ASSESSMENT OF LP AND GA AS RESERVOIR SYSTEM ANALYSIS TOOLS

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 9, Issue 11, November 2018, pp. 295–303, Article ID: IJCIET_09_11_029
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=11
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
ASSESSMENT OF LP AND GA AS RESERVOIR
SYSTEM ANALYSIS TOOLS
Anil S. Parlikar*
Research Scholar, Dept. of Civil Engg, S.G.G.S.I.E. & T. Nanded, Maharashtra, India
P. D. Dahe
Professor, Dept. of Civil Engg, S.G.G.S.I.E. & T. Nanded, Maharashtra, India
Corresponding author*
ABSTRACT
A reservoir is a huge manmade structure constructed for a number of reasons. It
uses natural water resources and helps in the development of a society. The quantum
of water in a reservoir is a function of the hydrologic characteristics of the region. An
efficient planning and operation of a reservoir is a skill of the water planner. The
works done by researchers in the system analysis of a reservoir are discussed in the
present paper. The most appreciated linear programming (LP) and genetic algorithm
(GA) are studied in the context of system analysis of Urmodi Reservoir in
Maharashtra, India. The objective function is set to minimize the sum of the squared
irrigation demand deficit. Results show that these tools seem to be versatile in nature
and efficiently adopted for reservoir operation purpose.
Keywords: Reservoir system analysis, linear programming, optimization, genetic
algorithm, Urmodi Reservoir
Cite this Article: Anil S. Parlikar and P. D. Dahe, Assessment of LP and GA as
Reservoir System Analysis Tools, International Journal of Civil Engineering and
Technology, 9(11), 2018, pp. 295–303.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=11
1. INTRODUCTION
The economic development of a nation depends mainly on the optimal use of water
resources. The fast growing population cause stress on water resources. The use of ground
water reserves for these purposes results in alarming decrease in it. Therefore, concerns have
grown over the optimal use of surface water. A number of dams and reservoirs are being
planned and operated to cater various requirements of the society.
Many researchers have discussed the reservoir system analysis problem in length.
Techniques involved for studying this crucial problem involve linear programming (LP), non-

Assessment of LP and GA as Reservoir System Analysis Tools
linear programming (NLP),dynamic programming(DP),evolutionary computation, artificial
neural networks(ANN), fuzzylogic, simulation technique, etc. Since last some decades, the
basic tools adopted in planning, design and operation of reservoir systems analysis are
classified into two categories-optimization and simulation. Optimization includes a diverse
set of techniques that preferably include linear programming and dynamic programming.
Simulation gives a better representation of the reservoir system and is based on trial and error
to identify near optimal solutions. However, the configuration of the system, nature of
objective function, constraints involved, availability of data are the deciding factors to choose
the technique. An emphasis on optimization methods in reservoir system analyses is given by
Yeh(1985).
A linear programming (LP) irrigation planning model was developed for the evaluation of
irrigation development strategy and applied to Sri Ram Sagar Project, Andhra Pradesh, India
(Raju K S). The system analysis of tank irrigation was studied in context with crop staggering
(Mayya et al.1987).The uneven distribution and insufficient rainfall during the initial crop
season develop stress in plants. The effect of these factors on the optimal use of irrigation
potential of a minor irrigation tank system was studied by developing a linear programming
model. A linear optimization model was developed to study the impact of lake evaporation
and rainfall on optimal reservoir capacity and water yield (Loaiciga et al.2002).The model
was applied to the Santa Ynez river basin of central California. A detailed study about yield
models was done and applied to a system of eight reservoirs in the upper basin of the
Narmada River in India (Dahe et al.2002).A yield model being an implicit stochastic linear
programming (LP) model that incorporates several approximations to reduce the size of the
constraint set needed to describe reservoir system operation and to capture the desired
reliability of target releases considering the entire length of the historical ﬂow record. The
basic yield model was extended and presented a multiple-yield model for a multiple-reservoir
system consisting of single-purpose and multipurpose reservoirs. The Integrated Reservoir
Yield Model (IRYM) was applied to a multiple reservoirs system consisting of two major and
four medium reservoirs of Maner sub-basin of the Godavari river basin(Shreshtha,2009).The
model was proposed to estimate the optimal annual multi–yields of predefined reliabilities
and the optimal crop plan.A comprehensive study was carried out for deterministic
distribution of future water storage shortages based on known existing demands and the
historical data (Sharma et al.2011).The study aimed at maximizing the annual safe reservoir
yield. The optimization-simulation models were used to study the systems analysis of a water
resources system (Ghassan et.al. 2013).Two linear programming models–complete
optimization and simplified optimization- were developed for estimating the maximum safe
yield for the Donkan dam in Iraq- a single reservoir system with allowable deficit with 75%
dependability for a year. An LP-based yield model (YM) has been used to re-evaluate the
annual yield available from the reservoirs for irrigation (Pattewar et al.,2013).The study
involves extension of the basic yield model and presents a yield model for a multiple-
reservoir system consisting of single-purpose reservoirs.
A genetic algorithm (GA) is great for finding solutions for complex problems like water
resources system analysis. The GA is an optimization approach based on Darwinian natural
selection process that combines the concept of survival of the fittest with natural genetic
operators. GAs use probabilistic transition rules and not the deterministic rules. A stochastic
simulation model embedded genetic algorithm model was developed for searching the
optimal rule curves (Kangrang, 2008).Single and multi-reservoir systems were applied to
assess the efficiency of the proposed technique. The study concluded that the stochastic
simulation model embedded genetic algorithm provided the optimal rule curves as
considering the risk of reservoir operation. The Sondur reservoir system was studied with two

