6

CHAPTER 2: LITERATURE REVIEW

2.1 RESERVOIR OPERATION

Since the 1960s water resources management policy and practice have shifted to a greater

reliance on improving water use efficiency. Water research teams in many countries

have conclusively demonstrated the value of adopting the modern tool of operations

research or systems analysis for assisting in the development, operation, planning and

management of the water resources project. However, these tools can only assist; they

can not replace the water resource decision making process. Furthermore, some studies

indicate a gap between theories of water resources models and the application of these

models in the real world. There are many analysis techniques and computer models

available in the real world for developing quantitative information for use in evaluating

storage capacities, water allocation, and release policies. Yeh (1985), Wurbs (1996) and

McKinney (1999), in their state-of-the-art review, discuss different optimization

techniques that are used in water resources system analysis at the basin level and

reservoir operation.

This chapter consists of five sections and presents the most relevant research developed

in the last two decades in the optimization of reservoir operation. The first section

introduces the concepts of reservoir operations. The second section presents the ideas

and concepts of main conventional optimization techniques (linear programming,

dynamic programming) and simulation used in this area of water resources planning and

management. The third section speaks about the concepts and application of rule curves

and hedging rule for fulfilling the primary demand with reduction in supply to other

requirements. The fourth section deals with the robust search technique-genetic

7

algorithms for the optimization of reservoir. The fifth section presents the importance of

simulation-optimization model used in the reservoir operation.

2.1.1 Irrigation Scheduling

Good irrigation management is required for efficient and profitable use of water for

irrigating agricultural crops. Irrigation scheduling is dependent on design, maintenance

and operation of irrigation system and availability of water. A major part of any irrigation

management program is the decision-making process for determining irrigation dates

and/or how much water should be applied to the field for each irrigation turn. This

decision-making process is referred to as irrigation scheduling. Efficient scheduling of

irrigation maximizes the production and prevents under and/or over watering of the crop.

Bras et al. (1981) and Rao et al. (1988) have studied the problem of irrigation scheduling

in case of limited seasonal water supply for a single-crop situation. Bishop and Long

(1983) developed a rotational schedule taking travel time into account to improve equity.

Pahalwan et.al. (1984) conducted field experiment during dry season of 1981 and 1982 to

determine the optimal irrigation schedule for summer groundnut in relation to

evaporative demand and crop water requirement at different growth stages. They have

suggested a combination approach for scheduling of irrigation to optimize the irrigation

management. Their combination approach considered the irrigation water to the

cumulative pan evaporation as well as the stage(s) susceptibility of groundnut to soil

moisture deficits.

A number of researchers have addressed the problem of allocation of a limited water

supply for irrigation in a multi-crop environment (Rao et al., 1990; Sunantara and

Ramirez, 1997; Paul et al., 2000; Reca et al., 2001; Teixeira and Marino, 2002;

8

Umamahesh and Raju, 2002; Gorantiwar and Smout, 2003; Smout and Gorantiwar,

2005). Manny irrigation systems throughout the world are operated by distributing water

sequentially amongst a group of users, normally within a tertiary unit. Such rotational

irrigation is typical of small holdings within large irrigation systems and has received

considerable attention, particularly with regard to improving equity (Latif and Sarwar,

1994). Wang et al. (1995) used integer programming to develop a schedule for a canal

whereby the duration of flow at an outlet could be specified by a user. Hill et al. (1996)

presented graphical calendars as a simplified means to provide irrigation scheduling to

farmers in developing-country settings.

Pawar et al. (1997) conducted field experiment to study the effect of scheduling of

irrigation to soybean cultivation during kharif season. Singh and Kandpal (1998)

prepared an irrigation schedule for rainfed cotton crop grown in Central India using the

Irrigation Scheduling Information System (IRSIS : Raes et al. 1988). The crop

evapotranspiration (ETcrop), irrigation dates and amounts were estimated using IRSIS.

Reddy et al. (1999) showed that a time-block model can be used to eliminate the

hypothetical constraint of all outlets having equal discharge. Nixon et al. (2001)

examined the use of genetic algorithm optimization to identify water delivery schedules

for an open-channel irrigation system. They have maximized the number of orders that

are scheduled to be delivered at the requested time and minimizing variations in the

channel flow rate. Tonny et al. (2004) developed two different models to reflect different

management options at the tertiary level for the irrigation scheduling problem using an

integer program solution. Anwar et al. (2004) developed four models to reflect the

different methods in which an irrigation system at the tertiary unit level may be operated

9

using heuristic approach. Hague et al. (2004) developed an irrigation water delivery-

scheduling model to increase the irrigation efficiency for a large-scale rice irrigation

project in Malaysia. They focused on modeling irrigation water delivery schedules

during the main season and off-season of the rice-based project. Water balance approach

is used in which rainfall was considered as a stochastic variable. The computed irrigation

schedules could save 19% and 11% of irrigation water in the main season and off season,

respectively when compared with the traditional irrigation schedules. Srinivasa Prasad et

al. (2006) developed a deterministic dynamic programming model which maximizes the

net annual benefit with optimal cropping pattern and irrigation water allocation. Parhi et

al. (2008) developed irrigation scheduling and the crop water requirement for wheat crop

in an irrigation command in semi-humid tropical region of Orissa, India using water

balance approach. The parameters viz., soil dryness coefficient, site specific crop

coefficient, daily rainfall etc. are considered in the irrigation schedule preparation. Jha

and Singh (2008) developed a methodology for developing optimal allocation of

resources like land, crop and water of Kosi irrigation system in Nepal. A multi-objective

model for irrigation development is presented with integrated use of surface and ground

water resources.

