Agriculture crop yield prediction using inertia based cat swarm optimization

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 14, No. 2, April 2024, pp. 1700~1710
ISSN: 2088-8708, DOI: 10.11591/ijece.v14i2.pp1700-1710  1700
Journal homepage: http://ijece.iaescore.com
Agriculture crop yield prediction using inertia based cat swarm
optimization
Dwaram Jayanarayana Reddy1
, Rudra Kumar Madapuri2
1
Department of Computer Science and Engineering, Jawaharlal Nehru Technological University Anantapur, Ananthapuramu, India
2
Department of Computer Science and Engineering, G Pullaiah College of Engineering and Technology (Autonomous), Kurnool, India
Article Info ABSTRACT
Article history:
Received Jul 25, 2023
Revised Oct 11, 2023
Accepted Oct 20, 2023
Crop yield prediction is among the most important and main sources of
income in the Indian economy. In this paper, the improved cat swarm
optimization (ICSO) based recurrent neural network (RNN) model is
proposed for crop yield prediction using time series data. The inertia weight
parameter is added to position equation that is selected randomly, and a new
velocity equation is produced which enhances the searching ability in the
best cat area. By using inertia weight, the ICSO enhances performance of
feature selection and obtains better convergence in minimum iteration.
The RNN is applied to produce direct graph using sequence of data and
decides current layer output by involving all other existing calculations. The
performance of the model is estimated using coefficient of determination
(R2), root mean square error (RMSE), mean squared error (MSE), and mean
absolute error (MAE) on the yield from the years 2011 to 2021 with an
annual prediction for 120 records of approximately 8 million nuts. The
evaluated result shows that the proposed ICSO-RNN model delivers metrics
such as R2, MAE, MSE, and RMSE values of 0.99, 0.77, 0.68, and 0.82
correspondingly, which ensures accurate yield prediction when compared
with the existing methods which are hybrid reinforcement learning-random
forest (RL-RF) and machine learning (ML) methods.
Keywords:
Cat swarm optimization
Crop yield prediction
Cultivation
Recurrent neural network
Time series data
This is an open access article under the CC BY-SA license.
Corresponding Author:
Dwaram Jayanarayana Reddy
Department of Computer Science and Engineering, Jawaharlal Nehru Technological University Anantapur
Ananthapuramu, India
Email: djnreddy@gmail.com
1. INTRODUCTION
Agriculture is one of the most important occupations in the development of the Indian economy.
Every farmer is interested in knowing the crop yield that is expected during the harvest period [1]. The
production of agriculture is needed to be improved to tackle the problem of food scarcity [2]. There are
several reasons for crop loss; the most important factor is that the crop productivity and fertilizers are not
accurately understood by the farmers [3]. The crop yield prediction along with the prediction of climate
change will be useful for the farmers in cultivation. The major challenge of crop prediction is climate change
as the weather decides the crops yield [4]. Over the last few years, various researchers have concentrated on
the improvement of crop yield prediction through a variety of methods such as crop growth process-oriented
methods and statistical empirical models [5]. The crop yield prediction is based on numerous environmental
components like soil, temperature, humidity, fertilizers, rainfall, pH value and other parameters [6]. Among
the various factors, soil plays an important role in agriculture to obtain good crop yields. There are several
techniques followed by farmers that include composite, organic, and physical procedures for crop cultivation
which help to manage the soil quality [7]. Crop yield prediction is performed using various techniques, but

Int J Elec & Comp Eng ISSN: 2088-8708 
Agriculture crop yield prediction using inertia based cat swarm … (Dwaram Jayanarayana Reddy)
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the most common approach is remote sensing. It produces reasonable temporal resolution and minimum-cost
non-destructive information on crops [8]. Additionally, machine learning techniques based on remote sensing
data are established for agriculture models [9]. Crop growth model, radiation use efficiency (RUE), and
empirical methods are the three crop yield prediction techniques used in remote sensing. Crop growth model
imitates the crop yield depending on remote sensors, while RUE evaluates the crop yield [10]. The empirical
method is related to the yield which is directly removed by the remote sensors [11]. Machine learning
techniques such as artificial neural network (ANN), support vector machine (SVM), decision tree (DT),
random forest (RF), principle component analysis (PCA), clustering, and reinforcement learning (RL) are
employed for crop yield prediction [12]. Among the several machine learning approaches, the RF and SVM
obtain better results in predicting the crop yield. The advantage of utilizing machine learning (ML)
techniques is that they decrease crop loss and help in achieving a high price [13]. Due to the data complexity,
crop yield prediction is a difficult task for farmers to carry out effectively. There are issues in creating an
empirical expert system through knowledge as it cannot be categorized as time-series data to predict crop
yield [14]. The mathematical studies and historical data from the previous years are helpful in certain regions,
but cannot be employed frequently [15]. Due to the limited resources, crop yield is utilized in remote areas
where the meteorological data is unavailable, but it struggles to handle the temporal dependencies and
patterns in time-series data [16].
