Neural Comput & Applic
DOI 10.1007/s00521-017-3160-z
ORIGINAL ARTICLE
Cuckoo optimization algorithm in optimal water allocation
and crop planning under various weather conditions (case study:
Qazvin plain, Iran)
Omolbani Mohammadrezapour1 • Icen Yoosefdoost1 • Mahboube Ebrahimi2
Received: 20 June 2016 / Accepted: 7 July 2017
Ó The Natural Computing Applications Forum 2017
Abstract As inferred from its biological nature, agriculture is a key consumer of water resources in many countries. Hence, today, water management plays an important
role in the use of water resources of these countries. The
present study aimed to optimize cultivation area, to manage
irrigation water, and to optimize total income gained from
the cultivation area of special crops in Qazvin plain (the
central plateau of Iran) under various weather conditions
using cuckoo optimization algorithm (COA). Under the
same objective function, the performance of the COA was
accessed through comparison with the genetic algorithm
(GA). The results of two models showed that because of its
high water requirement and low yield, the cultivation area
of sugar beet in every four different condition reduced (by
over 80%); that is, it is not wise to plant it in all different
weather conditions of the study area. Comparison of the
model results indicates that the COA can provide better and
more reliable optimal results in relative yield of crops,
higher farm income. So, in comparison with GA, less water
is allocated. Following the new cropping pattern delivered
by COA model, the water volume stored in the dam
reservoir at the end of the operation under wet, normal, dry,
and hot–dry conditions rose, respectively, by 264,745.3,
2,865,387, 275,789, and 655,918 m3. Meanwhile, the
farmers’ profit increased, respectively, by 6.2, 2.6, 1.27,
and 1.48% compared to the previous optimization occurred
& Omolbani Mohammadrezapour
mohammadrezapour@uoz.ac.ir;
omohammadrezapour@gmail.com
1
Department of Water Engineering, University of Zabol,
Zabol, Iran
2
Department of Agricultural, Payame Noor University (PNU),
Tehran, Iran
at the end of the operation. To conclude, COA is quite
promising in a cultivation area of crops optimization
problem in terms of its simple structure, excellent search
efficiency, and strong robustness.
Keywords Meta-heuristic algorithm Optimization Agricultural water management
1 Introduction
Due to its biological nature, agriculture is the largest
consumer of water resources in many countries. Nowadays,
irrigation plays a vital role in economy; hence, water
management in agricultural sector has its highest effect on
raising efficiency during drought and relieves its economic
and social damage.
Iran is located in the south of the northern temperate
zone, and because of its unique geographical location and
its sparse roughness and other influential factors such as air
masses, it is regarded as an arid area. In fact, low rainfall
has caused so severe fluctuations in the surface water that
with the advent of heating season, especially in the summer, its rate often drops dramatically. On the other hand, in
order to achieve higher profit, the farmers are willing to
cultivate plants such as rice, sugar beet, and corn, which
require more irrigation. However, considering the climatic
conditions of the country, this indiscriminate consumption
of the water resources would lead to irreparable damages in
the regional water potential.
As one of the central plains of Iran, Qazvin plain is
among the areas in which water resources are threatened
seriously due to non-optimal operation, and if continued, it
would leave irreversible economic and environmental
consequences in the region. Hence, implementing proper
123
Neural Comput & Applic
planning and management of irrigation and cropping patterns in the study area seems quite urgent.
Nowadays, a universal agricultural problem facing most
developing arid regions is the limited supply of water used
for irrigation in which the crop yield is unable to reach its
potential. For optimal allocation of irrigation water under a
limited water supply, there have been successful models
developed. The objective of most studies was to maximize
economic benefits, based on developing for optimal land
and water resources, maintaining the existing cropping
patterns or expressing farmers’ propensity to pay for irrigation water [1–5]. It was concluded that these problems
can be solved through mathematical programming
methods.
Recently, most researchers use heuristic methods such
as genetic algorithm (GA), particular swarm optimization
(PSO), leap-frog (LF) and linear programming commonly
applied for optimal utilization of water resources and
cropping pattern. In this case, Azaiez and Hariga [6]
offered a linear programming model in order to optimize
utilization of water resources and efficient use of groundwater and surface water and to assess optimum cropping
model under water shortage conditions in Chitradorgay,
India. To optimize reservoir performance of a single-purpose reservoir, Nagesh Kumar et al. [7] used genetic
algorithm and linear programming for irrigation of crops to
show the similarity between the yields of the genetic
algorithm and those of the linear programming. Azaiez [8]
developed a hybrid LP-DP model for optimal use of
farmland for a crop in northern Saudi Arabia. Georgiou and
Papamichai [9] used nonlinear programming model [simulated annealing (SA)] in Northern Greece to determine the
optimal cropping patterns under diverse weather conditions. Moghaddasi et al. [10] prepared a 3-layer nonlinear
programming (NLP) to manage the agricultural water
demand in Zayandeh-Rud, Isfahan (the central part of
Iran), in drought conditions to minimize the damage and to
allocate water distribution in the dam’s downstream. Dima
et al. [11] used linear programming model to study irrigation water optimization in five regions of the West Bank
of Palestinian and to indicate that changing cropping patterns under water and land restrictions could decrease
irrigation water consumption by 10%. Likewise, FallahMehdipour et al. [12] used the linear and nonlinear programming models such as GA, PSO, and leap-frog (LF) to
optimize water used for agricultural irrigation and multicrop cultivation patterns. The results indicated the superiority of linear to nonlinear algorithm as well as the LF to
other algorithms. Dai and Li [13] used a multistage
stochastic programming model for water allocation to
determine the optimum culture pattern under uncertainty
conditions in the Basin of Wang Zhang River. Khanjari and
Sabohi [14] also used a genetic algorithm to determine the
123
appropriate allocation of water and suitable cultivation
pattern for the farming areas irrigated with Droudzan dam
located in the southwest of Iran.