2.1.2 Water balance and Crop management

The management of water resources in irrigation is a fundamental aspect for their

sustainability. The current situation of irrigation throughout the world is characterized by

a decrease in available water resources, especially in arid and semiarid zones. This trend,

which will probably become more aggravated in the future, is due to the reduction in

available water (competition for different users, environmental conditions, global change

10

etc.) and is also caused by progressive deterioration of water quality (various sources of

pollution). Since water prices are progressively increasing, it is necessary to analyze the

factors that affect water uses in order to improve water management for sustainable

agriculture. Worldwide, irrigated agriculture is responsible for more than 80% of water

consumption in arid and semiarid zones. Thus, the improvement of water management in

agriculture should deal with different aspects in a coordinated and integrated way.

Among these aspects, Raman et al. (1992) developed an expert system for drought

management. A linear programming model was used to generate optimal cropping

pattern from past drought experience as also from synthetic drought occurrences for

Bhadra reservoir project, Andhra Pradesh, India.

Mohan (1994) enunciated the usage of fuzzy set theory and its application to water

resource allocation problem. He demonstrated the possible ways of identifying the

membership function and the suitability of fuzzy set approach in the decision making

context with lesser data availability. Prajamwong et al. (1997) developed a software

package called Command Area Decision Support Model (CADSM) to estimate crop

water requirements and to study management options for irrigated areas. Daily water and

salt balances are simulated for individual fields within command areas based on crop type

and stage of development, field characteristics, soil properties, possible ground water

contribution, salinity level. The model can also be applied on a daily time period to

analyse short-term water management issues when daily weather data are available

Pereira and Allen (1999), Tarjuelo and de Juan (1999) highlighted crop irrigation

scheduling, farm irrigation system, available infrastructure for irrigation water transport

and distribution and administrative management. Knowing the high cost of expanding net

11

irrigated area, substantial improvements in irrigation management will be needed to

enhance water productivity (Biswas, 1999). Innovations in both the technological and

policy dimension of water resources management are needed to achieve desired

improvements in irrigation practices and water use decisions (Batcheor, 1999; Biswas,

2000; Kijne, 2001; Plusquellec, 2002; Schultz and De Wrachien, 2002; Tanji and Keyes,

2002; Hamdy et al., 2003). Increasing the value of output generated per unit of water will

contribute to raising rural incomes and enhancing food security in developing countries

(Chaturvedi, 2000; Reidhead, 2001).

Mohan and Jothiproakash (2000) developed fuzzy system modeling for optimal crop

planning for an irrigation system to conjunctively utilize the irrigation water from the

reservoir and ground water acquifer. They have formulated a deterministic linear

programming model and fuzzy linear programming model for Sri Ram Sagar reservoir in

Andhra Pradesh. On comparison, they found that the fuzzy linear programming model

has resulted in an optimal cropping pattern with irrigation release and ground water

pumpage, which can suit the field conditions. Jothiprakash and Mohan (2001) developed

a fuzzy linear programming model for deriving optimal cropping pattern for an irrigation

system under water deficit condition with conjunctive use of surface and ground water

and compared with Linear programming model. They have found that, from the optimal

results the fuzzy linear programming model has resulted in an optimal crop plan with a

degree of truthness of 0.64 taking into account the fuzziness in different variables.

Irrigation will play a critical role in achieving the rate of growth in agricultural

production that is needed to feed the world’s increasing population (Rosegrant and Cai,

2002).

12

English et al. (2002) suggested that the information regarding crop-water requirements

and its impact on the water management decision on crop yields, food security and net

revenue had to be well informed to the farmers. Farmers also need assistance regarding

risk management and the long-term impacts of irrigation practices on soil salinity and

agricultural sustainability. Dennis Wichelns’ (2004) described how public policies

regarding water resources and agricultural production can motivate farmers to consider

scarcity values and off-farm impacts of irrigation and drainage activities. Ortega et al.

(2004) analyzed the effect of distribution uniformity of sprinkler irrigation water (solid

set system). The irrigation depths that maximize the gross margin of four crops in a

semiarid territory in order to determine the best strategy of water use in sustainable

agriculture. In many areas, improvements in water management will generate higher

levels of aggregate production, while also reducing some of the undesirable, long-term

consequences of inefficient irrigation, such as water logging and salimoenization.

2.2 TRADITIONAL OPTIMIZATION TECHNIQUES

2.2.1 Linear programming

The most important optimization techniques used in reservoir operation are linear and

dynamic programming. Linear programming is an operation research technique that has

been widely used in water resource planning and management. Its popularity is due to

the following considerations. Linear programming is applicable to a wide variety of

problems; efficient solution algorithms and computer software packages are available for

applying the solution algorithm. Various generalized optimization programs are

commercially available for solving linear equation with constraints.

13

2.2.2 Dynamic programming

Dynamic programming, developed by Bellman (1957) for dealing with sequential

decision processes, is not restricted by any requirement of linearity, convexity, or even

continuity. Nevertheless, it is restricted to specific forms of the objective function.