Paudel et al. [17] implemented a machine learning technique for crop yield production using the
data from European commission’s MARS crop yield forecasting system (MCYFS). ML was a technique
where huge numbers of data were gathered and joined with the agronomic principles of crop models to create
a guideline for huge-scale crop yield forecasting. The guideline had ample room for development in both the
fit-for-purpose optimizations and general design principles. Under this guideline, the data did not have a
generic method for preprocessing, and big data analysis was not implemented. Elavarasan et al. [18]
introduced a combination of correlation-based filter (CFS) and random forest-recursive feature elimination
(RF-RFE) wrapper that depended on extracting features by predicting crop yield using a ML model. This
model was utilized to identify the features of groundwater, climate and soil properties for building crop yield
prediction. The benefit of using this hybrid filter model among the other existing filter models was that the
computation time was shorter, and the result of this method gave better accuracy for predicting the crop
yield. But, in this paper, eternal variables related to weed infestations and pesticides were not considered for
crop yield prediction. Sun et al. [19] implemented a winter wheat yield prediction method depending on ML
and multi-source data in China from 2014–2018. In this paper, the RF and multiple linear regression (MLR)
models were employed to predict the crop yield by using climate, geographic and satellite data. The
advantage of using this model was better accuracy, and a simple, inexpensive and scalable framework.
Additionally, this model avoided the randomness of a single model. In this paper, the spatial distribution
interannual information was not considered from satellite data to minimize the errors in crop yield prediction.
Elavarasan and Vincent [20] introduced a deep reinforcement learning model for predicting crop yields using
sustainable Agrarian applications. In this proposed deep reinforcement learning (DRL)-based method, the
reinforcement agent was unable to appreciate the input data, and during the learning process, the samples
were not effectively learned. In this model, the agent performed some actions and received a score by
maximizing the prediction accuracy while minimizing the error value. In the DRL model, if the time series
was much longer, then it caused the gradients to disappear or explode for predicting the crop yield.
Rajagopal et al. [21] developed a technique for predicting crop yield through recurrent cuckoo search
optimization (RCSO) neural networks. The developed artificial intelligent (AI) system combined the several
factors like rainfall, soil and crop yield production to forecast market price. Feature selection was done by
following the feature extraction approach. The better features were optimized using the developed algorithm,
then the output was given as input for classification process which was done by using a discrete deep belief
network (DBN)-very deep convolutional networks (VGGNet) classifier. The advantage of using this model
was yielding the right crop at a given time, economic growth, balancing of crop production and minimizing
scarcity. However, the proposed model only performed well in theoretical aspects and not in practical
aspects. Gupta et al. [22] introduced a ML and feature selection for early and precise crop yield prediction.
The dataset included all information related to crops which were collected, and then the relief algorithm was
used for selecting the features. This selection was useful for achieving exact result by classifying significant
characteristics related to a specific real-world problem. The linear discriminant analysis (LDA) algorithm
was used for extracting the features. The ML algorithms like particle swarm optimization (PSO)-support
vector machine (SVM), random forest (RF) and K-nearest neighbor (KNN) were used for classifying the crop
yield. This method was most beneficial for farmers and policymakers to be able to accurately predict crop
yields through the successive seasons.
Ali et al. [23] implemented an online sequential extreme learning machine model (OSELM) with
ant colony optimization (ACO) for wheat yield prediction. The developed dual-phase hybrid ACO-OSELM
was estimated through ACO-RF and ELM methods using metrics. A parameter called pheromone in ACO

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was allocated for predictor stations that classified the predictors along with test or target station at the stating
stage. The developed dual-phase model provided better accuracy with minimum error statistics. Due to the
limited resources, the developed methodology was utilized in river areas where meteorological data was
unavailable. Elavarasan and Vincent [24] presented a reinforced random forest model for improving crop
yield prediction by incorporating agrarian parameters. A reinforcement learning (RL) process enclosed in RF
was equipped at every node to decide the measures. This model had a good learning speed with minimum
configurations and offered a better optimization framework. The model’s behavior was sensitive to
modifications in reward functions. The drawback of this method was the excessive baseline function which
was used to achieve tight error bound. Batool et al. [25] implemented a hybrid technique for tea crop yield
prediction by employing the machine learning model and simulation model using the food and agriculture
organization (FAO) of the United Nations’ AquaCrop crop growth model. This hybrid proposed method used
data on soil, weather and agriculture management from the national tea and high-value crop research institute
(NTHRI). By comparing both the model results, it is seen that the ML model performed better than the
simulation models. But this paper did not consider the superlative hybrid among the four machine learning
methods, RF, RL, SVM and DT that were carried out in the performance evaluation metrics. From the overall
analysis, the existing methods are seen to have the limitations such as struggles to handle temporal
dependencies and patterns in time-series data, data overfitting issues, good outcomes only in theoretical
aspects and not in practical aspects, and being utilized in river areas due to limited resources where the
meteorological data was unavailable which is crucial in crop yield prediction. The proposed improved cat
swarm optimization (ICSO) based recurrent neural network (RNN) model overcomes these limitations. It
enhances the outcome and obtains better convergence in minimum iteration. The inertia weight parameter is
added to the position equation that will be selected randomly, and a new velocity equation is produced which
enhances the searching ability in the best cat area. By using inertia weight, the ICSO is deployed to enhance
the performance in feature selection. The RNN is applied to produce a direct graph by using sequence of
data, and it decides the present layer output by involving all other existing calculations.
