Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 14, No. 3, 2025 

 

376 

Research	on	Crop	Planting	Strategies	Based	on	
Optimization	Algorithms	
Zhiwei Wen1, †, *, Chao Liang1, †, Yurui Yao2 

1College of Mathematics Science, Chengdu University of Technology, Chengdu, China 
2College of Management Science, Chengdu University of Technology, Chengdu, China 
† These authors also contributed equally to this work 

*Corresponding author: baire314@outlook.com 

 

Abstract: With the development of organic planting industry, choosing suitable crops and optimizing planting strategies are 
of great significance to the sustainable development of rural economy. In order to help a village design the optimal planting plan 
for crops in 2024∼2030, this paper first builds an objective function based on the treatment of expected sales exceeding the 
situation in multiple scenarios, sets constraints according to the requirements, models and solves to obtain the optimal planting 
strategy[1], and comprehensively examines the model's stability and and reasonableness based on the sensitivity analysis. 
Secondly, Monte Carlo algorithm is introduced to search for the optimal planting strategy of many simulated scenarios, and 
particle swarm algorithm is used to analyze the uncertainty and planting risk of global optimization of planting strategy. Pearson's 
correlation coefficient is then used to introduce linear regression model and nonlinear regression model to analyze the 
substitutability and complementarity between crops, and the best planting plan is obtained through comparison. 

Keywords: Crop Planting Strategies, Monte Carlo Simulation, Particle Swarm Algorithm, Pearson Related Analysis. 
 

1. Introduction 
A village in the mountainous region of northern China is 

located in a low-temperature environment, and most of the 
arable land can only be cultivated for one crop season per year. 
The village has 1,201 acres of open cultivated land, which is 
scattered on 34 plots of different sizes, including four types 
of land: flat dry land, terraced land, hillside land and watered 
land. There are also 16 ordinary greenhouses and 4 smart 
greenhouses in the countryside, each with an area of 0.6 acres. 
With the development of the organic farming industry, it is 
particularly important to select suitable crops and optimize 
the planting strategy. The expected sales volume, planting 
cost, acreage, and sales price of each crop, as well as the effect 
of the uncertainty factor “climate” on acreage, and the 
substitutability and complementarity of crops are all factors 

that will influence the planting plan for the region in 
2024~2030. The planning modeling will play a key role in the 
development of optimal cropping scenarios to improve the 
profitability of farming. 

2. Correlation Analysis 

2.1. Patterns of area utilization and yield 
distribution 

The total area of crops grown on each plot in 2023 was 
counted and then compared with the total area of the plot, so 
the utilization rate on each plot could be obtained, and it was 
found that the distribution of the area utilization rate of the 
plots was relatively simple, with only two cases, 50%, 66.7%, 
and 100%, and the specific quantities could be derived from 
Figure 1: 

 

 
Figure 1. 2023 parcel area utilization rate 

 
The pattern of yield distribution varies according to 

different crop types and different plot types and is visualized 
through Figure 2 and Figure 3: 

 



 

377 

 

 
Figure 2. Yield by type for different crops 

 

 
Figure 3. Yield of different plot types 

 
The following conclusions can be drawn from Figure 2: the 

yield of food grains is the largest among all crop types, 
followed by vegetables, and legumes are less productive than 
non-legumes, but more productive than edibles. Observation 
of Figure 3 shows that the total crop yield is highest in 
irrigated land, followed by crop yield in terraced land and 
lowest in greenhouses. 

2.2. Pearson correlation analysis 
Pearson correlation analysis is a statistical method used to 

measure the linear correlation between two variables. Based 
on the planting data of 2023, production, selling price and cost 
were taken as the research objects and correlation analysis 
was conducted using Pearson's correlation coefficient, and in 
order to visualize the results of the analysis, the correlation 
heat Figure 4 was plotted as follows: 

 

 
Figure 4. Heat map for correlation analysis of production, selling price and cost. 

 
By observing the correlation heat map 4 , we can find that: 

the correlation coefficient between planting cost and selling 
price is 0.76, indicating that there is a strong positive 
correlation between planting cost and selling price, that is to 
say, the selling price of the species with higher planting cost 
tends to be higher; the correlation coefficient between 
planting cost and yield is -0.40, indicating that there exists a 

certain negative correlation between planting cost and yield; 
there is a certain negative correlation between selling price 
and yield as well. The correlation coefficient between 
planting cost and yield is -0.40, indicating that there is a 
negative correlation between planting cost and yield. 

