K-means Cluster Analysis Method Research Articles

Identification of Priority Areas for Carbon Compensation in Chongqing Based on the Difference in Land Use Carbon Budget

This study aimed to explore the spatiotemporal patterns and balance characteristics of land use carbon budget, measure the value of carbon compensation, and delineate carbon compensation type zoning to provide scientific reference for further strengthening the connection between the construction of an ecological compensation system and the "dual carbon" target task. Based on the land cover data of Chongqing from 2000 to 2020, this study analyzed the spatiotemporal dynamics and balance relationship characteristics of the land use carbon budget. By using the revised carbon compensation model to measure the horizontal compensation standards, the normalized revealed comparative advantage （NRCA） index and K-means clustering analysis method were used to divide the carbon compensation area. The research results demonstrated that： ① the total land use carbon sequestration in Chongqing grew slowly from 2000 to 2020, whereas carbon emissions continued to increase significantly, and the net carbon emissions showed a distribution pattern of "high in the center and low in the two wings." ② The average coefficient of variation in Chongqing was 0.602, and the carbon emission economy contributive coefficient and carbon ecological support coefficient were concentrated between 0.64-1.14 and 0.00-32.86, respectively. The difference in the contribution of carbon emissions and economic benefits between districts and counties was relatively small, but there was a mismatch between carbon supply and demand. ③ A significant spatial difference existed in the value of carbon compensation, with a total of 1.098 billion yuan in carbon payment and 634 million yuan in carbon compensation, respectively. Moreover, it was ultimately determined that there were eight key payment areas, seven general payment areas, three key compensation areas, and 20 general compensation areas. In conclusion, the research results can provide a reference for implementing differentiated development strategies in different types of carbon compensation regions, improve the collaborative governance capacity of the regional ecological environment, and promote the achievement of carbon neutrality goals.

A novel integrated method for improving the forecasting accuracy of crude oil: ESMD-CFastICA-BiLSTM-Attention

The volatility of crude oil price can significantly impact the stability of the crude oil market and even the global economy. Effectively predicting global crude oil price and volatility provides a scientific basis for decision-making for market regulators and investors worldwide, promoting the sound development of the global economy. In this study, we integrate signal processing with deep learning methods to present an optimal forecasting strategy for global crude oil price and volatility. We select the daily price of the WTI crude oil market from April 4, 1983, to December 12, 2023, for calculating volatility. Subsequently, employing extreme-point symmetric empirical mode decomposition (ESMD), K-means clustering, and fast independent component analysis method, we decompose and reconstruct the forecasting data, obtaining independent components with non-Gaussian characteristics. These components serve as inputs to estimate the accuracy of various models, including BiLSTM, Attention, LSTM, SVR, RF, and their combinations, in predicting crude oil price and volatility from both a point prediction and interval prediction perspective. Empirical results demonstrate that data decomposition, reconstruction, and the BiLSTM-Attention model outperform other models in predicting crude oil price and volatility.

Анализ метафоры жизненного пути как инструмент взаимодействия в рамках психолого-педагогического сопровождения студентов

<p style="text-align: justify;">An author’s method is presented that allows for a qualitative change in the interaction between a teacher-psychologist and a student using a tool for analyzing the “Metaphor of the Life Path” and interpreting the data obtained within the framework of psychological and pedagogical support of the learning process at the university. The study involved 267 respondents aged 17 to 55 years (Mage = 28.6, SDage = 7.0, 31 men and 236 women). The study participants represent two groups: 101 — students receiving education at the time of the study, Mage = 22, SDage = 4.8, 166 — respondents who completed their studies at the university at the time of the study, Mage = 31, SDage = 5.8. The methodology of the metaphorical essay “Metaphor of the Life Path” is used. To process quantitative data, the k-means cluster analysis method is used. Content analysis is used to analyze metaphorical essays. The results obtained make it possible to complement the existing practices of working with metaphor, used within the framework of psychological and pedagogical support for students. Analysis of the life path metaphor is one of the effective tools for building interaction within the framework of psychological and pedagogical support for students.</p>

Evaluation and clustering of health security performance in Africa: A comparative analysis through the entropy-TOPSIS-K-means approach