Dynamic programming theory and its applications in various fields are covered in depth

in books by Cooper and Cooper (1981), and Denardo (1982). Mays and Tung (1992),

which describe the fundamentals of dynamic programming for the perspective of water

resources planning and management.

Unlike linear programming, for which many general-purpose software packages are

available, the availability of general dynamic programming codes is limited. Most

dynamic programming computer programs have been developed for specific applications.

Dynamic programming is not a precisely structured algorithm like linear programming,

but rather a general approach to solving optimization problems. Dynamic programming

involves decomposing a complex problem into a series of simple sub-problems which are

solved sequentially, while transmitting essential information from one stage of the

computations to the next using state concepts. Several dynamic programming models

have been developed in the field of reservoir operation.

2.2.3 Simulation

The mass curve techniques that are the earliest techniques used to design the reservoir

capacities are the first simulation models used in water resources planning and

management. Rippl (1883) developed a simple and earlier technique for analyzing the

relationship between reservoir inflows, desired draft rate and the storage capacity. This

mass curve technique is known as Rippl’s mass diagram. This mass diagram analysis is

14

still used today by many water resources planners. Different draft rates can be tried with

this model. In this technique, the cumulative inflows and the cumulative desired outflows

are plotted in a time chart. These plots are commonly called ‘mass curves’. The

maximum difference between the ordinates of the inflow mass curve and the outflow

mass curve at a common time gives the minimum capacity of the reservoir. The major

shortcoming of this method is that initial storage influences the minimum storage and the

economic aspect is not taken into consideration.

To overcome these drawbacks, Thomas (1963) developed a numerical technique called

‘Sequent Peak Procedure’. In this technique, the cumulative differences between inflows

and outflow are calculated. If it is desired that no draft deficiency be incurred by the

reservoir, then the cumulative difference should never be negative. The successive peaks

and troughs in-between were located such that the successive peaks are in the increasing

order. Then the minimum storage required to meet the given draft schedule is the

maximum difference among the successive peaks and troughs. This procedure is very

closely related to a linear programming problem where the objective function is to find

optimal capacity. Both the mass curve techniques are applicable to deterministic

hydrologic condition.

A simulation model is usually characterized as a representation of a physical system used

to predict the response of the system under a given set of conditions. The performance of

the reservoir under changing conditions can be analyzed by implementing the

management and operation simulation techniques. The simulation model cannot

generate an optimal solution to a reservoir problem directly. However, when making

15

numerous runs of model with alternate decision polices, it can detect an optimal or near-

optimal solution.

Yeh (1985) mentioned that the concepts inherent in the simulation approach are easier to

understand and communicate compared to other modeling concepts and also with the aid

of a simulation model one can evaluate the consequences of variations in certain model

inputs. A functional model of the decision problem is constructed usually on a computer

and relevant insights are gained through experimenting with different inputs. Scheduling

of water delivery is one of the important parameters and it is a core activity that has a

greater influence on the performance of the system compared to other irrigation activities

(Chambers, 1988).

Hydro-electric power benefits are maximized using constraints of flood control, water

supply, navigation and similar requirements. Typical simulation models associated with

reservoir operation include a mass-balance computation of reservoir inflows, outflows

and changes in storage. They may also include economic evaluation of flood damages,

hydroelectric power benefits, irrigation benefits, and other similar characteristics.

Simulation models are often used with historical period of records or critical period of

records.

Examples of applications of simulation date back to the early 1950s. In 1953 (Hall and

Dracup, 1970), the United States Army Corps of Engineers applied simulation in the

study of a water resource system on the Missouri river. The operational study involved

the simulation of six rivers with the objective of maximizing power generation subject to

the constraints of navigation, flood control and irrigation. Similar simulation studies

were performed on the Nile river basin.

16

The United States Army Corps of Engineers also simulated the Columbia River system,

using its storage dams with river. Some of the examples of simulation models were

HEC-3 and HEC-5; models developed by Hydrologic Engineering Centre (Feldman,

1981), Acres model (Sigvaldason, 1976), WASP (Kuczera and Dimant, 1988) and IRIS

model (IRIS, 1990) are some of the notable models developed for reservoir operation.

Review of generalised reservoir system simulation model is given in Wurbs (1993). The

Acres model was used to determine the reservoir releases in the Trent River basin using

reservoir zoning to represent the priorities of different storage levels in different

reservoirs. An out-of-kilter algorithm determined optimal operation of the system

according to an objective function based on the chief operator’s perception. WASP was

developed for the Melbourne water supply system. The penalty, incurred as a result of

violating 5 specified operating criteria, each with a different severity, is minimized in

order to determine the distribution of water.

Generally, simulation models permit very detailed and realistic representation of the

complex physical, economic and social characteristics of a reservoir system. Simonovic

(1993) used the simulation model for the reassessment of management strategies for

Wonogiri reservoir based on the continuity equation and the set of probabilistic criteria.

The model makes use of a direct search technique for finding minimum required

reservoir capacity. Using the initial storage value, provided by the user, the monthly

operation of the reservoir is simulated. By simulating the reservoir operation under given

inflow and demand conditions, four reliabilities were calculated and compared with the

desired values. Four probabilistic criteria used were 1) reliability of reservoir water

supply 2) yearly reliability 3) yearly vulnerability 4) monthly vulnerability of the

17

reservoir water supply. If these four criteria were not met, the reservoir size was

increased by a step size. The termination criterion for the model was to obtain a value of

optimally required reservoir storage capacity.