Recently, an effective meta-heuristic optimization
algorithm namely cuckoo optimization algorithm (COA)
was proposed by Rajabioun [15]. Since the COA, commonly versatile in many fields, is helpful in optimization
and is easy in application mainly due to its straightforward
structure. For example, COA was used by Gandomi et al.
[16] in structural optimization, by Kanagaraj et al. [17] in
reliability optimization, and by Marichelvam et al. [18] in
hybrid flow shop scheduling. More recently, Ming et al.
[19] applied the cuckoo search (CS) to the optimal operation of multi-reservoir system (OOMRS) to maximize the
energy production in China’s Wujiang multi-reservoir
system. The performance results of the C, analyzed through
comparing with the GA and the particle swarm optimization (PSO) under the same objective function, showed it
can provide better and more reliable optimal results than
those of GA and PSO.
The aims of present study to optimize cultivation area of
some main crops and management of irrigation water,
realis of reservoir and maximum total farm income in
cultivating a part of Qazvin plain farms. The study area
located in the central Plateau of Iran, where they provide
their required water through Taleghan dam. This is conducted under various weather conditions (wet, normal, dry
and hot – dry) with the help of cuckoo optimization
algorithm.
2 Materials and methods
2.1 The study area
With an area of 440 thousand ha is Qazvin plain located in
the central plateau of Iran (Fig. 1) which has a semi-arid
climate with hot summers and relatively cold winters. One
of the most significant rivers providing water for this plain
is Taleghan River across which Taleghan dam is built. The
dam is 135 km northwest of Tehran, and its geographical
coordinates are 50° 37’ -51° 51’ Longitude and 36° 5’
-36° 25’ latitude on Taleghan River in the rural area,
Rowshanabdar. Its capacity is 460 million m3, whereas its
dead capacity is 210 million m3. However, due to its severe
loss of inflow current, it has never been able to reserve over
210 million m3 water.
2.2 Statistical data and cropping pattern
Cultivation optimization and optimal release of the reservoir aimed to provide irrigation in the study area needs
accurate weather data about its weather conditions. These
Neural Comput & Applic
Fig. 1 Location of the Qazvin plain in Iran
data include minimum and maximum temperature, relative
humidity, sunny hours, wind speed, rainfall, evaporation,
estimated volume of the river inflow, volume of stored
water in the reservoir while irrigating, and characteristics
of the cultivated plants. For the annual crops (corn, wheat,
sugar beet, barley, and alfalfa), a series of critical data for
the indicated crops along with the main parameters
required for the optimization procedure, i.e., cultivation
area, some key traits of cultivated plants, production cost,
and cultivation date of the regional strategic crops within
the crop year 2010–2011 are given in Table 1. It is worth to
note that crops like alfalfa, corn, and sugar beet are summer
specific, whereas wheat is just a winter crop and barely
grows in both winter and summer.
Growth stage durations for different crops were chosen
based on local observations. During cost calculations, it
was assumed that farmers own the land; thus, the fixed cost
(B) equaled zero. The variable cost (C) for each crop was
computed from data supplied by the Region of Qazvin, Iran
(2014). Table 1 shows that the irrigation season starts in
April and ends in December. The year is divided into 36
periods; each month consisted of three periods; yet, the last
9 periods of the year, i.e., the 28th–36th periods, have no
irrigation activity. Although the proposed optimization
model can handle heterogeneous soil, the considered soil
under study was homogenous. It consists of one layer
characterized as clay loam (L) with FC = 0.25 cm3/cm3
and PWP = 0.12 cm3/cm3. Due to higher rainfall during
the no irrigation season, it is assumed that soil water
content at the beginning of the irrigation season is at FC, so
the values of Ky in the establishment stage are assumed to
be equal to zero, as also proposed by Tsakiris [20] and
Kotsopoulos [21]. The reference crop evapotranspiration
was derived from daily climatic data (mean temperature,
radiation, relative humidity, and wind speed) at Qazvin
meteorological station provided by the FAO Penman–
Monteith equation [22].
2.3 The definition of the model and related variables
The model, a nonlinear program, aims to introduce the
most appropriate use of the dam reservoir, to regard its
optimal allocation between different plants, and to rise
profits gained from the crops. The time span of the balance
equations is considered fixed for the whole model and is
equal to the irrigation cycle of Qazvin area (10 days). The
used objective function is also based on Eq. (1). The
objective function maximized the total gross income of the
area to achieve the optimal yield of Taleghan dam for
irrigating n crop in the j period during the irrigation period
[23].