ABSTRACT This study presents an analysis and comparison of the health security practices (HSP) of 47 African countries based on 2019 and 2021 data. Its objective is to assess, rank, and cluster the countries based on their HSP performance and progress over this period. A comprehensive Entropy-TOPSIS-K-means-based evaluation system was constructed for this purpose. Initially, the entropy method was utilised to analyze and compare investment priorities. Subsequently, the Entropy-TOPSIS was used to evaluate and compare the level of health security (HS) performance and the degree of improvements made by countries over the study period. Finally, the K-means cluster analysis method was applied to classify countries based on their comprehensive evaluation scores. Among the six identified criteria, prevention, detection, reporting, and health system practices were deemed crucial for HS decision-making in both cases. The study revealed significant differences in HSP levels and changes in countries’ improvement levels between their practices in 2019 and 2021. The study classifies the security levels of African countries into five clusters and provides a detailed analysis, implications, and recommendations to aid decision-makers in enhancing HS outcomes. Its results offer empirical evidence to support planning, resource allocation, and reallocation for strengthening HSP in the region.

INVESTIGATION OF THE EFFECT OF GEOMETRIC IRREGULARITIES ON CAPACITY OF TRAFFIC CIRCLES BY USING PARTIAL LEAST SQUARE REGRESSION METHOD

This paper examined the impact of geometric irregularities on the intersection capacity at traffic circles. A new empirical capacity relation was proposed to predict the capacity of the traffic circle as a function of geometric elements, exit and circulating flows. Within this scope, firstly, the relationship between the vehicles entering from the minor approach and the circulating flow from the turning movement in the traffic circle was examined based on the K-Means cluster analysis method. The analysis was created in accordance with an exponential relationship between entry and circulating flow. Secondly, two clusters were selected by the partial least squares regression method to improve the model's effectiveness. Lastly, to validate the model, "leave-one-out" cross validation was used to select the components that maximize the model's predictive ability. The results show that geometric parameters of a traffic circle create different effects on capacity, especially in different circulating flow conditions.

USING CLUSTER ANALYSIS TO CLASSIFY SOME ARAB COUNTRIES INTO HOMOGENEOUS GROUPS ACCORDING TO INSTITUTIONAL QUALITY CRITERIA

Objective: The objective of this study is to explore the application of cluster analysis in categorizing select Arab countries into cohesive groups based on institutional quality criteria, which consist of six indicators measuring good governance in country. These indicators cover various dimensions and allow describing the quality of services provided by the state in a specific area comprehensively. These dimensions include the scope of state intervention, these dimensions are The Political Dimension, The Economic Dimension and The Legal Dimension. Method: This study adopts a research methodology that combines both descriptive and quantitative approaches. The descriptive approach is based on presenting concepts and describing relationships among institutional quality criteria. The quantitative approach involves using cluster analysis methods: K-Means clustering and Hierarchical Clustering to classify 11 Arab countries: UAE, Bahrain, Algeria, Egypt, Jordan, Morocco, Qatar, Saudi Arabia, Sudan, Tunisia, and Yemen. This was done to conduct cluster analysis to test the homogeneity of these countries regarding institutional quality determinants, represented by the following variables: Participation and Accountability, Political Stability and Absence of Violence, Government Effectiveness, Legislative Quality, Rule of Law, Control of Corruption. Results and Discussion: The study reached the following results: - the K-Means Cluster Analysis Method is evident that The total number of cases classified in each cluster: Eleven countries were classified into seven countries: United Arab Emirates, Bahrain, Jordan, Morocco, Qatar, Saudi Arabia, and Tunisia in the first cluster and four countries in the second cluster: Algeria, Egypt, Sudan, and Yemen; -the variable Participation and Accountability does not significantly affect the classification of the Arab countries under study into homogeneous groups according to institutional quality indicators. However, variables such as Political Stability and Absence of Violence, Government Effectiveness, Regulatory Quality, Legislative Quality, Rule of Law, and Control of Corruption play a significant role in this classification; - the Hierarchical Clustering Analysis Method is evident that the Arab countries under study are distributed into two homogeneous groups. The first group forms Cluster 1, consisting of Jordan, Morocco, Tunisia, Bahrain, Saudi Arabia, Algeria, Egypt, the UAE, and Qatar. The second group belongs to Cluster 2, comprising Sudan and Yemen. This classification is based on institutional quality criteria. Originality/Value: This study sheds light on the importance of cluster analysis methods: the K-Means Cluster Analysis Method and the hierarchical cluster analysis method in classifying Arab countries according to the determinants of institutional quality, which are considered a determining factor for the economic growth of countries, and its consequent impact on various indicators reflecting economic, social, and political conditions. Consequently, institutional quality has emerged as a pivotal measure in highlighting developmental disparities among different countries. Many governments are endeavoring to create or adopt models to enhance the quality of their institutions, notwithstanding the similarities among Arab countries.

