stewart and Hagan

(1973) is used to simulate the crop yield.

Ya

Ym 1

Xnss1

KysSETms SETas

SETms

SETms XYES

tYSS

ETmt and SETas XYES

tYSS

ETat

11

Where Ya = actual crop yield; Ym = maximum potential yield; s = subscript for crop

growth stage; Kys = yield response factor for sth stage; SETms = maximum crop

evapotranspiration for sth stage (mm); SETas = actual crop evapotranspiration for sth stage

(mm); ns = total number of crop growth stages; YSS = starting day of sth crop growth stage,

YEs = ending day of sth crop growth stage. The net benefits per unit area of irrigated land

are estimated by calculating the cost incurred and benefits derived from cultivation of the

crops. The total net benefits are then estimated by summing up net benefits of each unit.

3 Elitist Genetic Algorithm Approach

The optimization process in genetic algorithm (GA) starts with generating a set of strings

(chromosomes) of variables that represent the decision variables. These strings are operated

successively by GA operators viz. selection, crossover and mutation till the prescribed

criteria of optimum solution are satisfied. The set of strings of variables that satisfies the

prescribed criteria consists of the optimal solution. The flow chart for optimization of

reservoir water release policy is given in Fig. 1.

Deb (2001) reported that the GA converges quickly to global optimum solution for some

functions in presence of elitism. Hence elitism was introduced in this study. In elitist GAformulation, some of the best parents i.e. strings are retained for next generation and additional

required strings are generated by crossover. The number of strings retained is indicated by a

parameter called Percentage of Elitism. Thus the strings of variables which consist of optimal

solution are randomly divided into two groups according to population to be retained. One

group is retained to form next generation. The cross over and mutation operators are applied to

another group till optimal solution is arrived as per prescribed criteria.

In the present formulation, the decision variables are rotation wise releases in the canal i.e.

Rip and this forms the string of the GA. Releases of each rotation from each canal i.e. Ripforms the gene. The total net benefits in response to application of rotation wise releases form

the fitness function. The studies of Oliveira and Loucks (1997), Chang and Chen (1998),

Wardlaw and Sharif (1999), Sharif and Wardlaw (2000), Deb (2001) and Taesoon and Jun-

Haeng (2004) revealed that real coded representation of the variables is more effective as

compared to binary coded representation. Hence real coded representation of the variables

was adopted in this study. Initially a specified number of strings of decision variables

involving rotation wise canal water release (called population) are generated randomly. The



7/19

population of strings is then subjected to following GA operators successively till the

prescribed criterion is satisfied.

3.1 GA Operators

Selection Roulette wheel selection proposed by Goldberg (1989) was commonly used in

earlier reservoir operation studies. However according to Goldberg and Deb (1990),

Cieniawski et al. (1995), Yang and Soh (1997), Wardlaw and Sharif (1999) and Deb (2000),

tournament selection scheme has the distinct advantage over other selection schemes and

hence it was used in this study. In this method specified number of (commonly two) strings

are chosen from the population and better one is selected. Tournament selection operator

satisfies the following three criteria:

(1) Any feasible solution is preferred to any infeasible solution.

(2) Between two feasible solutions, the one having better objective function value is

preferred.

(3) Between two infeasible solutions, one having smallest constraint violation is

preferred.

Fig. 1 The flow chart for optimization of reservoir water release policy with genetic algorithm



8/19

Crossover Goldberg (1989) and Michalewicz (1992) described various methods of cross

over viz. single point, multi point and uniform crossover. However Oliveira and Loucks

(1997), Sharif and Wardlaw (2000), and Kuo et al. (2003) recommended uniform cross

over, and hence it was used in this study. Goldberg (1989) suggested to adopt high

crossover probability for good performance of GA. Wardlaw and Sharif (1999) found crossover probability between 0.70.8 give optimal solution in least number of generations.

Mutation The two basic approaches to mutation for real-value representations are uniform

mutation and non uniform mutation (Michalewicz 1992). Uniform mutation that permits the

value of a gene to be mutated randomly within its feasible range of values has been used.

According to Wardlaw and Sharif (1999), mutation probabilities in the range of 0.002

0.208 are most suitable for reservoir operation optimization.