n X
Z ¼ Max
Pi ðYcÞi Ci Ai
ð1Þ
i¼1
where Z* = total farm income (Rial), P = production
price (Rial/kg) C = variable cost (Rial/ha), A: cropped
area (ha), i: cultivation crop and YC is the relative yield. In
123
Neural Comput & Applic
Table 1 Some characteristics of the annual crops under study in the Qazvin region
Growth stage parameter
Corn
Sugar beet
Wheat
Barley
Alfalfa
Establishment Ky
0.01
0.12
0.01
0.01
0.85
d
30
30
20
20
10
Vegetative Ky
0.4
2
0.2
0.2
0.95
D
40
50
35
45
10
Flowering Ky
1.5
0.6
0.6
0.6
1.1
D
20
25
20
20
15
Yield formation Ky
0.5
0.36
0.5
0.5
1.1
D
30
50
40
40
15
Ripening Ky
0.2
0.12
0.01
0.01
1
d
20
50
20
10
10
Maximum root depth (cm)
Variable cost C (Rial/ha)
120
1,976,343
100
3,873,256
110
3,160,421
110
1,273,198
110
2,183,652
Product price P (Rial/kg)
2000
2700
11,000
8500
7500
Planting day
4 May
20 March
5 December
5 August and 5 December
15 May
Maximum yield Ym (kg/ha)
8612.76
39,215.12
1639.9
2763.52
9402.9
fact, irrigation function of the crop, which is calculated
using the seasonal production, will function where the
sensitivity and evapotranspiration coefficients are regarded
in different growing stages of the plant. Jensen et al. [23]
suggested the relationship between the relative yield and
relative evapotranspiration as shown in Eq. (2).
n Y
Ya
ETa ci
YC ¼
¼
ð2Þ
Ymax i¼1 ETmax
2.4 Model’s constraints
This equation, initially introduced by Rao et al. [24], is
also provided in other forms. The main problem of these
models is associated with sensitivity coefficients in different stages of growth. Careless selection of these coefficients would lead to problems in implementing the
mathematical models and estimating the production [25].
To resolve this problem, Ky coefficients for different stages
of growth of many plants are reported in the 33rd journal of
Food and Agriculture Organization (FAO) entitled ‘‘Yield
Responses to water’’, where: Ya: is actual yield (kg/ha),
Ymax: is maximum yield of the crops under given management conditions that can be obtained with unlimited
water supply potential (kg/ha), ETa: is actual evapotranspiration (mm), ETmax: is maximum evapotranspiration
(mm), ki: is crop sensitivity index to water stress, by the
following formula:
In this study, ETREF software, which is based on the
Penman–Monteith formula, is used to calculate the reference evapotranspiration. The maximum evapotranspiration,
ETm, coincides with both crop evapotranspiration, which is
the product of a crop factor Kc and the reference evapotranspiration [22, 26, 27].
k ¼ 0:2418 K 3 0:1768 K 2 þ 0:9464K 0:0177:
ð3Þ
In this formula (3), k is the yield reaction coefficient to
water stress in different growth stages and is presented in
the FAO-56 magazine for each crop and during different
periods of growth.
123
Normally, every objective function has a series of restrictions that match the performance of the model with actual
conditions of the area. The following constraints are used
in model to make the objective function practical.
2.5 Crop evapotranspiration
2.6 Soil moisture balance
The first constraint, soil moisture, was the amount of water
available in soil surface. In the beginning of the irrigation
season, soil moisture is assumed to be known. Here, it is
assumed to be at field capacity for all soils and crops. Soil
water balance equation for a given crop i and time interval j
are given by Vedula and Mujumdar [28], Ghahraman and
Sepaskhah [29], and Georgio and Papamichail [9].
ðSMin Þi;jþ1 ¼ ðSMin Þi;j þ ERAINi;j þ IRi;j ðETa Þi;j
þ ðTAWi;jþ1 TAWi;j Þ
ð4Þ
where SMin = initial soil moisture level (mm),
ERAIN = effective rainfall (mm), IR = irrigation water
allocated (mm), ETa = actual evapotranspiration (mm),
Neural Comput & Applic
TAW = total available soil water (mm), i = cultivation
crop and j = time interval.
ðRmax Þij ¼
¼
ðIRmax Þij
ME 1 Pij TAWij þ ðETm Þij ðSMin Þij ERAINij
2.7 Water requirement
ð9Þ
The second restriction is water requirement of i plant in j
time displayed as ðIRmax Þij . The following formula was
used to calculate the plant’s water requirement:
ðIRmax Þi;j ¼ 1 Pi;j TAWi;j
þ ðETm Þi;j ðSMin Þi;j ERANi;j
ð5Þ
In this equation, ðIRmax Þij = is the maximum water
requirement (mm) of the crop i in the time interval j,
Pi,j = is the soil moisture depletion factor under non-water
stress conditions of the plant i at the period j which depends
on specific crop, and the maximum evapotranspiration ETm
can be extracted from FAO 24 [25]. ERAINi = is the
effective rainfall (mm), and (ETm)i, = is the maximum
evapotranspiration, ðSMin Þij = is the soil moisture level
(mm), and TAWi, = is the amount of total available soil
water accessible to the plant. If due to low irrigation the
plant’s yield drops by more than 70%, the crop production
will not be economically feasible for farmers. This issue is
also shown as restriction (6) to the model.
Ya
0:7:
ð6Þ
Ym i
2.8 Reservoir release
The third limitation Rij is the release from the reservoir
used for irrigation of the i crop in the j period. It was
calculated using Eq. (7), as also used by Georgiou et al.
[9, 30].
P
RijAi
:
ð7Þ
ðRÞij ¼
ME
Rij = is the release from the reservoir to meet irrigation
requirement, so it should be always smaller than the
maximum amount of water released from the reservoir. It is
obvious that this value must always be greater than zero.
This limit is shown as follows:
0 Rij Rij max
ME
ð8Þ
At any time, the released maximum from the reservoir is
in accordance with the amount of water allocated for irrigation of each crop per period as well as the irrigation
efficiency that are based on the formula [30]:
IRmax = maximum irrigation requirement (mm), Pij is
the depletion factor of soil moisture in terms of the i plant’s
water stress during the j period extracted from FAO’s 24th
magazine, and ME is the average efficiency including
application efficiency and conveyance efficiency, both
determined according to the regional experts’ opinions.