So overall, the correlation between the three is more 
significant. 



 

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3. Strategies for Handling Excess Sales 
Projections in Multiple Scenarios 

3.1. Proceeds from different expected sales 
volumes 

When the yield of a crop exceeds the marketing 
expectations, the excess crop will not be marketable and the 
objective function is to maximize the return on the marketable 
crop: 

 
6 2

1 1

max min ( ), 0i ijt ijtk ijt ijtk i
t k i j

P Y x C x W
 

 
    
 
 

   (1) 

 
Where 0iW  denotes the crop yield from sales in 2023. 
When the yield of a crop exceeds the sales expectation, the 

excess is sold at a 50% discount with an objective function: 
 

, , , , , ,

1
max ( ) max(0, ( )

2ijk ijk ijok ijk ijtk ijk ijk ijtk ijok
i j k t i j k t

P Y x C x P Y x x       (2) 

 
Different types of plots are suitable for different crops, and 

the planted area of each plot cannot exceed its maximum 
usable area per year. 

Various objective functions are added by setting the 
constraints of plot type and planting season limit, crop 
rotation limit, planting cycle of legume crops, minimum 
planting area, and finally the model is summarized. 

3.2. Rationalization of results 
The utilization rates of all parcels are counted and the 

distribution of the results can be analyzed with the help of 
Figure 5. According to the graph, the utilization rate of the 
plots varies from 0.6 to 1, and most of the utilization rates are 
located above 0.9, which is more similar to the situation of the 
utilization rate in 2023, which indicates that the area 
utilization rate of the plots is reasonable. 

 

 

Figure 5. Distribution of area utilization rates 
 

The stability of the model is tested and a sensitivity analysis 
is performed. Since the calculation of the unit price of sales is 
obtained by averaging the endpoints of the intervals directly, 
and the fluctuation of the price in the real scenario is not 
sufficiently taken into account, we consider randomly 
selecting 50% of the crops and simulating the price of these 
crops at the level of 1% ∼ 5% for seven consecutive times, 
and then re-optimizing the model by introducing the new 

price data, and then observing the change of the objective 
function (total profit), and the results are shown in Figure. 6. 
Based on the graph, it can be seen that the optimization 
algorithm is able to make timely adjustments to the planting 
strategy when continuous fluctuations in price occur, and 
makes the percentage change in profit fluctuation vary only 
between ∼1% and ∼4.5% at each time. 

 

 

Figure 6. Sensitivity analysis results 



 

379 

 

4. Strategies for Analyzing 
Uncertainties and Potential Planting 
Risks 

4.1. Monte-Carlo stochastic simulation 
Monte Carlo Simulation (MCS)[2] is a numerical 

computation method based on the generation of random 
numbers for estimating the outcome of complex systems or 
solving mathematical problems that are difficult to analyze. 
The method obtains a solution to the problem by introducing 
randomness in a large number of repeated experiments and 
analyzing the statistical properties of the results of these 
experiments, generating multiple possible market scenarios 
covering a variety of uncertainties such as fluctuations in 
yields, sales volumes, cultivation costs, and sales prices: 

Sales Volume Perturbation: generates multiple possible 
market scenarios covering various uncertainties such as 
fluctuations in production, sales volume, growing costs and 
sales price: 

 
2

1

, ,it ijtk ijk
k j

S x Y t j


               (3) 

 
And then the volume of a crop sold in 2023 is: 
 

2

0 0
1

,i ij k ijk
k j

S x Y j


                 (4) 

 

Define the change in sales volume  , 6,7Sit i  , denoting 

the numbering of wheat and corn. Wheat and maize: sales 
volume is expected to grow between 5% and 10% per year: 

 
~ (0.05,0.10), {6,7}

itS
U i               (5) 

 
For other crops: ±5% change in sales volume per year 

relative to 2023: 
 

~ ( 0.05,0.05), {1,2,...,5,8,...,41}
itS
U i          (6) 

 

Change in acreage: denote by ijktY  the acreage of crop i  

grown on plot j   in season k   of year t  , and denote by 

ijktY  the acreage of crop i  grown on plot j  in season k  

of year 2023, defining the change in acreage, ijktY  , with 

acreage of all crops fluctuating in the range of ±10% per year 
due to climate change: 

 
~ ( 0.10,0.10), , ,

ijktY U i j k                  (7) 