Abnormal dynamic functional connectivity in young nondisabling intracerebral hemorrhage patients.

Previous resting-state functional magnetic resonance imaging studies on intracerebral hemorrhage patients have focused more on the static characteristics of brain activity, while the time-varying effects during scanning have received less attention. Therefore, the current study aimed to explore the dynamic functional network connectivity changes of intracerebral hemorrhage patients. Using independent component analysis, the sliding window approach, and the k-means clustering analysis method, different dynamic functional network connectivity states were detected from resting-state functional magnetic resonance imaging data of 37 intracerebral hemorrhage patients and 44 healthy controls. The inter-group differences in dynamic functional network connectivity patterns and temporal properties were investigated, followed by correlation analyses between clinical scales and abnormal functional indexes. Ten resting-state networks were identified, and the dynamic functional network connectivity matrices were clustered into four different states. The transition numbers were decreased in the intracerebral hemorrhage patients compared with healthy controls, which was associated with trail making test scores in patients. The cerebellar network and executive control network connectivity in State 1 was reduced in patients, and this abnormal dynamic functional connectivity was positively correlated with the animal fluency test scores of patients. The current study demonstrated the characteristics of dynamic functional network connectivity in intracerebral hemorrhage patients and revealed that abnormal temporal properties and functional connectivity may be related to the performance of different cognitive domains after ictus. These results may provide new insights into exploring the neurocognitive mechanisms of intracerebral hemorrhage.

K-MEANS CLUSTER ANALYSIS RELATED TO UNMET NEED FOR FAMILY PLANNING IN BANYUWANGI, INDONESIA: A CASE STUDY

Background: The population growth rate in Indonesia from 2010-2020 was 1.25% per year. The rate of population growth must be accompanied by an increase in the quality of human life. Human quality of life begins from within the womb, so that preventive efforts can be undertaken. The Family Planning Program was implemented to overcome the problem of population density so that it becomes more controlled. However, in line with the existence of the family planning program, there are still incidents of unmet need for family planning that occur among couples of productive ages. Purpose: This study aims to undertake a cluster analysis to see which variables are the dominant reasons for couples of childbearing ages to have unmet needs. Methods: This research was conducted using the K-Means cluster analysis method, using secondary data in 25 sub-districts from the Banyuwangi Regency Social, Women's Empowerment and Family Planning Service. Results: Research showed that 3 clusters were formed, each cluster had a dominant incidence of unmet need. Cluster 1 was dominant in Drop Out incidents in 14 sub-districts, Cluster 2 was dominant in IAT incidents in 9 sub-districts, and Cluster 3 was dominant in TIAL incidents in 2 sub-districts. Conclusion: The implementation of cluster grouping can make it easier for officers to focus on reducing the number of unmet need incidents that occur among residents in each sub-district.

I Know You: User Profiling on Social Media Usage of Chinese Private University Students

Chinese university students’ use of social media is becoming increasingly diverse, and students from private universities in China have different group characteristics than those from public universities. This research endeavoured to establish a comprehensive user profile of Chinese private university students by examining their social media usage patterns. The purpose was to gain profound insights into the distinctive attributes of students in China’s private universities within the context of the current era characterised by extensive data availability. This study employed a questionnaire-based research approach to acquire a dataset consisting of 673 instances of social media usage among students enrolled in private universities in China. Subsequently, exploratory factor analysis was performed using the Statistical Package for Social Sciences (SPSS) software, extracting five (5) categorical feature tags. Combined with the extracted feature tags and the usage status and perception dimension data, the K-means cluster analysis method was used to perform rapid clustering to derive four (4) differentiated groups comprising information exchange-oriented users, instrument-oriented users, dependent-oriented users and entertainment-oriented users. Furthermore, thorough analysis and description of the essential attributes for these 4 user profile categories have been conducted by incorporating the fundamental user information.