Termination Criteria For termination of GA, criteria can be: 1) Fix number of generations

depending on string length, computing speed and desired accuracy, 2) Specified number of

generations giving same value of max fitness, 3) Specified difference in the successive values of

average fitness over specified number (say 10 generation giving specified% change in function

value) and 4) Fix number of generations together with specified number of generations giving

same value of max fitness. The first termination criterion was used for this study.

3.2 Optimization of Area to Be Irrigated

The elitist GA presented in this paper as stated in previous section optimises the waterrelease policies for known distribution of area under different crops for irrigation. However

the specified or prevalent crop area may not be optimum. In this case, the area for irrigation

under different crops needs to be optimised along with the water release policy. The

methodology for optimization of crop area to obtain maximum benefits is proposed in this

paper and presented in Fig 2. Area which offers maximum net benefits is selected.

4 Case Study

The developed model was applied to Waghad irrigation project in Godavari basin inMaharashtra, India. The dam is constructed across river Kolwan near village Waghad (20

14 N latitude and 73 43 E longitude) in Nashik district in Maharashtra state of India. The

catchment area of the reservoir is 119 km2 and area under submergence is 1090 ha. The

average annual rainfall in the catchment area is 902 mm. The average daily temperature in

the catchment and command area ranges between 12C to 40C. The gross storage capacity

of the project is 76480 thousand cubic meters. It has two canals: Waghad Right Bank canal

(WRBC) and Waghad Left Bank Canal (WLBC) irrigating 6750 ha area. The location and

index map of Waghad project is shown in Fig. 3.

Major crops grown in the command area are sugarcane, grapes, wheat, gram, maize,onion, tomato, hot weather groundnut and cauliflower. They are grown in three seasons

namely rabi (winter), hot weather (summer) and kharif (rainy). Crop calendar for the

project is shown in Fig 4. Normally there is less demand of water during kharifas the major

portion of rainfall is received during this season. The prominent soil types in the command

area are loamy sand, sandy loam, clay loam and clay. The command areas of outlets/minors/

distributaries from main canal were considered as unit with 31 units in the entire project



9/19

area. The conveyance losses were considered as 2% percent of canal flow per km and

distribution efficiencies as 80%. These values were obtained from diagnostic analysis

studies of WRBC and WLBC. The values of application efficiencies were 75% for surface

and 95% for drip irrigation method (WALMI 1987; 1996). The rotation wise actual water

releases of WRBC and WLBC during 200607 are presented in Table 1.On the basis of evapotranspiration values of different crops in different seasons, the

optimum irrigation interval values were proposed by Gorantiwar and Smout (2005) for the

state of Maharashtra. These are 4, 3 and 2 weeks for Kharif, Rabi and hot weather seasons

respectively. The irrigation season starts from 15th October in Maharashtra. Rabi season for

irrigation purpose is considered between 15th October to 28th February of next year and

hence first rotation is considered from 15th October to 4th November. Subsequent rotations

in this season are at an interval of 21 days till 28 th February of next year. The Rabi season

Fig. 3 The location and index map of Waghad irrigation project

Fig. 2 Flow chart for obtaining

the optimized irrigated area



10/19

thus constitutes 6 rotations. Hot weather season for irrigation purpose starts from 1st March

to 30th June. There are 9 rotations in hot weather season at an interval of 14 days and 4rotations in Kharif at an interval of 21 days. Thus 19 rotations during the year are

considered for this study.

As this project has two canals, each with 19 rotations, total decision variables were 38.

The string of GA thus consists of 38 decision variables (genes).

5 Results and Discussion

The developed model was applied to Waghad irrigation project for obtaining rotation wise

optimum water releases from both the canals of the reservoir. Three cases were considered in

order to explain the utility of GA based optimization, including existing policy. These are:

Case I: The evaluation of existing water release policy.

Case II: The water release policy for existing area but with more rotations by GA model.

Case III: The water release policy for the maximization of total net benefits by optimally

allocating the areas to different crops (without disturbing existing crop) mix by

GA model.