 
Change in planting costs: denote by ijktC   the cost of 

planting the i th crop in the k th season of year t  in plot j  , 

and by 0ijkC   the cost of planting the i  th crop in the k  th 

season of year 2023 in plot j . Define the change in planting 

costs, ijktC , with an average annual increase in planting costs 

of all crops of about 5 percent: 

~ (0.05,0.01), , ,
ijktC N i j k                 (8) 

 

Change in sales price: Denote by ijktP  the sales price of 

planting the i th crop on the j th plot in the k th season of 

the t th year, and denote by 0ijkP  the sales price of planting 

the i th crop on the j th plot in the k  the season of the 2023 

year, and define the change in sales price ijktP
 , where: 

Grain crops (number i  ,   1,2,... ,16i  ) have largely 

stable sales prices with no significant changes: 
 

0, {1,2,...,16}, ,
ijktP

i j k                 (9) 

 

Vegetable crops (number i  ,   17,18,... ,37i  ) numbered 

sales prices increase on average by about 5% per year: 
 

~ (0.05,0.01), {17,18,...,37}, ,
ijktP

N i j k         (10) 

 

Edible mushrooms (number i  ,   38,39,40,41i  show 

annual declines of between 1% and 5%, with a fixed decline 
of 5% for morel mushrooms (number i  = 41) in particular: 

 
~ ( 0.05, 0.01), {38,39,40}, ,

ijktP
U i j k           (11) 

 

41
0.05, ,

jktP j k                   (12) 

 
Monte Carlo simulation to generate multiple market 

scenarios. The parameters in each scenario are calculated 
based on the random variables described above and are 
chosen to generate 100 different market scenarios, each 
representing a possible future market state. 

4.2. Summary of non-linear optimization 
models 

The objective is to maximize total revenue between 2024 
and 2030, and production in excess of expected sales is 
treated as stagnant and disregarded, then the objective 
function is calculated as follows: 

 

 
, , ,

max ijkt ijkt ijtk ijkt ijtk
i j k t

P Y x C x             (13) 

 
The constraints are consistent with the above multi-class 

scenarios in which the expected sales volume exceeds the 
handling of the situation model, it is worth noting that the 
limitations of the expected sales volume is different from the 
former, in order to avoid the risk of exceeding the expected 
sales volume of stagnant sales, the requirements of the year, 
the production of a crop should not be more than the 
corresponding year's expected sales volume, then: 

 
2

1

, ,it ijtk ijkt
k j

S x Y t j


               (14) 

 
For each market scenario, we use nonlinear programming 



 

380 

to optimize the cropping strategy to maximize the total return 
to obtain the final nonlinear optimization summary model. 

4.3. Particle Swarm (PSO) Optimization 
Algorithm Solution 

Particle Swarm Optimization (PSO) is an optimization 
algorithm based on group intelligence. Based on the high 
dimensionality and dynamic scenario of the above-mentioned 
planning model, PSO performs well in high-dimensional 
optimization problems, and can handle a large number of 
variables. Its strong adaptivity as well as global search ability 
can effectively explore in the solution space to avoid falling 
into local optimums, which is suitable for solving 
optimization problems that change over time. Accordingly, 
PSO is used in this paper to solve the above nonlinear 
planning model. 

Each particle represents a possible planting scheme, which 

is represented by a vector containing the planting area ijktx  

of all crops on all plots. 
The fitness function is to maximize the total return over the 

period 2024 to 2030: 
 

 
, , ,

max ijkt ijkt ijtk ijkt ijtk
i j k t

P Y x C x            (15) 

 
The velocity and position update equations for each particle 

i  are as follows: 
 

   ( 1) ( ) best ( ) best ( )
1 1 2 2

t t t t
i i i i iv w v c r p x c r g x           (16) 

 

( 1) ( ) ( 1)t t t
i i ix x v                    (17) 

 
When the maximum number of iterations is reached or the 

global optimal solution converges to maximize profit at the 
time, the algorithm stops and outputs the optimal solution. 
The plot utilization rates are all above 0.9, indicating that each 
plot is quite fully utilized and the results are good, suggesting 
that this perspective is reasonable[3]. 

5. Strategies for Analyzing 
Substitutability and 
Complementarity Among Crops 

5.1. Crop correlation analysis 
First, substitution and complementarity are explained[4]: 

substitution refers to the fact that if there are many substitutes 
for a good, an increase in price may lead to a decrease in sales 
as consumers may switch to other options; complementarity 
refers to the fact that if a good is complementary to other 
goods, an increase in price may reduce sales of the 
complementary good and thus overall sales. The impact on 
sales of changes in the prices of complementary commodities 
needs to be considered. 