Similar simulation studies were performed on the Nile river basin also. Oliveira and

Loucks (1997) defined the operating policies as a set of rules that specify either

individual reservoir target storage volumes or target release.

2.3 RULE CURVES

The simulation analysis essentially requires an operation policy. Generally operation

policies are represented as rule curves. A rule curve is a graphical representation

specifying ideal storage or empty space to be maintained in a reservoir during different

times of the year. Here the implicit assumption is that a reservoir can best satisfy its

purposes if the storage levels or empty spaces as specified by the rule curve are

maintained in the reservoir at the specified time. The amount of water to be released

from the reservoir will depend upon the inflows to the reservoir. The rule curves are

generally derived through operation studies using historic flows or generated flows where

a long term historic-record is not available. Often due to specific conditions like low

inflows, minimum requirements for demands etc. it is not possible to rigorously stick to

the rule curve with respect to storage levels. Few important and commonly applied

operating policies are explained in the subsequent sections. Rule curves are discussed

and analyzed by many researchers (Maass et al., 1962; Stedigner, 1984; Lund and

Ferreria, 1996; and Ahmed, 1996).

18

2.3.1 Standard Operating Policy

The Standard Operating Policy (SOP) is the optimal operating policy with an objective to

minimize the total deficit over the time horizon. The effectiveness of the standard

operating policy is compared with policies derived from deterministic optimization by

Meija et al. (1974).

Standard Operating Policy (SOP) (Stedinger, 1984) is the policy that releases only the

target releases in each period, if possible. If sufficient water is not available to meet the

target, the reservoir empties. If copious water is available, the reservoir will fill and then

spill any excess water. Mathematically this rule can be expressed as,

CDQSifCQSR

CQSDifDR

DQSifQSR

tttttt

ttttt

tttttt

>−+−+=

≤+≤=

≤++=

−−

−

−−

11

1

11

Where Rt = Release at any time t; St-1 = Storage in the reservoir at time (t-1); Qt = Inflow

into the reservoir at time t; Dt = Demand in time t; C = Capacity of the reservoir. A

comprehensive table indicating the development of different models over the years and

the methodologies adopted are presented in Table 2.4.

2.3.2 Hedging Rule

An operating rule that places more penalties on large deficits than small ones is called

Hedging Rule (Maass et al., 1962). Bower et al. (1962) defined the term hedging as “the

complexity of how much water to be withheld from the immediate release made, and

retaining that water in storage for future use”. If the reservoir system manager tries to

meet the demand fully during early months of the critical period, he may incur severe

deficits on later periods. In order to prevent severe deficit in the later period, the

irrigation manager can tolerate some deficit during release periods. If a reservoir has been

19

designed for a lower safe yield than the yield it is currently being used to provide,

rationing could become a common experience. At the time of rationing, it is to be

determined that the quantities or some values that should be used to trigger rationing to

prevent larger deficit in the later period. The development of realistic rule for reducing

demand and therefore draft from the reservoir is based on the answers to the following

questions: (1) At what time and at what level of storage does the rationing begin? (2)

How much demand and therefore the draft are to be reduced during each time period?

Houck et al. (1980) and Neelakantan and Pundarikanthan (1999, 2000) used the reservoir

storage as a trigger for operating rules. The total available water which consists of

reservoir storage plus inflow can be used as a prompt to start hedging (Bayazit and Unal,

1990; Srinivasan and Philipose, 1998). Shih and Revelle (1994, 1995) mentioned the

complexity of simple choice of releasing the water or storing the water for future use due

to uncertain future inflows and nonlinear economic benefits for released water. Hill et al.

(1996) presented a graphical calendar as a simplified means to provide irrigation

scheduling to farmers in developing – country settings.

Neelakantan and Pundarikanthan (1999) developed a simulation optimization

methodology for optimizing the multiple hedging rules for the operation of drinking

water reservoir, by linking the simulation model to the optimization model. Ming et al.

(2003) developed a guideline for reservoir release using mixed integer linear

programming model that considers both reservoir rule curves and hedging rules.

Draper and Lund (2004) demonstrated that the optimal hedging policy for water supply

reservoir operation depends on a balance between beneficial release and carryover

20

storage values. You and Cai (2008 a&b) described a method for integrating hedging

policy with stochastic simulation processes for reservoir operations.

2.4 GENETIC ALGORITHM

Genetic algorithm (GA), invented by Holland (1975), have emerged as practical, robust

optimization and search methods. Goldberg (1989) describes genetic algorithm (GA) as

a stochastic numerical search method based on the natural genetics and natural selection.

They combine the concept of the survival of the fittest with genetic operators extracted

from nature to form a robust search mechanism. Excellent descriptions of GAs and

subsequent developments can be found in Goldberg (1989) and Forrest (1993). Any

nonlinear optimization problem without constraints is solved using GAs involving

basically three tasks, namely, coding, fitness evaluation and genetic operation. GAs differ

from conventional optimization and search procedures in four ways:

1. GAs work with a coding of the parameter set, not the parameter themselves.

2. GAs search from a population of solutions, not a single solution.

3. GAs use payoff information (objective function), not derivatives of other

auxiliary knowledge.