All the three cases consider the same set of crops and same crop mix or proportion. The

crops and crop mix that were considered are those that followed in the Waghad irrigation

Fig. 4 Crop calendar of Waghad irrigation project

Table 1 Rotation wise actual water releases from canals of Waghad irrigation project

Rotation

number

Waghad right bank canal Waghad left bank canal

Rotation period Quantity of released

water (thousand m3)

Rotation period Quantity of released

water (thousand m3)

1 24/11/2006 to 25/12/2006 8428 24/11/2006 to 25/12/2006 2327

2 05/01/2007 to 22/01/2007 6321 05/01/2007 to 22/01/2007 9803 01/2/2007 to 15/02/2007 5267 01/2/2007 to 15/02/2007 857

4 28/03/07 to 15/04/07 8158 21/2/2007 to 3/3/2007 674

5 26/04/2007 to 13/05/07 4533 28/03/07 to 15/04/07 1164

6 29/04/2007 to 13/05/07 919

Total 32707 6921



11/19

project. The purpose of Case I is to evaluate the existing situation i.e. existing water release

policy and hence the areas under different crops that were actually irrigated and rotations

that were actually followed are considered. Case II considers 19 rotations that arerecommended for this region instead of 5 to 6 rotations and optimization by GA was

performed to obtain 19 releases for the areas under different crops that were actually

irrigated. Case III also considers 19 rotations but at the same instance investigates the

possibility of irrigating more area under different crops than the actual ones for obtaining

more benefits with same crop mix by GA. This is performed by proportionally increasing

the area under different crops and obtaining the optimum water release policy and benefits

by GA for each instance and selecting the water release policy and area that provide

maximum net benefits.

Oliveira and Loucks (1997) reported that it is preferable to select a small population size

and allow it to evolve for more generations than to select a larger population and evolve forfewer generations. Large population sizes yield good policies if the algorithm is run for

many generations. Conversely, small population sizes perform well at the initial stages of

the evolution, but their relative performance decreases if the algorithm is run for many

generations. It is reported that the results are sensitive to population size. In this study, the

population size of 30 was considered and the GAwas terminated after 500 generations after

the initial trial run.

Sensitivity analysis was performed to determine the value of crossover and mutation

probability. The most appropriate crossover probability was found to be 0.7 (Fig. 5) for

mutation probability of 0.002. Sensitivity to mutation probability was carried out for crossover probability of 0.7. The value of fitness function (optimal value) decreased above

mutation probability of 0.005 (Fig. 6). The appropriate value of mutation probability was

found to be 0.002.

Fig. 5 Sensitivity analysis for

cross over probability

Fig. 6 Sensitivity analysis for

mutation probability



12/19

5.1 Case I: Evaluation of Existing Water Release Policy

The actual water release policies of 200607 shown in Fig. 7 for WRBC and WLBC were

evaluated. Irrigation was provided in five rotations to WRBC and six rotations to WLBCduring Rabi and hot weather seasons. These rotations were decided on discretion of

irrigation authorities by considering the general crop conditions and are less than the

proposed for the region. This also indicates the need of proper reservoir water release policy

that takes into consideration water availability and the demands on scientific basis. The area

under irrigation in this year was 23% of Irrigable Command Area (ICA) of the project. Total

water released for the purpose of irrigation was 39628 thousand m3 (Fig. 7). The total net

benefits for both the canals were estimated as 118.33 million rupees (M Rs) with simulation

model i. e. evaluation function of GA model. GA optimization model was not run for this case.

5.2 Case II: Water Release Policy for the Existing Irrigated Area

The optimum water release policies for WRBC and WLBC were determined by the

developed model for existing area. Nineteen rotations each from both the canals were

considered for this case. The parameters of GA formulation used for this purpose were:

population= 30, generations= 500, number of tournament selection= 10, cross over

probability= 0.7 and mutation probability=0.002. It was observed that the optimal total

net benefits increased to 140.5 M Rs. The results are presented in Fig. 8. The figure shows

two curves one for average total net benefits and another for maximum total net benefits.

As discussed in earlier sections, the GA operates on a set of solutions rather than singlesolution in each generation. Thus each generation of GA provides a set of solutions called

as population which is 30 in this case. The total net benefits of all 30 solutions were

averaged and shown by average total net benefit curve. The solution that provides the

Fig. 7 Actual water release

policy of right and left bank canal

of Waghad irrigation project

(Case I)

Fig. 8 Benefits of Waghad

irrigation project for existing area

(200607) over successive

generations (Case II)



13/19

maximum benefits amongst all the 30 solutions is shown by maximum total net benefits

curve. This solution is considered as the optimal solution. A number of possible near

optimal solutions at last generation of GA gives the decision makers a flexibility in

selection in different scenarios and this is considered as one of the greatest benefit of GA.