2.9 Reservoir storage
The fourth limitation applied to the objective function is
the water balance of the reservoir where Si is the amount of
water stored in the reservoir for any time period between
the maximum storage volume, Smax, and the minimum
storage volume (dead volume), Smin.
Smin Si Smax
ð10Þ
Hence, Sj is calculated based on the continuity Eq. (11).
Sjþ1 ¼ Sj þ Qj Rj EVPj þ SPj þ Rainj
ð11Þ
In this equation: Sj and Sj þ 1 are the volume of water
stored in the dam (m3), respectively, in the j period and
j þ 1 and Qj are the volume of inflow (m3) to the dam in
the j period, SPj is the volume of water overflow (m3) in the
j period, RAINj is the amount of precipitation on the dam
(m3) in the j period, Ri is the volume of release from the
reservoir for irrigation (m3) calculated based the following
equation:
Ri ¼
n
X
¼1 10 Ai Rij
ð12Þ
i
where Ri is the amount of water released from the reservoir
for irrigation of the i crop (mm) in the j period.
Ai is the cropped area of i crop (ha) (a factor of 10 for
conversion of hectares in mm into m3).
EVPj is the volume of water evaporated from the
reservoir during the j period in terms of cubic meters. It is
calculated based on Eq. (13).
EVPj ¼ 0:001 Ei f ðSi Þ
ð13Þ
where f ðSi Þ is the dam’s level (m2) during the j period and
Ej is evaporation rate from the dam level (mm) in the j
period (a factor of 0.001 for converting millimeter into
meter).
By substituting Eq. (13) in Eqs. (14), (15) is achieved.
123
Neural Comput & Applic
Sjþ1 ¼ Sj þ Qj n
X
2.12 Weather condition classification
¼1 10Ai Rij 0:001Ej F ðSi Þ SPj
i
þ RAINj
ð14Þ
Sjþ1 ¼ min Smax; Sj þ Qj n
X
¼1 10Ai Rij 0:001Ej F ðSi Þ
i
ð15Þ
In Eq. (15), the reservoir water volume in each period
was limited to two volumes: the maximum volume and the
dead volume of the dam. Thus, the volume of water
overflow is deleted from Eq. (15).
2.10 Actual evapotranspiration
Eq. (16) is the limit of evapotranspiration. Actual evapotranspiration is always less than or equal to maximum
evapotranspiration. This limitation shows that when soil
moisture is higher than a critical value, ETa ¼ ETm but in
cases of lower moisture levels, both ETa and ETm depend
on the residual moisture in soil; hence, the actual evapotranspiration would be smaller than a proportion of its
maximum value. In this study, the actual rate of maximum
evapotranspiration is given by Doorenbos and Kassam
[31], Georgiou et al. [9, 30]:
ETa ðX; T Þ ¼ dx=dt ¼ f ð xÞETm ðtÞ
ð16Þ
(
)
1ð1 pÞ
. . . x TAW
x
f ðxÞ ¼
. . . 0 x ð1 pÞTAW :
½ð1 pÞTAW
ð17Þ
In Eq. (16), ETa = is actual evapotranspiration, X = is
soil moisture in the root zone, t = is time period, and F ð X Þ
is water drain from the soil and ETm = is maximum
evapotranspiration. Other relevant parameters were
described earlier.
2.11 Cropped area
The last constraint is the limit-cropped area. Obviously, the
area under cultivation for each crop should be between the
maximum Amax and the minimum Amax cultivation.
According to Eq. (18), this limit is displayed.
Amin Ai Amax
ð18Þ
Most of these constraints and relationships are accessible in the references (Khanjari and Sabohi [14] and Ghadami et al. [32] and Ghahraman and Sepaskhah [33],
Georgiou et al. [9, 30].
123
The irrigation scheduling is provided to offer the farmers
guidelines for adjusting irrigation schedules with actual
weather conditions. In fact, developing such plan requires
information on rainfall as well as evapotranspiration
levels expected with different probabilities. Interestingly,
the probability of rainfall coincides with probabilities of
inflow. Four weather conditions are distinguished through
combining the various probability levels of rainfall,
evapotranspiration, and inflow [34]: wet, normal, dry, and
hot–dry weather conditions along with the probability
levels of expedience of rainfall and evapotranspiration.
To find the base year upon which the weather conditions
are simulated, the models were first implemented without
regarding the weather conditions for the 8-year operation
of the reservoir, which was daily recorded. The most
optimal solutions offered by the cuckoo algorithm were
witnessed in the base year, 2010–2011. Moreover, considering past data, various probability values of rainfall,
reference evapotranspiration, and water inflow were
estimated for the irrigation year, 2010–2011. Based on
rainfall probability, the inflow to the dam, and the reference evapotranspiration (Table 2), four weather conditions, hot–dry, dry, normal, and wet, are considered for
the model as follows.
Based on the above probabilities and the frequency
curves, the rainfall and evapotranspiration levels of a
10-day period are shown in Fig. 2. In addition, the 10-day
inflow levels are shown in Fig. 3.
2.13 Cuckoo optimization algorithm
Inspired by cuckoo’s life style, Rajabion proposed COA
in 2011. The basic idea of this algorithm was taken from
the way it lays eggs as well as the specific way it grows.
Unlike most other birds, these kinds of birds avoid
nesting and parenting and leave the nurture of its chicks
effortlessly and subtly to other birds, so they are a socalled brood parasite. Cuckoo is the most famous brood
parasite. A cuckoo destroys one of the host bird’s eggs
and lays her egg among the eggs in the nest. Thus, the
host bird will be in charge of maintaining the egg.