The major contribution of this research is mentioned as: i) The dataset is collected from Andhra
Pradesh and it consists of the monthly yield of crops from 10 districts from the period of 2011-2021, with an
annual production for 120 records of 8 million nuts approximately. ii) By using inertia weight, the ICSO is
utilized to enhance the performance of feature selection and obtains better convergence in minimum iteration.
And iii) The RNN is utilized for classification that produces direct graph using sequence of data and decides
present layer output by involving all other existing calculations.
The rest of the manuscript is organized as follows: section 2 illustrates the proposed method. The
improved cat swarm optimization-based feature selection is presented in section 3. The results and discussion
are illustrated in section 4. Section 5 describes the conclusion of this paper.
2. PROPOSED METHOD
This proposed methodology is developed for predicting the agriculture crop yield. The inertia
weight parameter is added to the position equation that is selected randomly, while a new velocity equation is
produced which enhances the searching ability in the best cat area. By using inertia weight, the ICSO is
utilized to enhance the performance of feature selection and obtains better convergence in minimum iteration.
In this paper, Figure 1 illustrates four different steps that include data collection, preprocessing, feature
selection, classification.
2.1. Data collection
The dataset is collected from Andhra Pradesh and it consists of the monthly yield of crops from 10
districts namely, Kakinada, Anakapalli, East Godavari, West Godavari, Guntur, Eluru, Prakasam, Tirupati,
Chittoor and Visakhapatnam from the period of 2011-2021 with annual production for 120 records of
approximately 8 million nuts. The features such as region, soil, season, year, tones, crop, acres, water, area,
temperature, production, solar radiation and pH value are taken into consideration. This dataset can be further
split into two parts: 80% for training set and 20% for testing set. After collecting the dataset, data is
preprocessed by using the min-max normalization method.
2.2. Preprocessing
Data preprocessing is a process of converting raw data into a desired format as the dataset from
several resources may consist of incomplete data. So, for further analysis, this data requires to be filtered and
normalized [26]. Data normalization is the process of preprocessing the input data. Andhra Pradesh District
dataset is standardized using min-max normalization method. The highest score of the feature is transformed

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into 1, the smallest score of the feature is transformed into 0, and other values of the feature are transformed into
an integer between 0 and 1. The mathematical representation of min-max normalization [27] is shown in (1).
𝑣′
=
𝑣−𝑚𝑖𝑛𝐴
𝑚𝑎𝑥𝐴−𝑚𝑖𝑛𝐴
(𝑛𝑒𝑤𝑚𝑎𝑥𝐴
− 𝑛𝑒𝑤𝑚𝑖𝑛𝐴
) + 𝑛𝑒𝑤𝑚𝑖𝑛𝐴
(1)
where, 𝑣′
is the respective min-max normalization value of the attribute, 𝑣 is the primary value of the
attribute, 𝑛𝑒𝑤𝑚𝑎𝑥𝐴
is the new maximum score of the feature, 𝑛𝑒𝑤𝑚𝑖𝑛𝐴
is the new smallest score of the
feature. After the preprocessing step, the features are selected by using optimization algorithm.
Figure 1. Proposed method for crop yield prediction
3. IMPROVED CAT SWARM OPTIMIZATION BASED FEATURE SELECTION
In this proposed method, an improved cat swarm optimization algorithm [28] is used to select a
count of six features which are, soil, temperature, water, production, solar radiation and area. In this ICSO,
first how many cats to be used is chosen, and then the cats within the ICSO model are implemented to
resolve the optimization issues. The behaviors of the cat are classified into two modes as, seeking mode and
tracing mode. The ICSO obtains better performance at the final output, until it reaches the iterations at the
end. A deep learning-based methodology is proposed for predicting agriculture crop yield. The inertia weight
parameter is added to the position equation that is selected randomly and a new velocity equation is produced
to enhance the searching ability in the best cat area. By using inertia weight, the ICSO is utilized to enhance
the outcome of feature selection and classification, and hence obtain better convergence in minimum
iteration.