Impact of Diverse Rainfall Patterns and Their Interaction on Soil and Water Loss in a Small Watershed within a Typical Low Hilly Region

Assessing the impact of varied rainfall patterns on soil and water loss within a hilly watershed over an extended temporal scope holds paramount importance in comprehending regional runoff and sediment traits. This study utilized continuous rainfall and sediment data spanning from 2013 to 2021, and the K-means clustering method was employed to analyze rainfall types. Subsequently, the rain-type characteristics underwent further analysis through LSD, and a multiple linear regression equation was formulated. The result showed that: within the Qiaotou small basin, rainfall, maximum rainfall intensity within 30 min (I30), and rainfall erosivity exhibited notable effects on sediment yield and loss. The water-sediment attributes of 305 rainfall events were characterized by rainfall below 100 mm, I30 of less than 35 mm/h, a runoff coefficient below 0.5, and sediment content under 0.6 g/L. According to the characteristics of different rainfall types and the degree of influence on water and sediment in small watersheds, 305 rainfall events in the basin were divided into three types by the K-means clustering analysis method: A (heavy rainfall, moderate rain), B (small rainfall, light rain), and C (medium rainfall, heavy rain). The most frequent rain type observed was B, followed by C, while A had the lowest frequency. Despite the lower intensity of B-type rainfall, it holds significant regional importance. Conversely, C-type rainfall, although intense and short, serves as the primary source of sediment production. The multiple regression equation effectively models both sediment yield modulus and flood peak discharge, exhibiting an R2 coefficient exceeding 0.80, signifying significance. This equation enables the quantitative calculation of pertinent indicators. Sediment yield modulus primarily relies on sediment concentration, runoff depth, and rainfall, while peak discharge is significantly influenced by runoff depth, sediment concentration, and I30. Furthermore, the efficacy of various soil and water conservation measures for flow and sediment reduction correlates with I30. Overall, the impact of different measures on reducing flow and sediment increases with a higher I30, accompanied by a reduced fluctuation range.

Investigation of hearing loss in elderly vertigo and dizziness patients in the past 10 years.

Vertigo and hearing loss are both prevalent in the elderly. This study retrospectively analyzed hearing test results from elderly patients experiencing vertigo and dizziness at ENT outpatient over a 10-year period, in order to study the patterns of hearing loss in this patient population. Nine thousand three hundred eighty four patients over 50 years old underwent retrospective collection and screening of outpatient diagnosis, pure tone audiometry, acoustic immittance measurement (tympanogram) and auditory brainstem response (ABR) test. The patient's audiograms are divided into 7 subtypes according to a set of fixed criteria. Meanwhile, K-Means clustering analysis method was used to classify the audiogram. The Jerger classification of tympanogram in elderly patients with vertigo and dizziness showed the majority falling under type A. The leading audiogram shapes were flat (27.81% in right ear and 26.89% in left ear), high-frequency gently sloping (25.97% in right ear and 27.34% in left ear), and high-frequency steeply sloping (21.60% in right ear and 22.53% in left ear). Meniere's disease (MD; 30.87%), benign recurrent vertigo (BRV; 19.07%), and benign paroxysmal positional vertigo (BPPV; 15.66%) were the most common etiologies in elderly vestibular diseases. We observed statistically significant differences in hearing thresholds among these vestibular diseases (P < 0.001). K-Means clustering analysis suggested that the optimal number of clusters was three, with sample sizes for the three clusters being 2,747, 2,413, and 4,139, respectively. The ANOVA statistical results of each characteristic value showed P < 0.001. The elderly patients often have mild to moderate hearing loss as a concomitant symptom with vertigo. Female patients have better hearing thresholds than males. The dominant audiometric shapes in this patient population were flat, high-frequency gently sloping, and high-frequency steeply sloping according to a set of fixed criteria. This study highlights the need for tailored strategies in managing hearing loss in elderly patients with vertigo and dizziness.

Mechanical behavior and failure analysis of 2D C/SiC screwed/bonded hybrid joints

The mechanical behavior and failure mechanisms of 2D C/SiC screwed/bonded hybrid joints have an essential impact on the safe service of vehicles. Tensile experiments for screwed/bonded hybrid joints were carried out to clarify the mechanical characteristics. And the acoustic emission signal acquisition system combined with the digital image correlation techniques was used to monitor the failure process. K-means cluster analysis method was adopted to determine the damage modes and the corresponding frequency ranges. Combining the results of Micro-CT and failure morphologies, a refine modeling method describing the SiC distribution is proposed. A progressive damage model coupled with the cohesive theory is employed to simulate different mechanical responses and failure modes. It is demonstrated that the response fluctuation is mainly affected by the SiC distribution, and the failure mode and strength of the hybrid joints vary with the assembly angle.