Anil S. Parlikar and P. D. Dahe
objectives of the system. Genetic Algorithm formulation with preference based approach was
used to derive optimal operating policies (Chauhan et al., 2008). AGA model was developed
for optimum reservoir operation (Mathur et al,2009). The objective of the study was to
minimize the squared deviation of monthly irrigation demand deficit along with squared
deviation of mass balance equation. The optimum releases from the reservoir considering
heterogeneity of the command area and responses of the command area to the releases were
studied (Garudkar et al.,2011).An optimization model was developed for the reservoir
releases based on elitist GA approach considering the heterogeneity of the command area and
applied to Waghad irrigation project in upper Godavari basin of Maharashtra, India. A
genetic algorithm (GA) and a backward moving stochastic dynamic programming
(SDP)model was developed for derivation of operational policies for a multi-reservoir system
in Kodaiyar River Basin, Tamil Nadu, India (Jothiprakash et al.,2011). A genetic algorithm
(GA) model was developed and used for optimizing the allocation of water resources within a
complex multiple reservoir system located in Tunisia (Mohamed et al.,2011). An optimal
operating policy and optimal crop water allocations from an irrigation reservoir were studied
by using genetic algorithm (Nagesh kumar,2006).A comparative study was undertaken by
developing two models - Genetic Algorithm (GA) model and Linear Programming (LP)
model to be applied to real-time reservoir operation in an existing Chiller reservoir system in
Madhya Pradesh, India (Azamathulla,2008).The model formulation was based on the
conceptual model for soil moisture accounting and the reservoir storage continuity
relationships. In the present work, a study of linear programming and genetic algorithm is
done in context with the reservoir system analysis.
2. MODEL FORMULATION AND APPLICATION
The objective function of the present study is to minimize the sum of the squared irrigation
demand deficit. Mathematically, the objective function is presented as
K = Minimize ∑ ( ) (1)
Where Rel t = Release in the month„t‟; Dem t = Demand in the month„t‟
The fitness function (1) is subjected to the following constraints
2.1. Mass - balance constraint
The relationship between storages of successivetime periods in a year is given by mass –
balance constraint equation. It is given by
S t+ It -Rel t- Spt–Et= St+1 t=1 12 (2)
Where S tandSt+1 =Initial and final storages in the month„t‟; Spt=Spilled over quantity;
Et= Monthly Evaporation loss; It =Monthly inflow into reservoir
2.2. Active storage volume capacity
The storage in a time period should be less than active storage volume capacity. It is given by
S t ≤ S max∀ t (3)
And St≥ S min
S max =Max. reservoir capacity; S min= Min. reservoir capacity

2.3. Release constraint
Rel t ≤ Dem t ∀ t (4)
2.4. Surplus constraints
Spt = S,t+1 – S max if S,t+1≥ S max (5)
=0 if S,t+1≤ S max
2.5. Evaporation loss constraints
Evaporation loss in a month is the product of evaporation depth in that month and the average
water spread area during that month. The linear programming method uses the linear
relationship between the water spread area and the reservoir storage, while GA uses a
nonlinear relationship between them.
3. APPLICATION OF GA
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. Any
nonlinear optimization problem is solved using GAs involving basically three tasks, namely
coding, fitness evaluation and genetic operation. GAs differs from conventional optimization
and search procedures in four ways:
 GAs work with a coding of the parameter set, not the parameter themselves.
 GAs search from a population of solutions, not from a single solution.
 GAs use payoff information (objective function), not derivatives of other auxiliary
knowledge.
 GAs use probabilistic transition rules, not deterministic rules.
Figure 1 Typical flowchart of GA