Cuckoos do this by imitating the color and pattern of the
eggs in each nest in order for their eggs resemble the
actual eggs of the host. The more similar the eggs, the
greater their opportunity to grow and survive. Two kinds
of cuckoos are used in this model: mature cuckoos and
laying-egg cuckoos.
The following steps summarize the pseudo-code of the
optimization algorithm:
Neural Comput & Applic
Table 2 The four different
weather conditions
Weather condition
Probability level of expedience
Evapotranspiration (%)
Rainfall (%)
Inflow (%)
Hot and dry
80
0
0
Dry
60
20
20
Normal
50
50
50
Wet
40
80
80
Fig. 2 Ten-day rainfall and
evapotranspiration with various
weather conditions
Fig. 3 Ten-day inflow with
various weather conditions
1.
2.
3.
Determine the primary habitat of the cuckoos (initial
response) with selecting several random points on the
function.
Assign some eggs to each cuckoo.
Identify egg laying radius or ELR for each cuckoo.
ELR rate for each cuckoo is calculated according to the
number of eggs and its distance to the destination using
the following equation:
ELR ¼ a ðnumber of available cuckoo’s eggs=total numbers of eggsÞ
ðVarhi Varlow Þ
where Varhi and Varlow are the maximum and minimum
values of the variables, respectively. a is an integer that
controls the maximum ELR.
4.
5.
6.
7.
8.
Set cuckoos lay eggs within their respective ELR.
Remove eggs with low target function.
Determine the target function for any adult cuckoo.
Limit the maximum number of the cuckoos available
in the environment.
Classify the cuckoos and determine the superior
habitat.
123
Neural Comput & Applic
The parameters, determined by trial and error, are used
in the COA and are shown in Table 3.
3 Results and discussion
The model was solved as a two nonlinear programming
namely cuckoo optimization and genetic algorithms in 4
weather conditions namely wet, normal, dry, and hot–dry.
MATLAB software was used to write the codes. Here, the
results of implementing the model for different weather
conditions for both algorithms are expressed. Furthermore,
the COA optimization model was used to compute the
irrigation scheduling and optimal cropping pattern for five
crops (corn, alfalfa, wheat, barley, and sugar beet) with
data gathered from all weather conditions. The time
interval was 10 days for all five crops, and the irrigation
period (from April to December) was sub-divided into 27
periods.
3.1 Relative yield
Fig. 4 The flowchart of cuckoos algorithm [15]
Table 3 Parameters of cuckoo optimization algorithm
Title of parameters
Selected value
Initial number of cuckoos
50
Minimum number of eggs per cuckoo
2
Maximum number of eggs per cuckoo
5
Maximum number of alive cuckoos
50
Maximum number of iteration
100
Number of groups or categories
3
X
p/6
Convergence criterion
1 9 10-10
Their classification is performed by K-means clustering
method, where k group (usually 3–5 groups) is selected and
based on the variation range of profit function in cuckoos,
the average income of each group is determined, and each
cuckoo will belong to a group that is closest to the average
of the group.
9.
Migration of new cuckoos toward superior habitat.
In its migration toward the target habitat, the cuckoo
does not fly all the way through. It flies k% of the path with
u radian deviation (Fig. 4), so these two parameters search
more spots of the problematic space. For each cuckoo, k is
a random number between zero and one (equally distributed) and u is a random number between x and -x (x
of about p/6 is appropriate). In case of occurrence of stop
conditions, the algorithm will end; otherwise, go to the
second step. In Fig. 4, the cuckoos algorithm flowchart is
presented.
123
One of the most efficient outputs is the relative yield of
crops under different weather conditions. In cases where
the water allocated to the crop equals its maximum water
requirement, the relative yield is one. However, in cases
with less water requirement, the relative yield is less than 1.
Two algorithms have calculated the yields of wheat, barley,
and alfalfa in wet weather as one, so in this weather, the
water allocated to these crops is sufficient to meet its water
requirements. The relative yields under the four weather
conditions are given in Table 4.
As shown in Table 4, the crops’ yields differ greatly in
different climatic conditions. In other words, reduced
rainfall and hotter condition would lower their yields so
significantly in hot–dry conditions that the estimated yields
made by the cuckoo and genetic algorithms for crops such
as sugar beet, barley, and alfalfa are significantly less than
their economical rate (0.7). It is inferred that mainly due to
their high water demand and reduced yield, their cultivation in these weather conditions is not economical. Moreover, in terms of reduced rainfall, sugar beet had the least
yield of all. However, due to its high water demand, this
result was quite expected.
3.2 Total farm income in optimal cropping patterns
The main output of the model corresponding with the
objective function of the model includes the output of the
profit and the level of cultivation per crop. The calculated
amounts prepared by using COA and GA for hot–dry, dry,
normal, and wet weather conditions, allocation of water
from reservoir and cropped area for various weather
Neural Comput & Applic
Table 4 Relative yield of cultivated crops in the Qazvin plain for
various weather conditions (Ya/Ym)
Crop
Wet
GA
COA
Normal
Dry
GA
GA
COA
Hot and dry
COA
GA
COA
Corn
1
1
1
0.97
0.98
0.92
0.75
0.7
Alfalfa
1
1
0.81
0.82
0.79
0.79
0.7
0.63
Barely
Sugar bee
1
0.99
1
0.97
1
0.95
0.99
0.94
0.98
0.79
0.95
0.81
0.78
0.63
0.58
0.53
Wheat
1
1
1
0.98
0.97
0.91
0.81
0.71
conditions are represented in Table 5. It should be noted
that in the models, the rates of the farmer’s profit in different weather conditions are calculated immediately
before and after optimization.