Energy Storage Charging Pile Management Based on Internet of Things Technology for Electric Vehicles

The traditional charging pile management system usually only focuses on the basic charging function, which has problems such as single system function, poor user experience, and inconvenient management. In this paper, the battery energy storage technology is applied to the traditional EV (electric vehicle) charging piles to build a new EV charging pile with integrated charging, discharging, and storage; Multisim software is used to build an EV charging model in order to simulate the charge control guidance module. On this basis, combined with the research of new technologies such as the Internet of Things, cloud computing, embedded systems, mobile Internet, and big data, new design and construction methods of the energy storage charging pile management system for EV are explored. Moreover, K-Means clustering analysis method is used to analyze the charging habit. The functions such as energy storage, user management, equipment management, transaction management, and big data analysis can be implemented in this system. The simulation results of this paper show that: (1) Enough output power can be provided to meet the design and use requirements of the energy-storage charging pile; (2) the control guidance circuit can meet the requirements of the charging pile; (3) during the switching process of charging pile connection state, the voltage state changes smoothly. It can provide a new method and technical path for the design of electric vehicle charging pile management system, which can effectively reduce the system’s operation and maintenance costs and provide more friendly and convenient charging services.

Effect of volume ratio and hybrid mode on low-velocity impact properties of unidirectional flax/carbon fiber hybrid reinforced polymer composites

Hybrid fiber reinforced polymer composites have attracted widespread attention because they can fully utilize the advantages of two different types of fibers. To produce fiber reinforced polymer composites with excellent impact properties, unidirectional carbon/flax hybrid fiber reinforced polymer composite (HFRP) plates were developed using a filament-winding technique. The effects of the carbon fiber content and hybrid mode (a carbon–flax–carbon or flax–carbon–flax structure) on the impact properties and residual compressive properties of the HFRP plates were studied. Acoustic emission tests were performed to characterize the damage during impact, and the K-means cluster analysis method was used to investigate the HFRP damage development during post-impact compression. The test results indicate the higher carbon fiber contents enhanced their specific energy absorption (SEA), as the impact-induced brittle fracturing of the carbon-fiber layers was more severe. The hybrid mode and impact energy level critically influenced the HFRP SEA behavior. The HFRP plate with flax skin exhibited high SEA at a low impact energy, whereas that with carbon fiber skin exhibited high SEA at a high impact energy along with perforation. A more severe extension of the damage caused by the original impact occurs in the impacted HFRP under a compressive load.

Glass classification and identification based on logistic regression model and K-means clustering analysis

In order to investigate the effect of chemical composition on weathering, all post-weathering data were transformed into pre-weathering, for which the basis for the classification of high potassium and lead-barium glasses was inferred using a support vector machine algorithm. Afterwards, a detailed subclass differentiation method was determined for the two main classes of glass based on the K-means cluster analysis method. Further classification is then carried out on the basis of what is known about the classification. To identify unknown glasses, logistic regression was also carried out on the composition of weathered samples to predict the pre-weathering content.

Research on the Investment Value of Growth Enterprise Market Stocks in China

To study the value investment of stocks, this paper randomly selects 30 stocks from China's Growth Enterprise stock market. Based on financial statement data disclosed by listed companies, firstly select relevant sixteen indicators that can reflect the companies' financial status from four aspects of solvency, risk status, operating condition, and profitability. Then construct the stock value investment index system by using the factor analysis of the principal component method. Extract four factors and calculate the factor scores of 30 listed companies. Finally, according to the results of factor analysis, using the k-means cluster analysis method, the stocks of 30 listed companies are divided into three categories: ordinary stocks, risk stocks, and potential stocks. The results show that the mediocre stocks in the GEM make up the majority, and there are fewer high-yield, high-risk and potential stocks. Provide investment advice based on the characteristics of investors to help investors reduce investment risks and maximize returns.