4. GAs use probabilistic transition rules, not deterministic rules.

The decision variables for the given optimization problem are first identified. These

variables are then coded using binary coding into string like structures called

chromosome. The length of the chromosome depends on the desired accuracy of the

solution. The decision variables need not necessarily have the same sub string length

(Deb, 1995). Corresponding fitness function is next derived from the objective function

and is used in successive genetic operations. If the problem is for maximization, fitness

21

function is taken as directly proportional to the objective function. The fitness function

value of a string is known as the string’s fitness. Once the fitness of each string is

evaluated, the population is operated by three operators, viz., reproduction, crossover and

mutation for creating new population of points. In reproduction, good strings are selected

to form a mating pool.

An important characteristic of GA is the coding of the variables that describe the

problem. The most common coding method is to transform the variables to a binary

string of specific length. If the problem has more than one variable, a multivariable

coding is constructed by concatenating as many single variables coding as the number of

the variables in the problem. Each variable may have its own length corresponding to the

minimum and maximum possible values that the variable can take (Wardlaw and Sharif,

1999). GAs have had little application in reservoir system optimization; however, in the

last 10 years water resources researches started to use this tool successfully in many

reservoir systems around the world.

2.4.1 Water Management using GA

Oliveira and Loucks (1997) used a GAs to evaluate operating rules for multireservoir

systems, they demonstrated that GAs can be used efficiently to identify effective

operating rules and the focus was on the use of genetic search algorithms to derive these

multireservoir operating policies. The GAs used real-valued vectors containing

information needed to define both system release and individual reservoir storage volume

targets as function of total storage in each of multiple within-year periods. The proposed

GAs was applied to a reservoir system used for water supply and hydropower.

Significant benefits were perceived to lie in the freedom afforded by GAs in the

22

definition of operating policies and their evaluation. Wardlaw and Sharif (1999)

explored the potential of several alternative GAs formulations in application to four

reservoir systems, deterministic, finite-horizon problem. This paper enunciates the

potential use of GAs in real-time reservoir operation with stochastic inflow forecasts.

The problem addressed here differs from that considered by Oliveira and Loucks (1997),

who were concerned with the optimization of parameters in operating policies rather than

with deterministic real-time reservoir releases. Sharif and Wardlaw (2000) applied GA

for the optimization of multi-reservoir system (ten-reservoir problem) in Indonesia

(Brantas Basin), by considering the existing development situation in the basin and two

future water resource development scenarios and proved that the GA was able to produce

solutions very close to those produced by dynamic programming. They mentioned that

the problem is complicated not only in terms of size, but also because of many time-

dependent constraints on storage. The purpose of applying GAs to this kind of problem

has been to demonstrate that the technique is capable of addressing large problems.

Furthermore complexity introduced through nonlinearities in any part of the system

would not present any difficulties for the GAs approach, and this is a particular strength

of this technique. Conclusions of this research demonstrated that GAs provides robust

and acceptable solutions to the multi-reservoir, deterministic, finite horizon problems,

and can reproduce the known global optimum. The results obtained indicate that there is

potential for application of GAs to large finite-horizon multi-reservoir system problems,

where the objective function is complex and other techniques are difficult to apply. A

significant merit of the GAs approach is that no initial trial release policy is required.

The approach is easily applied to nonlinear problems and to complex systems. Another

23

conclusion found in this study is that GAs will generate several solutions that are very

close to the optimum, and this gives added flexibility to an operator of a complex

reservoir system.

Tung et al. (2003) applied genetic algorithm to optimize operation rules and applied to

the LiYuTan Reservoir in Taiwan. The designed operation rules were operation zones

with discount rates of water supply. The results indicated that operation zones optimized

had smaller shortage indices and lower average deficits. Ponnambalam et al. (2003)

developed soft computing based tools including fuzzy inference systems (FIS), artificial

neural networks (ANN), and genetic algorithms (GA)s to tackle the minimization of

variance of benefits from reservoir operation. Akter and Simonovic (2004) applied a GA

approach to solve a reservoir system optimization problem with nonlinear penalty

functions. Two kinds of uncertainties associated with reservoir operation were addressed

in this study: firstly the vagueness in defining the penalty functions; and secondly the

imprecise definition of the release target value. Fuzzy set theory was applied to represent

these uncertainties.

Kim and Heo (2004) applied multi-objective GAs to optimize multi-reservoir system of

the Han river basin in South Korea. A curve identifying the population points that define

optimal solutions was derived. It was reported that GA multi-objective has limited

application in multi-reservoir system optimization. Jothiprakash and Shanthi (2006)

developed a GA model to derive operational policies for a multi-purpose reservoir. The

objective was to maximize the irrigation releases thereby reducing the square of the

irrigation deficit. Since the rule curves were derived through random search it is found

that the releases are same as that of demand requirements. Xia et al., (2005), Chen and

24

Chang (2007) and Ahmadi et al., (2010) used GAs in their work for the optimal reservoir

dispatching. Mohan et al. (2009) reviewed the application of genetic algorithm in water

resources.

2.4.2 Comparison of GA with linear programming

Cai et al. (2001) solved nonlinear water management models using a combined genetic

algorithm and linear programming approach. They stated that gradient-based nonlinear

programming methods can solve problems with smooth nonlinear objective and

constraints. However, in large and highly nonlinear models, these algorithms can fail to

find feasible solutions, or converge to local solutions which are not globally optimal.