3.1. Seeking mode
The seeking mode is employed for processing the cat which moves carefully and slowly. In the
seeking mode, there are four necessary elements which are, seeking memory pool (SMP), seeking range of
selected dimension (SRD), counts dimensions to change (CDC) and self-position consideration (SPC). The
SMP is employed to decide the measurements of an individual cat and it represents the desired position of the
cat. From the memory pool, the cat selects a position by using the corresponding rules. The SRD is specified
as the selected dimension of the mutative ratio, and it has a condition for transforming the size measurement.
In the seeking mode, the measurement is chosen for mutating where the comparison between the existing
score and the new score is within a specified limit. The CDC exhibits the value of how many size
measurements differ. In the seeking mode, these factors play a significant role. The SPC determines the cat’s
standing areas which are the moving positions of the candidate. The SPC score is considered as a Boolean
value, either true or false. The procedures of the seeking mode are represented:
a. Consider the current position in 𝑗 number of copies for 𝑐𝑎𝑡𝑘, here 𝑗 = 𝑆𝑀𝑃 if the 𝑆𝑃𝐶 score is considered
as true, and 𝑗 = 𝑆𝑀𝑃 − 1 if 𝑆𝑃𝐶 score is considered as false. Then, the present position is considered as
an individual candidate solution.

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b. For all the copies that depend on 𝐶𝐷𝐶, 𝑆𝑅𝐷 process of the present value is minimized or maximized, and
then the existing value is replaced as presented in (2),
𝑋𝑗𝑑𝑛𝑒𝑤 = (1 + 𝑟𝑎𝑛𝑑 × 𝑆𝑅𝐷) × 𝑋𝑗𝑑𝑜𝑙𝑑 (2)
where, 𝑋𝑗𝑑𝑛𝑒𝑤 and 𝑋𝑗𝑑𝑜𝑙𝑑 are the updated position and the existing position of 𝑐𝑎𝑡𝑘, respectively.
𝑑 represents the dimensions, 𝑗 illustrates the total amount of cats and 𝑟𝑎𝑛𝑑 is the random number
between the range of [0,1].
c. The fitness value of the overall candidates is estimated.
d. If the entire fitness value is not accurately the same, the selecting possibility of all the candidates is
evaluated using the below formula, or else the selecting possibility of all the candidates is to be fixed to 1.
e. Selecting the random position moving from candidate point and replacing the position of 𝑐𝑎𝑡𝑘 is
formulated as shown in (3),
𝑃𝑖 =
|𝐹𝑆𝑖−𝐹𝑆𝑏|
𝐹𝑆𝑚𝑎𝑥−𝐹𝑆𝑚𝑖𝑛
(3)
If the goal of the fitness score is to reduce, then 𝐹𝑆𝑏 = 𝐹𝑆𝑚𝑎𝑥, or else 𝐹𝑆𝑏 = 𝐹𝑆𝑚𝑖𝑛, where the 𝐹𝑆𝑚𝑖𝑛
and 𝐹𝑆𝑚𝑎𝑥 represents the smallest and highest candidate fitness scores, correspondingly.
f. The candidates are classified and selected by 𝑃𝑖 and the position of 𝑐𝑎𝑡𝑘 is replaced.
3.2. Tracing mode
The tracing mode is a process of tracing some targets. Once the cat is within the trace mode, it shifts
every dimension to its corresponding speed. The procedure of tracing mode is represented in the following
steps:
Step 1: The velocity of all dimensions (𝑣𝑘,𝑑) are updated corresponding to (4),
𝑉𝑘,𝑑 = 𝑉𝑘,𝑑 + 𝑟1𝑐1(𝑋𝑏𝑒𝑠𝑡,𝑑 − 𝑋𝑘,𝑑) (4)
where, 𝑉𝑘,𝑑 is the velocity of the 𝑐𝑎𝑡𝑘 in 𝑑 dimension, 𝑟1 and 𝑐1 illustrate the random score in the
range of [0,1] and the fixed value, respectively. 𝑋𝑘,𝑑 is a coordination of 𝑐𝑎𝑡𝑘 in 𝑑 dimension, 𝑋𝑏𝑒𝑠𝑡,𝑑
is the coordination with the better result in the dimension 𝑑.
Step 2: It is verified that the velocity of each cat is adjacent to the highest speed. In that instance, the updated
speed score is in the high range, and the updated score is set equivalent to the restricted limit.
Step 3: The cat’s position is updated by inserting the updated speed and then the entire cat's position is gained
as formulated in (5),
𝑋𝑘,𝑑 = 𝑋𝑘,𝑑 + 𝑉𝑘,𝑑 (5)
where, 𝑉𝑘,𝑑 illustrates velocity of the 𝑐𝑎𝑡𝑘 in the 𝑑𝑡ℎ
dimension, 𝑋𝑘,𝑑 illustrates the coordination of the
𝑐𝑎𝑡𝑘 in the 𝑑𝑡ℎ
dimension. Then the fitness score of updated cat position of entire cat is estimated. At
that time, the tracing mode and searching mode are merged by employing a mixture ratio. Most of the
time, the cats rest, and the remaining time, they move slowly and carefully. As the cat spends a huge
time in the searching mode, it is concluded that the mixture ratio is a minimum value.