In the present GA model, the number of generations is used as the stopping criteria. As an
initial search, the release is determined by considering population of 20 chromosomes, 60%
crossover probability, 0.1% mutation probability and 20 numbers of generations. After
performing the sensitivity analysis, the best parameters of GA are fixed.
4. APPLICATION OF LP
Linear Programming is the mostly preferred tool for the system analysis of a
reservoir.Although the reservoir operation is a complex task to deal with, however, Linear
Programming (LP) technique is adopted to facilitate the preliminary studies of reservoir
operation to decide the release policies. In the case study, a historical 33 years (1975- 2007)
inflow data is used. The mean monthly inflows were used for solving the objective function.
In LP model, the objective functions as well as constraints are considered to be linear. The
objective function used in the present study is the maximization of the sum of monthly
releases.
i.e. Max. ∑ Rt ( 6 )
The objective function is subjected to continuity constraints similar to presented in eq.
(2).
i.e. S t+ -Rel t- Spt–Et= S,t+1 t=1..12 (7 )
Also, the objective function is subjected to active storage volume constraint, release
constraints, surplus constraints and the evaporation loss constraints. The evaporation loss is
determined by approximating the reservoir storage and area by a straight line (Fig.2) above
the dead storage level. It is the product of evaporation rate during a month and the water
spread area.
Figure 2 Surface Area versus storage volume
The evaporation loss is given by
Et= Aoet + m et[(S t + S,t+1)/2] (8)
Where, Aois the surface area at the dead storage level
etis the evaporation rate during a month
m is the slope of the straight line of reservoir storage and surface area

5. SYSTEM DESCRIPTION
The system considered for the study is Urmodi reservoir in Krishna Basin in
Maharashtra,India. The Urmodi Project is located at Parali, Taluka and District Satara. For
the historical inflow data of 33 years from 1975 to 2007, it is observed that the maximum
inflow into reservoir from the catchment area is 968.85 MCM while the minimum inflow is
123.92 MCM. For all the 33 years the average inflow into reservoir is 349.32 MCM out of
which about 77.5% inflow occurs in the months of July and August. The evaporation rate in
the months of March, April and May have almost 48.5% share in the total annual evaporation
of 1727mm.
Figure 3 Location of Urmodi Project
Figure 4 Monthly inflows into Urmodi Reservoir
Table 1 Salient features of Urmodi reservoir
Maximum height of dam 50.10 m
TBL(Top of Bund Level) 699.00 m
MWL (Max. water level) 696.56m
FRL(Full reservoir level) 696.00m
MDDL (Min. Drawdown level) 665.65m
Gross catchment area 116.86sq km
Gross capacity of reservoir 282.14 MCM
Dead storage capacity of reservoir 8.867 MCM
Live storage capacity of reservoir 273.273 MCM
6. RESULTS AND DISCUSSION
The monthly demands are the higher bounds for monthly releases. The proposed model was
run for 100% reliability. The linear programming model was developed and applied to the
Urmodi Reservoir using the commercially available software LINDO6.1 (Linear, INteractive,

and Discrete Optimizer). The initial state of the reservoir was found to be important for
computation of reservoir releases. The evaporation losses also play crucial role in reservoir
releases computation. A comparative graphical plot is shown in Fig.5 .
The GA model was run for various population sizes, crossover probabilities and mutation
probabilities. The GA model uses chromosomes, each containing 12 substrings representing
monthly releases as decision variables. The initial population was generated randomly from
which the parent selection was done using Roulette Wheel Selection method. The system
performance was evaluated for various population sizes. The optimal population size was
found to be140; thereafter the system performance was constant (Fig.6 ).
Figure 5 Comparative study of reservoir releases
The population size of 140 was adopted and the crossover probabilities varied to evaluate
the system performance. For the varying mutation probabilities, the optimal probabilities for
crossover and mutation were found to be 0.72 and 0.01 respectively ( Fig.7 ).
Figure 6 Sensitivity to Population Size
7. CONCLUSION
Reservoir system analysis requires frequent updating of tools to be implemented. An in-depth
knowledge of reservoir system and techniques are the essential requirements of policy makers
and operators. Although a variety of tools are available for reservoir system analysis, linear
programming and genetic algorithm seem to be more powerful to cater different situations. A
linear programming and genetic algorithms are used to minimize the sum of the squared

irrigation demand deficit of Urmodi Project in Maharashtra, India. The objective function
was subjected to mass-balance constraint, active storage volume constraint, release
constraints, surplus constraints and the evaporation loss constraints. The Linear Programming
(LP) and Genetic Algorithm (GA) when applied to the developed model gave the minimum
sum of the squared deficits of 2128.25 and 2950.77 respectively. From the sensitivity analysis
of GA model, the optimal values of genetic parameters found were: population size 140,
Crossover probability 0.72 and mutation probability 0.01. The storages were observed to be
low before the start of high inflows and high during the monsoon period.
Figure. 7 Sensitivity to crossover probability
ACKNOWLEDGMENTS
The author appreciates all those who participated in the study and helped to facilitate the
research process. The author is thankful to the Authorities of Urmodi Reservoir Project,
Satara, Maharashtra for providing the necessary help and technical information to complete
this research work.
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