The optimum water release policies for both the canals are shown in Figs. 9 and 10. Total

water used for this case is 27570 thousand m3 which is obtained by summation of all the

releases (Figs. 9 and 10).

Comparison of two policies i.e. actual (Case I) and GA based (Case II) indicates that

more water (39628 thousand m3) was used in less number of rotations (five to six rotations)

in actual policy as compared to less water (27570 thousand m3) in more number of rotations

(nineteen) in GA based policy. In Case-I, water application was more than the requiredquantity. Hence it resulted into deep percolation losses as water holding capacity of the soils

is limited. Similarly the interval between water applications was also prolonged. This

caused deficit irrigation even with more application of water that resulted into less yield and

total net benefits. In GA based policy, number of rotations increased from 6 to 19 which

resulted in to less deep percolation losses even though conveyance losses were marginally

increased. The water application interval in this case nearly matched with consumptive use

and hence with 30% less quantity of water, total net benefits were increased by 19%.

5.3 Case III. Optimal Water Release Policy

In case II, the optimum water release policy was obtained for the presently irrigated area

with the help of GA model. There was saving of water which can be used to irrigate

Fig. 9 Water release policy for Waghad right bank canal for existing area (Case II)

Fig. 10 Water release policy of Waghad left bank canal for existing area (Case II)



14/19

additional area as existing area was only 23% of irrigable command area (ICA). Hence

there is a possibility to increase the total net benefits by increasing the area under irrigation

proportionally of the present beneficiaries by practicing the optimized deficit irrigation

(Gorantiwar and Smout 2003). Therefore the optimal total net benefits were estimated by

successively increasing the area under irrigation with the help of GA model (Fig. 2). The

same existing cropping mix was also considered in this case.

The GA formulation used for this purpose was: population=30; generations=500; no of

tournament selection=10; cross over probability=0.7 and mutation probability=0.002. The

results are shown in Table 2. It is observed from Table 2 that there is gradual increase in

total net benefits till the area under irrigation is up to 50% of ICA. The total net benefitsobtained for irrigated area equal to 50% of ICA is maximum (155.15 M Rs). The average

total net benefits and maximum total net benefits over the generations for the area equal to

50% of ICA are shown in Fig. 11 and corresponding optimal water release policies for

WRBC and WLBC are presented in Figs. 12 and 13 respectively. The results of Case III

indicate that 50% of ICA can be brought under irrigation resulting into 31% increase in

total net benefits compared to Case I. This was possible because the change in irrigated area

provided the flexibility to GA model to release water according to consumptive use for the

optimal benefits.

5.4 Use of Elitist GA

Elitism was introduced in the developed GA model and applied to Case III. Twenty percent

elitism was used in this study. The maximum total net benefits increased to 158.68 M Rs

Fig. 11 Benefits of Waghad

irrigation Project for the

optimized irrigated area

(50% ICA)(Case III)

Table 2 Different irrigable areas and corresponding maximum total net benefits for the existing crop mix

Sr No Area under irrigation (% of ICA) Maximum total net benefits (M Rs)

1 20 135.46

2 25 141.823 30 144.83

4 35 147.12

5 40 149.44

6 45 152.37

7 50 155.15

8 55 150.04

9 60 141.08



15/19

(Fig. 14) compared to 155.15 M Rs by introduction of elitism in GA. The optimal reservoir

operating policies for WRBC and WLBC with elitist GA are presented in Figs. 15 and 16

respectively. The irrigated area, water releases and corresponding benefits for various cases

are presented in Table 3. As stated before in GA based cases the solution that provided the

maximum total net benefits amongst all the solutions of last generation were considered.

5.5 Discussion

It is seen from Table 3, that if the irrigation is provided in more rotations that takes intoaccount the crops, their growth stages and soil, it is possible to increase the total net benefits

by about 19% for the same area that is being currently irrigated. The GA based model has

indicated the possibility of increasing the area under irrigation from 23% to 50% and

increase in total net benefits by 31% by following the approach prescribed in this paper.

Thus the effect of adopting the proposed schedule and increased irrigated area would be to

increase the benefits to the existing farmers. The refinement in GA algorithm by

introducing elitism has the capability to further improve the allocation policies.