In this paper, the ICSO is proposed to enhance the performance of feature selection and to obtain better
convergence in minimum iteration. The inertia weight parameter is added to the position equation that is
selected randomly, and a new velocity equation is produced to enhance the searching ability in the best cat area.
By using this parameter, the global and local search ability are balanced. A maximum inertia weight simplifies
the global search, while a minimum inertia weight simplifies the local search. Initially, the high value is utilized
and then is gradually lowered to the minimum value. For every iteration, maximum inertia weight occurs at the
first dimension which is then decreasingly updated in each dimension, and the velocity is updated to a new form
that is modifiable in every cat. The computational process of ICSO is represented below:
Step 1: Every parameter like velocity, cat position, population, 𝑆𝑅𝐷, 𝑆𝑀𝑃, structure of neighborhood, 𝛼, 𝛽
and 𝑐 is initialized.
Step 2: 𝑁 number of cats are located in random search space.
Step 3: Cat fitness function (FF) is calculated and the cat’s best position is stored in memory.

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Step 4: Based on 𝑀𝑅, the flag is allocated and corresponding to flag value, and then the cats are randomly
distributed into the tracing mode (TM) and seeking mode (SM).
Step 5: 𝐼𝑓 (𝐹𝑙𝑎𝑔 == 1), then the cat is in SM.
Step 6: 𝑘 copies of every cat are made.
Step 7: The bit score for all cats are evaluated through 𝑆𝑅𝐷 and every cat is added or removed to/from the
shifting scores.
Step 8: The FF of all new cat positions is evaluated and the cat’s best position is stored in memory.
Step 9: Else, cat is in TM.
Step 10: The velocity and position of all cats are updated by (4) and (5).
Step 11: The FF of newly produced cat’s position is evaluated and the cat’s best position is stored in memory.
Step 12: The cat’s position is updated and also the best position of cat is decided.
Step 13: The final solutions are achieved.
The ICSO provides key points according to the CSO i.e., the cat position and best key points are selected as
the best cat position.
3.3. Fitness function
In the proposed ICSO algorithm, fitness function is employed for estimating the fitness of cat. To
solve the imbalance issues in the optimization algorithm, the frequently used fitness function is taken as the
weighted average classification accuracy (avg) for classifying the imbalanced data. The fitness function is
mandatory to give the weight, but also the assurance of weight is specific. To commonly treat the majority
and minority class, the weight w= 0.5 is used. In imbalanced data classification, the area under curve (AUC)
and Pearson correlation are significant measures and are also used in fitness functions. In common,
glenohumeral joint osteoarthritis (GJO) with AUC as a fitness function consumes large training time and
gives better outcomes in evaluation. AUC is represented in (6), (7) and (8),
𝐴𝑈𝐶𝐹 = ∑
1
2
× (𝐹𝑃𝑅𝑖+1 − 𝐹𝑃𝑅𝑖)(𝑇𝑃𝑅𝑖+1 − 𝑇𝑃𝑅𝑖)
𝑁−1
𝐼=1 (6)
where, 𝑁 is the threshold number, 𝐹𝑃𝑅𝑖 and 𝑇𝑃𝑅𝑖 are the 𝑖𝑡ℎ
threshold of false positive rate and true positive
rate respectively.
𝐴𝑈𝐶𝑤 =
∑ ∑ 𝐼𝑤𝑚𝑤 (𝑃𝑖,𝑃𝑗)
𝑗∈𝑀𝑎𝑗
𝑖∈𝑀𝑖𝑛
|𝑀𝑖𝑛|∗|𝑀𝑎𝑗|
(7)
where,
𝐼𝑤𝑚𝑤(𝑃𝑖, 𝑃𝑗) = {
1, 𝑃𝑖 > 𝑃𝑗 𝑎𝑛𝑑 𝑃𝑖 ≥ 0
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(8)
where, 𝑃𝑖 and 𝑃𝑗 represent the output values taking an instance of 𝑖 and 𝑗 from the minority class and
majority class as input respectively. |𝑀𝑖𝑛| and |𝑀𝑎𝑗| illustrate the number of minority class and majority
class instances, respectively. Pearson correlation is formulated in (9),
𝑟 =
𝑁∑𝑥𝑦−(∑𝑥)(∑𝑦)
√𝑁∑𝑥2−(∑𝑥)2][𝑁∑𝑦2−(∑𝑦)2]
(9)
where 𝑟 is the Pearson correlation coefficient, 𝑁 is the pair scores count, ∑𝑥𝑦 is the sum and product of
scores, ∑𝑥 and ∑𝑦 is the sum of x and y scores, ∑𝑥2
and ∑𝑦2
is the sum of squares of x and y scores.