Evolutionary search procedures, in general, and GAs specifically, are less susceptible to

the presence of local solutions. However, GAs often exhibit slow convergence,

especially when there are many variables, and have problems finding feasible solutions in

constrained problems with narrow feasible regions.

In this work, they describe strategies for solving large nonlinear water resources models

management, which combine genetic algorithms with linear programming. This GAs and

LP approach was applied to two nonlinear models; a reservoir operation model with

nonlinear hydropower generation equation and nonlinear reservoir topologic equation,

and a long-term dynamic river basin planning model with a large number of nonlinear

relationships. For large instances, the GAs and LP approach found solutions with

significantly better objective values.

2.4.3 Comparison of GA with dynamic programming

Esat and Hall (1994) showed the significant potential of GAs in water resources systems

optimization, and clearly demonstrated the merits of GAs over standard dynamic

25

programming techniques in terms of computational requirements. This paper used GAs to

solve the four-reservoir problem. The objective was to maximize the total net benefits

from power generation and irrigation water supply subject to constraints on storages and

releases from the reservoirs.

Fahmy et al. (1994) also applied a GAs to a reservoir system, and compared performance

of the GA approach with that of dynamic programming. They concluded that GAs had

potential in application to large river basin systems. Also, they have investigated the

potential of a GAs based technique to optimize the operation of a complex water resource

problem. Two different optimization techniques were applied to a simple water resources

problem namely a dynamic programming model and GAs model. They found that there

was an increase in complexity as the problem grew when dynamic programming was

used. The GAs approach experienced a much smaller increase in calculation time. The

GA was able to guide the search to better operating strategies, demonstrating the potential

of GAs to optimize the operation of realistic systems models when they are available.

Huang et al. (2002) developed genetic algorithm-based stochastic dynamic programming

(GA-based SDP) to cope with the dimensionality problem of a multiple-reservoir system.

From the results it was observed that though the employment of GA-based SDP may be

time consuming as it proceeds through generation by generation, the model can overcome

the “dimensionality curse” in searching solutions.

Ahmed and Sarma (2005) developed a GA model for deriving the optimal operating

policy and compared its performance with that of stochastic dynamic programming

(SDP) for a multi-purpose reservoir. The objective function of both GA and SDP was to

minimize the squared deviation of irrigation release only. The irrigation releases rules

26

were assumed as piecewise linear functions, and based upon this number of linear rule

functions four policies were developed using GA model. It was found that GA model

released nearer to the required demand and concluded that GA model is advantageous

over SDP model in deriving the optimal operating policies.

Chiu et al. (2007) and Li and Wei (2008) proposed a novel approach for optimizing

reservoir operation through a hybrid evolution algorithm, i.e. genetic algorithm with

simulated annealing. In the hybrid search procedure, the GA provides a global search

and the SA algorithm provides local search. From the analysis of results it was found the

hybrid GA-SA conducts parallel analyses that increase the probability of finding an

optimal solution while reducing computation time.

A comprehensive table indicating the development of GA over the years and the

methodologies adopted are presented in Table 2.5.

2.5 COMBINED SIMULATION-OPTIMIZATION MODEL

The simulation model may not directly find the best operation policy. The simulation

model has to be operated with different combinations of operating decision variables and

the policy that appears to perform best has to be selected. However, when there are

several decision variables, this kind of selection process could be extremely time

consuming, even on fast computers. Therefore, it can be realized that a more efficient

procedure is needed for systematically finding the ‘best’ of at least the ‘near best’

operating policy among the many possible alternative combinations. By combining

simulation and optimization, there is greater likelihood of finding optimal policy without

having to consider all possible combinations of alternatives.

27

Most of the times, the optimization problems in water resources management do not

oblige the mathematician by changing into analytically solvable type. The search

algorithms provide a mechanism to systematize and automate the series of iterative

executions of the simulation model required to find a near optimum decision policy.

Much research has been done in the past four decades and scores of procedures, methods

and algorithms have been suggested with the sole object of making the successive steps

converge to the objectives as rapidly as possible. This subject is very closely related to

the numerical solution of nonlinear equation.

Gate et al. (1992), Gate and Alshaikh (1993) and Alshaikh and Taher (1995) used

simulation-optimization model for the design of hypothetical irrigation canal structures.

They used Colorado State University Water Delivery Model for simulation and Hooke

and Jeeves algorithm for optimization.

Simonovic (1992) presented a reservoir simulation-optimization model that makes use of

a direct search technique for finding the minimum required capacity, as an example to

show how the systems approach may respond to practical needs of a water resources

engineer. He suggests that such combination of simulation and optimization will reduce

the gap between theory and practice in the reservoir operation studies.

Majority of the literatures in reservoir operation, irrigation scheduling and optimum crop

planning spell out the different models and methodologies to be adopted to achieve the

desired objective. In the reservoir operation, various models are developed to achieve the

optimal operation of reservoir with minimum deficit. In the irrigation scheduling,

irrigation release dates and its duration is estimated in the crop period based on various

parameters. In the optimum crop planning, area of the different crops (crops which are

28

regularly cultivated in the command area) to be cultivated with the available storage

position and release policy is ascertained by using different models. But the adoption of

a particular type of model and methodology for the chosen system is highly system

specific. It is understood from the literature survey that there exist a research gap in the

crop calendar adjustment of crops that are cultivated in the system. Hence the objective

of this thesis is set to adjust the crop calendar of the crops, which are cultivated in the

command area. The chosen system, Sathanur irrigation system is a unique water deficit

system in which the crop cultivation is started after the end of rainfall season. Hence in

this thesis, crop calendar adjustment of crops cultivated in the Sathanur command area is

attempted using simulation-optimization method.