The existing water release policy of Waghad Irrigation Project consists of providing 5 to

6 irrigations during Rabi and hot weather season and none or one irrigation in Kharif

season. The number of irrigations are normally decided by the irrigation authorities on the

Fig. 13 Optimum water release policy for Waghad left bank canal for the existing crop mix (Case III)

Fig. 12 Optimum water release policy for Waghad right bank canal for the existing crop mix (Case III)



16/19

basis of general crop conditions. However as discussed in this paper, it is necessary to

match the periods of water delivery with the periods of water requirement and the water

delivery amount must match with the water requirement to minimize the loss of water due

to deep percolation. Therefore there is a necessity to optimize the irrigation interval during

different seasons of a year considering the heterogeneity in crop, soil, climate and

conveyance and distribution losses. Gorantiwar and Smout (2005) worked out these

intervals to be 4, 3 and 2 weeks for Kharif, Rabi and hot weather seasons respectively. The

developed model has the capability to consider this set of irrigation interval and alternative

sets of irrigation interval so that the model could also be used for other regions. The less

number of irrigation tends to apply large quantity of water and the soil may not hold this

amount of water. This leads to additional losses compared to providing the water according

to the water holding capacity of the soil in more number of irrigations. This is the reason asto why the GA derived policy with 19 irrigations provided 19 to 33% more total net

benefits than existing policy.

6 Conclusions

The yields and total net benefits derived from growing different crops in command area of

an irrigation project depend on various factors such as climate, crop growth stage, soil type,

Fig. 15 Water release policy for Waghad right bank canal obtained by elitist GA for existing area (Case III

with elitism)

Fig. 14 Benefits for optimum

water release policy with elitist

GA for the existing area over

successive generations (Case III

with elitism)



17/19

temporal and spatial distribution of water which collectively represents the non linear

phenomenon. In the situation of water scarcity, it becomes imperative to maximize the total

net benefits and find out corresponding water releases. The conventional optimization

techniques have limitations in representing the heterogeneity of the command area. The GA

based model presented in this paper showed the ability to decide the optimum water

releases from the reservoir to the command area by representing the heterogeneity in the

system, by way of evaluating the fitness function that represent the complex heterogeneoussystem appropriately.

The application of GA model to the case study of Waghad irrigation project indicated

that the total net benefits by adopting GA based water release policy could be increased

over the existing water release policy for the same irrigated area by 19%. The GA based

model presented in this study also has the capability to optimize the area under irrigation. It

is found that the area to be irrigated can be increased to 50% and total net benefits by 31%

by using the approach presented in this paper. Introduction of elitism to GA further

increased the total net benefits by 2% as elitism in GA retains better solutions in subsequent

generations. Thus the proposed irrigation schedules enable the existing farmers to increase

their area under irrigation and also increase in benefits.

Fig. 16 Water release policy for Waghad left bank canal obtained by Elitist GA for existing area (Case III

with elitism)

Table 3 Details of various strategies, water use and total net benefits

Sr No Strategy Irrigated area

(% ICA)

Reservoir releases

(thousand m3)

Total net benefits

(Million rupees)

Percentage

increase in

net benefits

1 Actual water release policy 23% 39628 118.33

2 GA based release policy

for actual area

23% 27570 140.5 19%

3 GA based release policy

for optimal area

50% 39117 155.15 31%

4 Elitist GA based release

policy for optimal area

50% 38343 158.68 33%



18/19

References

Ahmed JA, Sarma AK (2005) Genetic algorithm for optimal operating policy of a multipurpose reservoir. J

Water Resour Plng and Mgmt 19(2):145161

Chang FJ, Chen L (1998) Real-coded genetic algorithm for rule-based flood control reservoir management. J

Water Resour Manag 12:185198

Yu-Ming C (1997) Management of water resources using improved genetic algorithms. Comput Electron Agr

18:117127

Cieniawski SE, Eheart JW, Ranjithan S (1995) Using genetic algorithms to solve a multiobjective

groundwater monitoring problem. Water Resour Manag 31(2):399409

Crawley PD, Dandy GC (1993) Optimal operation of multireservoir system. J Water Resour Plann Manag

119(1):117

Dandy GC, Connarty MC, Loucks DP (1997) Comparison of methods for yield assessment of multiple

reservoir systems. J Water Resour Plann Manag 123(6):351358

Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Meth Appl Mech Eng

186(3):11338

Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, UK

Fereres E, Goldfien RE, Pruit WO, Henderson DW, Hagan RM (1981) The irrigation management program:

a new approach to computer assisted irrigation scheduling, Proceedings of irrigation scheduling for water

and energy conservation in the 80s, ASAE, St. Joseph, Mich :p 202207

Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley,

Reading

Goldberg DE, Deb K (1990) A comparative analysis of selection schemes used in genetic algorithms.