3.4. Classification
After selecting the features from the crops, the recurrent neural network (RNN) is utilized for
classification. The RNN is one category of neural network that produces a direct graph by using a sequence
of data [29]. RNN decides the current layer output by involving all other existing calculations. It differs from
a classic neural network, in which all the input values are autonomous to each other. The following steps
constitute the training flow of RNN in classification.
Step 1: The network is supplied with an individual time of input.
Step 2: The present input and earlier state are used for evaluating the present state.
Step 3: For the upcoming time steps, the present state ℎ𝑡 is transferred to the ℎ𝑡 − 1.
Step 4: All times steps are built based on the problems. The instruction is merged from the earlier state.
Step 5: After completing all the time steps, the last present state is employed by the outputs.

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Step 6: For updating the weights, the fault is back-propagated to the network. Therefore, RNN is trained.
In RNN, every input is transferred to the next layer while the output of every layer fully depends on
the previous layer. Hence it is called a recurrent neural network, and it accomplishes the same function for
every component. The function of RNN with time-series data [30] and the output of RNN obtain the best
result which is utilized to determine the earlier information. The RNN combines the output and forgets the
gate into a specific update gate 𝑢𝑝𝑑, in which the linear interpolation method is used to obtain a better result.
Assume that the 𝑒𝑑 ← 𝐹𝑟𝑘∗ is the input feature of dimension 𝑑, then 𝐻𝑑−1 represents the hidden previous
state. Equations (10) and (11) represent the output of the update gate 𝑢𝑝𝑑 and reset gate 𝑟𝑠𝑑.
𝑢𝑝𝑑 = 𝑎𝑐𝑣(𝑊𝐹𝑒𝑢𝑝
𝑒𝑑 + 𝑊𝐹𝐻𝑢𝑝
𝐻𝑑−1) (10)
𝑟𝑠𝑑 = 𝑎𝑐𝑣(𝑊𝐹𝑒𝑟𝑠
𝑒𝑑 + 𝑊𝐹𝐻𝑟𝑠
𝐻𝑑−1) (11)
where, 𝑎𝑐𝑣 represents the activation function, in general, it is a logistic sigmoid function. 𝑊𝐹𝑑
=
𝑊𝐹𝑒𝑢𝑝
, 𝑊𝐹𝑒𝑟𝑠
, 𝑊𝐹𝐻𝑢𝑝
, 𝑊𝐹𝐻𝑟𝑠
is denoted by the weight function which is tuned through training algorithm
to decrease error variation among actual and forecasted outputs. The hidden unit candidate state represented
in (12).
𝐻𝑑 = 𝑡𝑎𝑛(𝑊𝐹𝑒𝐻
𝑒𝑑 + 𝑊𝐹𝐻𝐻(𝐻𝑑−1 ⊗ 𝑟𝑠𝑑)) (12)
where, ⊗ is the element-wise multiplication. The linear interpolation between candidate state 𝐻𝑑 and 𝐻𝑑−1
Additionally, the hidden activation function in the term 𝑑 is represented as 𝐻𝑑 of RNN as illustrated in (13).
𝐻𝑑 = (1 − 𝑢𝑝𝑑) ⊗ 𝐻𝑑 + 𝑢𝑝𝑑 ⊗ 𝐻𝑑−1𝐻𝑑 = (1 − 𝑢𝑝𝑑) ⊗ 𝐻𝑑 + 𝑢𝑝𝑑 ⊗ 𝐻𝑑−1 (13)
where, 𝐻𝑑−1 denotes the hidden previous state and ⊗ is the element-wise multiplication. In neural networks,
all output and input values are independent, whereas in the RNN, the data in the hidden layer is remembered
and it is completed in a previous hidden layer. The remembered data is permitted as input to the next layer so
that it can perform operations on the data. This procedure is continuously repeated until it obtains the
preferred output which is formulated in (14), (15), and (16),
ℎ𝑡 = 𝑓(ℎ𝑡−1, 𝑥𝑡) (14)
ℎ1 = 𝑡𝑎𝑛 ℎ (𝑊ℎℎℎ𝑡−1 + 𝑊𝑥ℎ𝑋𝑡) (15)
𝑦𝑡 = 𝑊ℎ𝑣ℎ𝑡 (16)
This RNN takes the sequence of inputs from 𝑥0 and it outputs the sequence as ℎ0 which combines
with the 𝑥1which is the input for the next process. Then, the 𝑥1 and ℎ0 are inputs for next process and
similarly, ℎ1 and 𝑥2 are inputs for the next step. By selecting six different features of soil, temperature, water,
production, solar radiation and area, the RNN produces a direct graph using the sequence of data and decides
present layer output by involving all other existing calculations.