29

Table 2.4 Development of various models and methodologies adopted over the years.

Sl. No. Author & Year Heading Location

Areal extension

Km2

Optimization method

Nature of Objective function

No. of objective function

Parameter Optimised

No. of crops consi-dered

1 Mohan & Keskar 1991

Reservoir Operation

Bhadra reservoir 938.8 Goal

programming Minimize 2

1. Deviation from storage target. 2. Deviation from release target

NA

2 Ramesh & Simonovic 2002

Reservoir Operation NA NA Simulated

annealing Maximize 1 Release & benefit NA

3 Teixeria & Marino 2002

Reservoir Operation NA NA Forward DP

Maximize (Two models) 1.Interseasonal 2. Intraseasonal

1 Net benefit 2

4 Ponnambalam et al 2003

Reservoir Operation NA NA FIS, ANN &

GA Minimize 1 Variance of benefit from Reservoir

NA

5 Mohan &

Jothiprakash 2003

Reservoir Operation

Sriram Sagar reservoir Andhra Pradesh

3921 LP

Optimisation Simulation

Maximize 1 Net benefit 8

6 Vasan &

Srinivasaraju 2004

Reservoir Operation

Bisalpur Project

Rajasthan 767 DE & LP Maximize 1 Net benefit 9

30

7 Nageshkumar &

Janga Reddy 2006

Reservoir Operation

Hirakud reservoir 2640.2 Ant colony

optimisation

Minimize, Minimize & Maximize

Multi objective

Flood risk Irrigation deficit Hydropower production

NA

8 XIAO Feipeng et al. 2009

Reservoir Operation

Sichuan Province NA DE Maximize Multi

objective NA NA

9 Regulwar & Kamodkar 2010

Reservoir Operation

Jayakwadi reservoir Stage II,

Maharashtra

NA FLP (3 models) Maximize 3

1. Release for Irrigation 2. Hydropower 3. Degree of statisfaction or truthness

NA

10 George Kuczera & Glen Diment

1988

Irrigation Scheduling

Melbourne City NA WASP

Network LP Minimize 1 Cost flow NA

11 Mansingh & Kandpal 1998

Irrigation Scheduling Nagpur NA

IRSIS (Water requirement of crop & Irrigation

Scheduling)

NA NA NA 1

12 Yen & Chen 2001

Irrigation Scheduling

Peikangchi Taiwan NA LP Maximize &

Minimize 2

1. Net benefit 2. Right of water usage or Purpose of water usage

NA

13 Jothiprakash & Mohan 2002

Irrigation Scheduling

Lower Bhawani Reservoir

Project

837.7 LP Maximize 1 Crop yield 5

31

14 Mohan & Magesh 2004

Irrigation Scheduling

Bhandra reservoir NA LP Maximize 1

Total annual hydropower production

NA

15 Srinivasa Prasad et al. 2006

Irrigation Scheduling

Nagarjuna Sagar Right

Canal 4500 Deterministic

DP Maximize 2

1. Seasonal relative yield 2. Total annual benefit

9

16 Raman et al. 1992

Crop Planning &

Management

Bhadra reservoir 938.8 LP BDD

expert system Maximize 1 Total area under irrigation 4

17 Mohan &

Jothiprakash 2000

Crop Planning &

Management

Sriram Sagar reservoir Andhra Pradesh

3690 LP & FLP Maximize 2

1. Net benefit from reservoir. 2. Degree of satisfaction

Kharif -6

Rabi - 6

18 Jothiprakash & Mohan 2006

Crop Planning &

Management

Lower Bhawani Reservoir

Project

837.7 LP & FLP Maximize 1

1. Net benefit from reservoir. 2. Degree of satisfaction

5

19 Madan Mohan Jha & Ranvir Singh 2008

Crop Planning &

Management

Kosi Irrigation System Nepal

135 Multi

Objective Model

Maximize 3

1. Net benefit 2. Nutrition requirement (Protein & calories requirement) 3. Total irrigated crop area

7

32

Table 2.5 Development and methodologies of GA over the years

Study No.

Author & Year of

Publish of the study

Study Location(s)

Areal extent

of study

(Km2 )

Time Step

Data Type

Optimi- zation

method

Para- meter opti- mised

Selection type

Pop. Size

No. of gen.