Foundations of genetic algorithms, Morgan Kaufman, San Mateo, California: p 6993

Gorantiwar SD, Smout IK (2003) Allocation of scarce water resours using deficit irrigation in rotational

systems. J Irrigat Drain Eng 29(3):55163

Gorantiwar SD, Smout IK (2005) A multilevel approach for optimizing land and water Resour and irrigation

deliveries for tertiary units in large irrigation schemes: 2. application. J Irrigat Drain Eng 131(3):264272

H

nal OA, Altan-Sakarya B, Metin Ger A (2011) Optimization of multireservoir systems by geneticalgorithm. J Water Resour Manag 25:14651487

Jothiprakash V, Shanthi G (2006) Single reservoir operating policies using genetic algorithm. J Water Resour

Manag 20:917929

Karamouz M, Houck MH, Delleur JW (1992) Optimization and simulation of multiple reservoir system. J

Water Resour Plann Manag 118(1):7181

Kuo JT, Cheng WC, Chen L (2003) Multi objective water resources systems analysis using genetic

algorithms -application to chou-shui river basin, Taiwan. Water Sci Tech 48(10):7177

Labadie JW (2004) Optimal operation of multi reservoir systems: state-of-the-art review. J Water Resour

Plann Manag 130(2):9311

Loucks DP, Stakhiv EZ, Martin CR (2000) Sustainable water resources management. J Water Resour Plann

Manag 122(2):4347

Lund JR, Ferreira I (1996) Operating rule optimization for Missouri river reservoir system. J Water ResourPlann Manag 122(4):237295

Michalewicz Z (1992) Genetic algorithms + data structures = evolution programs. Springer, New York

Momtahen Sh, Dariane AB (2007) Direct search approaches using genetic algorithms for optimization of

water reservoir operating policies. J Water Resour Plann Manag 133(3):202209

Kumar N, Raju S, Ashok B (2006) Optimal reservoir operation for irrigation of multiple crops using genetic

algorithms. J Irrigat Drain Eng 132(2):123129

Oliveira R, Loucks DP (1997) Operating rules for multi reservoir systems. J Water Resour Research 33

(4):839852

Sabu P, Panda SN, Nagesh Kumar D (2000) Optimal irrigation allocation: a multilevel approach. J Irrigat

Drain Eng 126(3):149156

Raju S, Kumar N (2004) Irrigation planning using genetic algorithms. J Water Resour Manag 18:163176

Sharif M, Wardlaw R (2000) Multi reservoir systems optimization using genetic algorithms: case study. JComput Civ Eng 14(4):255263

Kuo S-F, Merkley GP, Liu C-W (2000) Decision support for irrigation project planning using a genetic

algorithm. J Agricultural Water Manag 45:243266

Stewart JI, Hagan RM (1973) Functions to predict effects of crop water deficits. J Irrigat Drain Eng 99

(4):421439

Taesoon Kim, Jun-Haeng Heo (2004) Multi reservoir system optimization using multi-objective genetic

algorithms. World Water and Environmental Resour Congress 2004, Salt Lake



19/19

Vedula S, Majumdar PP (1992) Optimal reservoir operation for irrigation of multiple crops. J Water Resour

Research 28(1):19

WALMI (1987) Gravity methods and efficiencies, Water and Land Management Institute, Aurangabad,

Maharashtra, India, Publication no 15.

WALMI (1996) On-farm development works, Water and Land Management Institute, Aurangabad,

Maharashtra, India, Publication no. 12 (fifth reprint)Wardlaw R, Barnes J (1999) Optimal allocation of irrigation water supplies in real time. J Irrigat Drain Eng

125(6):345354

Wardlaw R, Sharif M (1999) Evaluation of genetic algorithm for optimal reservoir system operation. J Water

Resour Plann Manag 125(1):2533

Yang JP, Soh CK (1997) Structural optimization by genetic algorithms with tournament selection. J Comput

Civ Eng 11(3):195200


Genetic Algotitm in Water Management

Documents