Difference between global and regional aerosol model classifications and associated implications for spaceborne aerosol optical depth retrieval

AbstractAerosol model are generally adopted to describe the physical and optical characteristics of aerosols in different regions, and this is important for climate and environmental studies as well as satellite aerosol retrieval. However, current mainstream aerosol retrieval algorithms still lack differentiated and dynamic descriptions of aerosol models, and the aerosol optical depth (AOD) retrieval accuracy is hence largely compromised. Therefore, in this study, we aimed to investigate the difference between global and regional aerosol model classifications and the impact of these differences on satellite AOD retrieval. We developed global and regional (for China) aerosol models through the K-means cluster analysis method, and used the 6SV radiative transfer model based on these global and regional aerosol models to simulate air pollution events. The cluster analysis revealed that both global and regional aerosols can be clustered into five main aerosol types with different optical and physical parameters. The aerosol types include strongly absorbing, moderately absorbing, weakly absorbing, dust and coarse-fine mixed aerosols. These two aerosol models exhibited distinct seasonal variations. Comparing the clustering results obtained with the two models at five Aerosol Robotic Network (AERONET) sites, we found that the proportion of strongly absorbing aerosols in the global results is low. According to the China clustering results, a higher proportion of strongly absorbing aerosols occurred in autumn, winter, and early spring, and dust aerosols attained an increasing proportion in spring. Comparing the aerosol parameters with observational data, the regional aerosol model performed better than the global aerosol model. Simulations of AOD during a pollution episode and in different seasons at the Beijing-CAMS site with the 6SV radiative transfer model further confirmed that the regional aerosol model achieved a better simulation accuracy than the global model. The findings suggest that regional aerosol models can provide a useful reference for satellite remote sensing algorithm, climate change and air pollution assessment, and that the dynamic description of the aerosol model is a key parameter in satellite AOD retrieval algorithms.

Analysis and Application of Eco-environmental Value of Saihanba Forest Farm Based on Fuzzy Analytic Hierarchy Process and K-Means Clustering

In this paper, we aim to establish an evaluation model for the impact of Saihanba on the ecological environment to quantitatively evaluate its impact due to its significant role on maintaining ecological balance and stability. We apply the fuzzy analytic hierarchy process method on building an evaluation model of Saihanba with a multilevel evaluation factor system. In addition, we promote the model with the help of the K-means clustering analysis method after optimizing to determine which geographical locations in China and Pakistan need to establish ecological reservation.

Classification and identification of glass products based on K-means clustering analysis and Fisher's linear discriminant method

Ancient glass is very susceptible to weathering due to the buried environment, and the internal elements of the weathered glass will exchange with the elements in the environment thus leading to changes in the composition ratio. In order to classify and identify glass objects, this paper analyzes the classification laws of high potassium glass and lead-barium glass based on the data of samples of known types; selects the appropriate chemical composition for each category and then divides it into subcategories, gives specific division methods to establish a classification model, and uses this model for the chemical composition of glass artifacts of unknown categories to identify the types to which they belong

Systemic approach in the development of functional foods for various noncommunicable diseases

The article presents a hierarchy of requirements necessary for the successful design of food products with given composition and properties considering age restrictions and various diseases. The need for generalization and systematization of scientifically based principles, specific medical and biological requirements for food products, diets for the most common nutritional diseases in the knowledge base is shown. Using the k-means cluster analysis method, 1) meat raw materials were analyzed for inclusion in functional food for gerodietetic nutrition according to the most significant descriptors (protein, methionine + cystine amino acids, tryptophan), 2) spicy herbs and spices were analyzed for inclusion in the Muhammara recipe as natural antioxidant sources according to the descriptor of antioxidant properties. Using the example of the Muhammara recipe change, all stages of a systemic approach in the development of functional foods are shown. The first stage is related to obtaining information from the knowledge base about scientifically based nutritional principles and specific biomedical requirements for the given age group. At the second stage, the clustering of raw materials of animal and vegetable origin is carried out in order to reasonably include in the recipe of food product being developed. At the third stage, a system of balance linear algebraic equations for the chemical composition of the food product being developed (mass fraction of fat, protein, water, carbohydrates, vitamins, macro- and microelements, amino acids, etc.) is formed. The fourth stage is associated with the establishment of the target function (optimization criterion), and restrictions for recipe and balance. At the fifth stage, the problem is solved using a high-level language in a modern programming environment. At the final (sixth) stage, the nutritional value of the optimal balanced recipe is analyzed considering the target function and the given restrictions. As a result, we receive a modified Muhammara recipe with optimized protein: fat ratio. Mathematical simulation was carried out using the R Studio software with open-source lpSolve and lpSolveAPI libraries.