As shown in Table 5, in hot–dry condition, due to lack
of rainfall and input current in one hand and increased
evaporation on the other hand, the dam reservoir used for
irrigating the crops reduced. It was followed by a decreased
rate of the acreage of the crops consuming high amounts of
water. Yet, in case of the crops requiring less water, it
increased significantly in two models. Consequently, wheat
and corn, respectively, have taken the first and the second
positions. In addition, the acreage of sugar beet dropped
from 1425 ha to 0 and 31 (ha), respectively, in COA and
GA, mainly due to its extremely high water demand. Following the new optimal crop pattern provided by the
models, under hot–dry weather conditions, the volume of
water consumption witnessed a great increase by the end of
the operation. It was also economically beneficial for the
farmers so that implementing the model would increase the
relative profit of the farmers by 6.2 and 3.63% in COA and
GA models. In dry weather conditions, the first place of
cultivation was allocated to wheat, and corn and alfalfa had
the following ranks. As it can be seen, the cultivation of
sugar beet dropped significantly by 147 (ha) in COA and
by 137 (ha) in GA compared to the previous optimization.
Here again, the benefits increased by 2.6 and 2.55% in
COA and GA, respectively. In normal weather conditions,
the maximum area under cultivation was devoted to wheat,
alfalfa, barley, and corn. The acreage of sugar beet in this
condition, which was less than the period prior to implementation of the model, dropped to 204 and 157 (ha), and
the farmers’ profit increased 1.27 and 4.96% in COA and
GA models, respectively. As shown in Table 5, in wet
weather conditions, rainfall and input flow to the dam are
higher than other conditions, so it is expected that the
acreage of all crops with high water needs increases more
than other weather conditions. For example, in this case,
the increased cropped area of sugar beet [by 271 and 174
(ha) in COA and GA models] signifies its significant
increase compared to other weather conditions. This is due
to increased yield of sugar beet in wet conditions. By
contrast, the overall benefit of the farmers only decreased
in COA and GA by 1.46 and 1.58%.
As shown in Table 5, the allocated water increased in
hot–dry and dry conditions because the crops required the
highest depth of irrigation water in both models. By contrast, in wet and normal conditions, the allocated water
Table 5 Total farm income, allocation of water from reservoir, and optimum cultivation area for various weather conditions by COA and GA
Crop
Cropped area (ha)
before optimization
Wet
Normal
Dry
Hot and dry
Cropped
area (ha)
Water
(m3)
Cropped
area (ha)
Water
(m3)
Cropped
area (ha)
Water
(m3)
Cropped
area (ha)
Water
(m3)
Wheat
34,583
34,929
1.011
34,949
1.27
34,966
1.56
35,702
1.97
Corn
Barley
9608
9893
9723
10,123
0.815
0.549
9730
10,137
1.037
0.719
9735
10,148
1.259
0.738
10,229
6596
1.689
1.23
Sugar beet
1425
271
1.316
204
1.629
147
1.968
0
0
Alfalfa
9548
10,009
0.326
10,036
0.412
10,059
0.499
11,155
0.750
COA
Total income (10 Rial)
150,670,907,040
131,970,730,080
124,307,287,233
68,562,559,902
GA
Wheat
34,958
1.01
34,963
1.278
34,866
1.57
35,001
2.14
Corn
34,583
9608
9732
0.81
9734
1.03
9835
1.24
9747
1.7
Barley
9893
10,143
0.515
10,146
0.718
10,158
0.921
10,171
0.822
Sugar beet
1425
174
2.05
157
2.132
137
2.144
31
2.677
Alfalfa
9548
10,048
0.321
10,055
0.411
10,050
0.509
10,105
0.833
Total income (10 Rial)
150,861,600,000
137,094,675,876
124,229,887,233
66,697,894,772
Total income before
optimization (10 Rial)
148,473,169,701
130,287,334,273
121,054,220,961
64,274,856,196
123
Neural Comput & Applic
Fig. 5 Water values stored in
the reservoir after optimization
during the operational period
dropped. For example in COA model, the water allocated
to wheat increased from 1.011 in wet to 1.97 in hot–dry
condition.
The results of two models indicated that wheat crop
could adopt well in all weather conditions because of its
low water requirement and appropriate yield, so it is
optimal for the study area. In contrast, sugar beet has lost
80% cultivation area in all climatic conditions; hence,
given the current water shortage and high water requirement of sugar beet and its low profitability, it is not suitable for cultivation. In other words, it is recognized as a
plant with high water requirements and low yield.
3.3 The volume of water stored in the dam
in different weather conditions
Figure 5 shows the water values stored in the reservoir by
the difference of water storage in reservoir before and after
optimization during the operational period.
During wet weather condition, the volume of the stored
water increased mainly due to increased rainfall and inflow
into the dam. Likewise, the potential of the output flow in
the reservoir rose. Consequently, more water is allocated
for the crops with high water demand, so the area was
123
highly dedicated to cultivation of these crops. Therefore,
compared to other conditions, less water was stored in the
reservoir (Fig. 5). On the other hand, in dry conditions,
extremely high temperatures would result in increased
evaporation. Reduced rainfall will also lower the inflow to
the dam. Of course, it is possible to release water for the
least amount of acreage. In normal conditions with
increased rainfall and inflow, the acreage of cropped area
with high water required less expansion; therefore, the
stored value in reservoir is more than other conditions.