In order to investigate the substitutability and 
complementarity between crops, this paper firstly judges the 
correlation between mu yield and sales price and planting cost 
in different crop types, including grain (beans), grain, 
vegetables (beans), vegetables and edible fungi. Pearson's 
correlation coefficient was used to calculate the correlation 
between different variables, and the heat map of correlation 
was obtained and some of the results were visualized and 
displayed in Figure 7. 

 

 
Figure 7. Heat map of food-related relationships 

 
Accordingly, we obtained the correlation coefficients of 

different crop types of grain (beans), grain, vegetables (beans), 
vegetables, edible mushrooms in the expected sales volume 
and sales price, planting costs, in order to obtain the 
correlation matrix, the closer the correlation coefficient is to 
1, indicating that the stronger the positive correlation, i.e., the 
stronger the complementarity; the closer the correlation 
coefficient is to -1, indicating that the stronger the negative 
correlation, i.e., the stronger the substitutability. 

5.2. Linear regression models 
Multiple linear regression models were used to predict the 

relationship between acreage value and selling price and cost 
of planting. Stepwise Regression is a variable selection 
method used to select the optimal set of variables from 
multiple candidate independent variables to construct a 
regression model. Stepwise regression optimizes the 
predictive and explanatory power of a model by gradually 



 

381 

adding or removing variables. Using stepwise regression, the results of solving the regression model are shown in Table 1: 
 

Table 1. Results of linear regression analysis 
Linear regression analysis results 

 

Non-standardized 
coefficient 

Standardized 
coefficient 

T P R2 F 
B 

Standard 
error 

Beta 

Constant 20112.495 1484.847 0 13.545 0.000*** 
0.12 

F=28.724, 
P=0.000*** Planting Costs 

(yuan/mu) 
-2.784 0.519 -0.346 -5.36 0.000*** 

 
From the analysis of the results in Table 1, it can be 

obtained that the significance p-value is 0.000∗∗∗, the level is 
significant, and the original hypothesis that the regression 
coefficient is 0 is rejected. And p-value 0.000∗∗∗∗, indicating 
that the planting cost has a significant effect on the expected 

sales volume, the model is well constructed, and collated to 
get the fitting effect Figure 8. and this paper uses a common 
nonlinear regression model for fitting, and analyzed using 
SPSSPRO to get the nonlinear fitting effect Figure 9: 

 

 
Figure 8. Plot of linear fitting effects 

 

 
Figure 9. Plot of non-linear fitting effects 

 

5.3. Summary of optimization models based on 
uncertainty and potential planting risk 
analysis strategies 

Substitutability and complementarity among crops and 
correlation of expected sales volume, sales price, and planting 
cost were considered. A multivariate correlation model was 
developed by combining the matrix of correlation coefficients 
for different crop types and the regression equations for sales 
price, and planting cost[5]. 

Based on the uncertainty and potential planting risk 
analysis strategy, stochastic planting cost, acreage, and unit 
sales price parameters for a given crop and values in the 
correlation matrix were used to adjust these stochastic 
parameters to simulate new market scenarios under 
substitutability and complementarities (constraints were 
consistent and were solved using the pso particle swarm 
algorithm[6] as well.). Again, through simulation, 100 
different market scenarios are chosen to be generated, each 
representing a possible future market state, resulting in an 



 

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optimized model summary. 

5.4. Comparative analysis of model summary 
results 

For the two planting strategies, the total yield of each crop 

was calculated separately and compared and analyzed using 
line graphs, as shown in Figure 10, there is a large discrepancy 
between the distribution of the total yields of the different 
crops planted in the two questions, with the former having a 
more centralized distribution of yields and the latter having a 
more decentralized distribution of yields. 

 

 
Figure 10. Comparison of total yields considering uncertainty and considering substitutability and complementarity between 

crops 
 

6. Conclusion 
In this paper, through the analysis of experimental results 

and sensitivity test, the stability and reasonableness of the 
model based on the handling of the expected sales exceeding 
the situation in different situations are effectively confirmed. 
At the same time, based on the uncertainty of influencing 
factors and potential planting risks, and considering the 
substitutability and complementarity between various crops, 
Monte Carlo simulation and optimization algorithms were 
used to find the optimal planting strategy, and the obtained 
optimization model summarizes the strategy as an excellent 
planting strategy that can be adapted to a variety of real-world 
scenarios. 

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