The proposed RNN model contains advantages like enhancing crop yields, real-time crop analysis,
choosing effective parameters, and making smart decisions. Additionally, it helps to reduce the loss to the
farmers when unfavorable conditions occur. The RNN performs well in time series forecasting issues like
crop yield prediction. It can capture long-term dependencies in the data which enables it to learn complex
relationships and patterns. It also learns relevant features automatically from the input data. Due to the ability
to capture complex relationships and patterns, RNN can yield higher prediction accuracy compared to
traditional statistical models.
4. RESULTS AND DISCUSSION
In this paper, the proposed model is simulated through python environment with the system
requirements of RAM 16 GB, Intel core i7 processor, and a Windows 10 (64 bit) operating system. Statistical
parameters like the coefficient of determination (R2), root mean square error (RMSE), mean squared error
(MSE), and mean absolute error (MAE) are used for estimating the model. These parameters are calculated
from the predicted yields of all the years for each district. The mathematical representation of these
parameters is shown in (17) to (20),

1707
𝑅2
= 1 − ∑ (
(𝑦𝑖−𝑦𝑑𝑖)2
(𝑦𝑑𝑖−𝑦𝑚)2)
𝑛
𝑖=1
(17)
𝑀𝐴𝐸 =
1
𝑛
∑ |𝑦𝑖 − 𝑦𝑑𝑖|
𝑛
𝑖=1
(18)
𝑀𝑆𝐸 =
1
𝑛
∑ (𝑦𝑖 − 𝑦𝑑𝑖)2
𝑛
𝑖=1 (19)
𝑅𝑀𝑆𝐸 = √𝑀𝑆𝐸 = √
1
𝑛
∑ (𝑦𝑖 − 𝑦𝑑𝑖)2
𝑛
𝑖=1 (20)
where, 𝑛 is number of points, 𝑦𝑖 is predicted value obtained from neural network, 𝑦𝑑𝑖 is real value, and 𝑦𝑚 is
mean of the real value.
4.1. Quantitative analysis
This section shows the quantitative analysis of the ICSO-RNN model without augmentation in R2,
MSE, MAE, and RMSE with actual and optimized features. Tables 1 and 2 illustrate the quantitative analysis
of various classifiers with actual and optimized features. Table 3 illustrates the quantitative analysis of
various optimization algorithms. The features such as region, soil, season, year, tones, crop, acres, water,
area, temperature, production, solar radiation and pH value are considered. Out of these 13 features, only 6
features are extracted, the remaining 7 features contain contributions which enhance the model’s
performance. The model’s performance decreases because it does not extract seven features.
The performance of classifiers with actual features is shown in Table 1 and Figure 2. The R2, MSE,
MAE, RMSE of ANN, convolutional neural network (CNN), long short-term memory (LSTM) and RNN are
measured and compared with the proposed ICSO-RNN. The obtained result displays that the proposed ICSO-
RNN model achieves a better result with the R2, MAE, MSE, and RMSE values of 0.95, 0.75, 0.76 and 0.87,
respectively while considering feature selection compared to other classifiers.
The performance of classifiers with optimized features is compared to that with actual features is
shown in Table 2 and Figure 3. The R2, MSE, MAE, RMSE of ANN, CNN, LSTM and RNN are measured
and compared with the proposed ICSO-RNN. The obtained results show that the proposed ICSO-RNN model
exhibits better performance with the R2, MAE, MSE and RMSE values of 0.99, 0.77, 0.68 and 0.82,
respectively while considering feature selection compared to other classifiers.
Table 3 and Figure 4 describe the performance of RNN using various optimization techniques like
PSO, genetic algorithm (GA), and ICSO. The obtained results display that the proposed ICSO-RNN achieves
better results with the R2, MAE, MSE and RMSE values of about 0.99, 0.77, 0.68 and 0.82, respectively
while evaluating feature selection compared to another optimization algorithms.
Table 1. Performance of the various classifier with actual features
Methods R2 MAE MSE RMSE
ANN 0.70 0.89 0.88 0.93
CNN 0.85 0.85 0.85 0.92
LSTM 0.89 0.79 0.81 0.9
RNN 0.92 0.77 0.79 0.88
ICSO-RNN 0.95 0.75 0.76 0.87
Table 2. Performance of the various classifier with optimized features
ANN 0.75 0.87 0.85 0.92
CNN 0.89 0.84 0.81 0.9
LSTM 0.92 0.81 0.77 0.87
RNN 0.97 0.79 0.72 0.84
ICSO-RNN 0.99 0.77 0.68 0.82
Table 3. Performance of the proposed methodology
RNN 0.87 0.84 0.85 0.92
PSO-RNN 0.95 0.81 0.82 0.9
GA-RNN 0.98 0.79 0.79 0.88
ICSO-RNN 0.99 0.77 0.68 0.82

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Figure 2. The performance of the classifier with actual features
Figure 3. The performance of the classifier with optimized features
Figure 4. The performance of the proposed methodology
4.2. Comparative analysis
This section shows the comparison of RNN classifier in terms of R2, MSE, MAE, and RMSE as
shown in Table 4. Existing researches such as ACO-OSELM [23], hybrid RF-RL [24] and ML [25] are used
for evaluating the efficiency of the classifier. The proposed model is trained, tested and verified by applying
a time series data. The proposed ICSO is evaluated for efficient classification by overcoming overfitting
problems and classification by using the RNN technique.