This model would decrease the acreage of the crops
requiring high irrigation. In fact, the model is designed in a
way that during the critical (low water) years, the cultivation
area allocated for high-consuming crops would reduce, so the
area would be left to crops requiring less water with higher
economic profit, resulting in both proper consideration of the
farmers’ profit and optimal monitoring of the dam water
allocated to irrigation. Following the new cropping pattern
extracted from these models, the volume of water stored in
the dam reservoir in wet, normal, dry, and hot–dry conditions
will increase, respectively, by 264,745.3, 2,865,387, 275,789,
and 655,918 m3 for COA and 262,045.2, 2,862,686.6,
273,089, and 955,542 for GA compared to the previous
optimization occurred at the end of the operation.
Neural Comput & Applic
Fig. 6 Effective rainfall
(ERAIN), maximum
evapotranspiration (ETm),
reservoir release to meet
irrigation requirement (R), and
actual evapotranspiration (ETa)
for wet, normal, and dry
weather conditions for two
crops (wheat and sugar beet)
under study by COA
In comparison with GA, the results showed that COA
could provide better and more reliable optimal results in
relative yield of crops, higher farm income, and lower
water consumption. So, the results of COA are presented
below for allocation of irrigation water.
3.4 Allocation of irrigation water
Allocation of irrigation water and the cropped area for each
crop depends mainly on factors such as net profit per unit
yield (price, maximum yield obtainable per unit area,
profit, cost, and net profit for maximum yield) (Table 1).
According to the formulas introduced in the Materials and
Methods, calculating water allocated to these crops
requires information on soil moisture, potential evapotranspiration, and irrigation efficiency. The model is
designed in a way that in cases when the crop’s water need
is provided by rainfall, no more irrigation is required. In
other words, the model initially provides the plant’s irrigation need through green water. If not sufficient, it will
123
Neural Comput & Applic
Fig. 6 continued
allocate water from reservoir. Therefore, the allocation of
irrigation water to the crops in normal and wet weather
conditions is less than that of dry weather. In addition,
using the coefficient ky in designing the model has made it
to reconsider the growth periods of the plant, so more water
is allocated to this period than the output and harvesting
stages. During the sleep (dormant) period, no irrigation is
done. In Fig. 6, the amount of water allocated per hectare,
the effective rate of rainfall, potential and actual evapotranspiration of wheat and sugar beet (with high water
requirement) and wheat (with low water requirement) in
each period and under three weather conditions (dry, wet,
and normal) are shown.
123
According to Fig. 6, it can be seen that following
weather pattern variation, increased rainfall, and reduced
evaporation, the irrigation rates needed for the crops
reduces alike. Therefore, under wet conditions, the model
would reduce the maximum required water of wheat and
sugar beet to less than 80 and 100 mm, respectively.
Likewise, in dry conditions, due to significant reduction of
rainfall volume and increased temperature, followed by
increased evaporation, these values for wheat and sugar
beet are, respectively, higher than 120 and 160 mm.
As water loss increases, ETa will lessen more to less
than ETm values. Yet, due to unequal yield sensitivity
indices, these declines differ greatly at different time
Neural Comput & Applic
Fig. 7 Comparison of the convergence trajectories of cuckoo and genetic algorithms in wet conditions
intervals. It is necessary to note that as expected, for the
time intervals with nonzero effective rainfall, the corresponding release is adequately small or even null (Fig. 6).
3.5 Convergence performance of Cuckoo algorithm
Figure 7 shows a sample graph of maximum objective
function for cuckoo and GA with maximum iteration.
As shown in Fig. 7, cuckoo algorithm in wet weather
conditions with 25 of iterations and genetic algorithm with
65 of iteration has led to optimal solution iteration. Figure 7 indicates that the convergence speed of the COA is
obviously faster than the GA.
4 Conclusion
In this study, the COA is used for better management of
water resources of Taleghan dam and for determination of
maximum profit gained from the crop cultivation under
various weather conditions in Qazvin plain located in
Iran’s central plateau. Meanwhile, under the same objective function evaluation, COA and GA performances were
accessed. The results of cropped area in two models
showed that regardless of whether condition, the net profit
for maximum yield of wheat is much higher than all other
crops. Regarding variety of the weather conditions and the
rate of water available, the acreages of sugar beet will
decrease sharply, for it requires extremely deep irrigation.
Comparison of the results of two models indicated that the
COA could provide better and more reliable optimal results
in relative yield of crops, farm income, and lower water
consumption than GA. Following the new cropping pattern
offered by COA model, in wet, normal, dry, and hot–dry
conditions, the volume of stored water of the reservoir at
the end of the operation will increase, respectively, by
264,745.3, 2,865,387, 275,789, and 655,918 m3. Meanwhile, farmers’ profit will increase, respectively, by 6.2,
2.6, 1.27, and 1.48% compared to the previous optimization occurred at the end of the operation. Therefore, it can
be summarized that COA is quite promising in cultivation
area of crops optimization problem because of its simple
structure, excellent search efficiency, and strong
robustness.
Compliance with ethical standards
Conflict of interest The authors whose names are listed in this
manuscript certify that they have NO affiliations with or involvement
in any organization or entity with any financial interest or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials
discussed in this manuscript.
References
1. Yanga G, Guoa P, Huob L, Ren Ch (2015) Optimization of the
irrigation water resources for Shijin irrigation district in north
China. Agric Water Manag 158:82–98
2. Salman AZ, Al-Karablieh E (2004) Measuring the willingness of
farmers to pay for groundwater in the highland areas of Jordan.