Cross over type

Muta- tion type

Prob. of Cross over

Prob. of Muta tion

String represen Tation

1 Wardlaw and

Sharif (1999)

hypothetical reservoirs NA NA

hypo thetical

data

Real coded multi

objective GA NA

Tourna-ment selection

100 500 Uniform non uniform 0.7 0.02 Real

2 Sharif and Wardlaw (2000)

Brantas Basin, East

Java 12000 mont

hly Real time

Real coded multi

objective GA NA

Tourna- ment

selection NA 1000 NA NA NA NA Real

3

Srinivasa raju and Nagesh

kumar (2004)

Sri Ram Sagar Project,

Andhra Pradesh

1781 Monthly

Real time Simple GA NA NA 50 200 Uniform

Uniform 0.6 0.01 Binary

4 Akter and Simonovic

(2004)

Green reservoir in Kentucky,

USA

NA daily Real time

Fuzzy Multi obj GA

NA Tourna-

ment selection

NA NA Uniform non uniform 0.7 0.02 Real

5 Ahmed &

Sarma (2005)

Pagladia multipurpose

reservoir

NA

Monthly

Real time Simple GA NA Random

generation NA 5000 Single point Random 0.8 0.05 Real

6 Reis et. Al., (2005)

Hypothetical system NA yearly

hypo -thetical

data

Hybrid GA-LP NA

Roulette wheel

selection 30 1500

Single point arith-

metic

Uniform 0.7 1/string length Real

33

7 Xia et al. (2005)

Hypothetical system NA Mont

hly

hypo -thetical

data Simple GA NA

Fitness based

selection 100 230 Uniform Uniform 0.75 0.05 Real

8 Jyothiprakash and Shanthi

(2006)

Pechiparai Reservoir

System in the Kodaiyar

river basin, Kanyakumari

1533 monthly

Real time

Simple Binary

GA NA

Roulette wheel

selection 150 175 Uniform Modified

uniform 0.76 0.02 Binary

9 Reddy and

Kumar (2006)

Badra reservoir

Karnataka NA NA Real

time Multi obj

GA NA NA 200 1000 Simu- lated

binary

poly nomial 0.9 0.03 Real

10 Nageshkumar

et al. (2006)

Malaprabha reservoir

Karnataka 12.9

10 days perio

ds

Real time Simple GA NA NA 10 20 Uniform NA 0.8 0.05 Real

11 Chiu et. Al (2007)

Shihmen Reservoir,

Taiwan 1163 yearly Real

time Hybid

GA-SA NA Proportio- nate 300 30 BLX-α Jump 0.8 0.05 Real

34

12 Chen and

Chang (2007)

Tan-Shui River basin

reservoir system

2762 daily Real time

Hyper cubic distributed

GA NA Ranking 100 5000

Blend (BLX-

0.5) Gaussian NA NA Real

13 Chang (2007)

Shihmen Reservoir,

Taiwan 1163 yearly Real

time Penalty type

GA NA Roulette wheel

selection NA NA

Single and

Multi point

Jump NA NA Real

14 Li and Wei (2008)

Wujiang River, China 87,920 mont

hly Real time

Hybid GA-SA NA

Weighted roulette wheel

100 150 Uniform & non

uniform

Uniform & non

uniform 0.75 0.05 Real

15

Seema Chauhan & Shrivastava

(2008)

Sondur reservoir

Chhattisgarh India

122.6 Monthly

Real time

GA model with

preference based

approach

NA Roulette wheel

selection 60-120 1000 Single

point Random 0.75-0.9 0.01-0.1 Real

16 Vasan and

Raju (2009)

Mahi Bajaj Sagar Project,

Rajastan 800 mont

hly Real time

Real coded multi

objective GA NA Tournamen

t selection 1000 NA NA Random by gene 0.85 0.01 Real

17 Pinthong et

al. (2009)

Pasak Jolasid Dam,

Thailand 4245.5 Mont

hly Real time

Hybrid GA-Neurofuzzy computing

NA Roulette wheel

selection 48 10 Single

point Random 0.8 0.01 Real

18 Jotiprakash and Shanthi

(2009)

Perunchani reservoir

Tamilnadu Mont

hly Real time

Comparison of SDP and

GA NA

Roulette wheel

selection 150 175 Uniform Modified

uniform 0.76 0.02 Real

19 Mohite and

Narulkar (2010)

Pathanpur reservoir 5312 Mont

hly Real time

Hybrid GA with

Quadratic Program-

ming

NA NA 500 1000

Probability

distribution

Self adaptive chaotic

0.75 0.002 Real

35

35

2.6 MODEL ADOPTED IN THE PRESENT RESEARCH WORK

The present research work is carried out on Sathanur reservoir located in Sathanur

village, Thiruvannamalai district in Tamilnadu state. It is one of the unique irrigation

systems in which the crops are cultivated in the post monsoon period in the direct

command. The water received in the monsoon period is stored in the reservoir and used

for cultivation during the post monsoon season. The Sathanur irrigation system has

multiple constraints and riparian rights. Models like linear programming, dynamic

programming and their variance work under rigid framework and it is very cumbersome

to make the model flexible to accommodate multiple constraints for more realistic

modeling. Hence heuristic models viz., genetic algorithm is highly suited to optimize the

reservoir operation, as it is highly flexible. In recent past, genetic algorithm - one of the

most often used optimization tools, is used by many researchers for its efficiency in fast

convergence to optimal solution. Simulation model is the best model which has to be

operated with different combinations of operating decision variables to obtain the best

policy. But the existence of several constraints and decision variables makes the selection

process of decision variable extremely time consuming, even on fast computers. For

selecting the best operating decision variables that control the performance of the best

policy, optimization techniques have to be used. In the present research work, heuristic

model namely GA is used for finding the operating decision variables. Hence in the

present research work, a combined water balance simulation-optimization model is

adopted to find the best crop calendar of the paddy crop which fetch the farmers

maximum benefit from the cultivation. The GA optimization is the outer driven model

and water balance simulation model is the inner one.