4.2.1. Discussion
This section illustrates the proposed method’s advantages and the limitations of the existing
methods. The existing models such as the ACO-OSELM [23] model is utilized in remote areas where the
meteorological data is unavailable because of limited resources. The hybrid RF-RL [24] model struggles to
handle temporal dependencies and patterns in time-series data which is crucial for crop yield prediction. The

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inputs of the ML [25] model is extremely affected by sampling errors and limitations in data availability. For
these reasons, the ICSO based RNN model is proposed to overcome these limitations. The introduced model
enhances the outcomes and obtains better convergence in minimum iteration. The inertia weight parameter is
added to the position equation that is selected randomly, and a new velocity equation is produced to enhance
the searching ability in the best cat area. By using inertia weight, the ICSO is utilized to enhance the
performance of feature selection, and hence obtains better convergence in minimum iteration. The RNN is
applied to produce a direct graph by using sequence of data, additionally, it decides the present layer output
by involving all other existing calculations.
Table 4. Comparative analysis of existing models with the proposed ICSO-RNN model
Author Period R2 MAE MSE RMSE
Ali et al. [23] 1981-2013 0.99 42.37 N/A 67.12
Elavarasan and Vincent [24] 2011-2016 0.87 0.17 0.06 0.23
Batool et al. [25] 2016-2019 N/A 0.12 0.02 0.15
Proposed ICSO-RNN 2011-2021 0.99 0.77 0.68 0.82
5. CONCLUSION
In this research, a new ICSO-RNN model is developed for effective agriculture crop yield
prediction. This method contains multiple objective functions like min-max normalization and ICSO model
for effective classification. The dataset is collected from Andhra Pradesh and it consists of the monthly yield
of crops from 10 districts during the period of 2011-2021, with annual production for 120 records of
approximately 8 million nuts. In min-max normalization, the highest score of the feature is transformed into
1, the smallest score of the feature is transformed into 0, and other values of the feature are transformed into
an integer between 0 and 1. The inertia weight parameter is added to the position equation that is selected
randomly, and a new velocity equation is produced to enhance the searching ability in the best cat area. By
using inertia weight, the ICSO is utilized to enhance the performance of feature selection and to obtain better
convergence in minimum iteration. RNN is utilized for producing a direct graph by using a sequence of data,
and it decides the current layer output by involving all other existing calculations. The evaluated result shows
that the proposed ICSO-RNN model delivers the evaluation metrics of R2, MAE, MSE, and RMSE with
values as 0.99, 0.77, 0.68, and 0.82, respectively which ensures accurate yield prediction.
The proposed methodology has limitations such as its slow convergence in complex and high-
dimensional problems, and generating complex and non-intuitive models, making it difficult to interpret. The
data contains noise and uncertainties due to various factors. In time series data, it struggles to capture long-
term dependencies. The future scope for the research is utilizing the hyperparameter tuning with deep
learning algorithms like recurrent neural network for the better prediction of crop yield in time series data.
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BIOGRAPHIES OF AUTHORS
Dwaram Jayanarayana Reddy is research scholar, Department of Computer
Science and Engineering, JNTUA, Ananthapuramu-515002, Andhra Pradesh, India. Received
M.Tech degree in computer networks and information security from JNTU Hyderabad,
Andhra Pradesh, India. He is a life member of CSI, and he has published many research
papers in national and international journals, and conferences. His research interests include
artificial intelligence, machine learning and computer networks. He can be contacted at email:
djnreddy@gmail.com.
Rudra Kumar Madapuri is working as professor, he received B.Tech. in
computer science and engineering from Sri Venkateswara University, Tirupati, Andhra
Pradesh, India. He received M.Tech. degree from Jawaharlal Nehru Technological University,
Anantapur, Andhra Pradesh, India. He received Ph.D., from Jawaharlal Nehru Technological
University, Anantapur, Andhra Pradesh, India. He is a life member of CSI, and he has
published many research papers in national and international journals, conferences. He
authored three books and also has six patents. His main research interests include software
engineering, machine learning, internet of things and cloud computing. He can be contacted at
email: mrudrakumar@gmail.com.

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