Agric Water Manag 68(1):61–76
3. Brown PD, Cochrane TA, Krom TD (2010) Optimal on-farm
irrigation scheduling with a seasonal water limit using simulated
annealing. Agric Water Manag 97(6):892–900
4. Singh A, Panda SN (2012) Development and application of an
optimization model for the maximization of net agricultural
return. Agric Water Manag 115:267–275
5. Nazer DW, Tilmant A, Mimi Z, Siebel MA, Van der Zaag P,
Gijzen HJ (2011) Optimizing irrigation water use in the West
Bank, Palestine (Retracted article. See vol. 98, pg. 732, 2011).
Agric Water Manag 97(2):339–345
123
Neural Comput & Applic
6. Azaiez MN, Hariga M (2001) Theory and methodology: a singleperiod model for conjunctive use of ground and surface water
under severe overdrafts and water deficit. Eur J Oper Res
133:653–666
7. Nagesh Kumar D, Srinivasa Raju K, Ashok B (2006) Optimal
reservoir operation for irrigation of multiple crops using genetic
algorithms. J Irrig Drain Eng 132(2):123–129
8. Azaiez MN (2008) Modeling optimal allocation of deficit irrigaton: appliction to crop production in Saudi Arabia. J Math
Model Algorithms 7:277–289
9. Georgiou PE, Papamichail DM (2008) Optimization model of an
irrigation reservoir for water allocation and crop planning under
various weather conditions. Irrig Sci 26:487–504
10. Moghaddasi M, Araghinejad Sh, Morid S (2009) Long-term
operation of irrigation dams considering variable demands: case
study of Zayandeh-rud reservoir, Iran. J Irrig Drain Eng (ASCE)
136(5):309–316
11. Dima WN, Amaury T, Ziad M, Maarten A, Siebel PV, Huub JG
(2010) Optimizing irrigation water use in the West Bank,
Palestine. J Agric Water Manag 97:339–345
12. Fallah-Mehdipour E, Bozorg Haddad O, Marino MA (2013)
Extraction of multi-crop planning rules in a reservoir system:
application of evolutionary algorithms. J Irrig Drain Eng
139(6):490–498
13. Dai ZY, Li YP (2013) A multistage irrigation water allocation
model for agricultural land-use planning under uncertainty. Agric
Water Manag 129:69–79
14. Khanjari Sadati S, Speelman S, Sabuhi M, Gitizadeh M,
Ghahraman B (2014) Optimal irrigation water allocation using a
genetic algorithm under various weather conditions. Water
6:3068–3084
15. Ramin Rajabioun (2011) Cuckoo optimization algorithm. Appl
Soft Comput 11:5508–5518
16. Gandomi AH, Yang X-S, Alavi AH (2011) Cuckoo search
algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35
17. Kanagaraj G, Ponnambalam SG, Jawahar N (2013) A hybrid
cuckoo search and genetic algorithm for reliability-redundancy
allocation problems. Comput Ind Eng 66(4):1115–1124
18. Marichelvam MK, Prabaharan T, Yang XS (2014) Improved
cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan. Appl Soft Comput 19:93–101
19. Ming B, Chang JX, Huang Q, Yi-min Wng Y, Huang Sh (2015)
Optimal operation of multi-reservoir system based-on cuckoo
search algorithm. Water Resour Manag 29:5671–5687
123
20. Tsakiris G (1982) A method for applying crop sensitivity factors
in irrigation scheduling. Agric Water Manag 5:335–343
21. Kotsopoulos SI, Svehlik ZJ (1989) Analysis and synthesis of
seasonality and variability of daily potential evapotranspiration.
Water Resour Manag 3:259–269
22. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration: guidelines for computing crop water requirements.
Irrigation and Drainage Paper, No 56. FAO, Rome
23. Jensen ME (1968) Water consumption by agricultural plants. In:
Kozlowski TT (ed) Water deficits and plants growth, vol II.
Academic Press, New York, pp 1–22
24. Rao NH, Sarma PBS, Chander S (1988) A simple dated water
production function for use in irrigated agriculture. Agric Water
Manag 13:25–32
25. Ghahraman B, Sepaskhah AR (1997) Use of water deficit sensitivity index for partial irrigation scheduling of wheat and barley.
Irrig Sci 18:11–16
26. Wright JL (1981) Crop coefficients for estimates of daily crop
evapotranspiration. In: Irrigation scheduling for water and energy
conservation in the. 80’s, ASAE, pp 18–26
27. Wright JL (1982) New evapotranspiration crop coefficients. J Irrig Drain Div ASCE 108:57–74
28. Vedula S, Mujumdar PP (1992) Optimal reservoir operation for
irrigation multiple crops. Water Resour Res 28:1–9
29. Ghahraman B, Sepaskhah AR (2004) Linear and non-linear
optimization models for allocation of a limited water supply. Irrig
Drain 53:39–54
30. Georgiou PE, Papamichail DM, Vougioukas SG (2006) Optimal
irrigation reservoir operation and simultaneous multi-crop cultivation area selection using simulated annealing. Irrig Drain
55:129–144
31. Doorenbos J, Kassam AH (1979) Yield response to water. Irrigation and Drainage Paper, No 33
32. Ghadami SM, Ghahraman B, Sharifi MB, Rajabi Mashhadi H
(2009) Optimization of multireservoir water resources system
operation using genetic algorithm. Iran Water Resour Res
5(2(14)):1–15
33. Ghahraman B, Sepaskhah AR (2002) optimal allocation of water
from a single reservoir to an irrigation project with predetermined
multiple cropping patterns. Irrig Sci 21:127–137
34. Raes D, Sahli A, Van Looij J, Ben Mechlia N, Persoons E (2000)
Charts for guiding irrigation in real time. Irrig Drain Syst
14:343–352