The optimal configuration and allocation of a microgrid are one of the key issues to guarantee the economic and reliable working of a microgrid. This is a multi-objective optimisation problem within which the economic index and the load power shortage rate index should be considered when optimising the configuration. In this article, a differential multi-agent multi-objective evolutionary algorithm (DMAMOEA) was designed to optimise the capacity configuration of a microgrid system, which includes three kinds of equipment: wind turbine, photovoltaic equipment and battery. The final optimisation results were compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm. Simulation results showed the effectiveness of the algorithm. At the end of this article, the representative solutions in the calculation results are compared and explained and the environmental benefits are analysed, which show the effectiveness of the implementation of the microgrid system.
Keywords
- allocation optimal
- microgrid
- multi-agent
- multi-objective
- environment protection
Compared with traditional fossil energy, renewable and clean energy such as wind energy and solar energy are safe, pollution-free, widely distributed and conducive to small-scale decentralised utilisation [1]. With the growth of these clean and renewable energies, distributed generation has created a steadily increasing amount of research interest. To improve security, stability and power quality, it is an effective way to exert the efficiency of distributed generation system in the form of a microgrid [2].
A microgrid is an automatic and stand-alone system, which can realise self-control, safeguard and administration. From the macroscopic view, a microgrid can be seen as a ‘virtual’ power supply source or a load in the network. The optimal configuration of a microgrid is one of the key issues to ensure the economic and reliable operation of the microgrid. It is generally necessary to consider the following aspects: economic indicator, self-power supply capacity indicator and environmental protection indicator in the microgrid allocation optimisation problem. The economic indicator mainly reflects the economy of microgrid operation, such as the construction of distributed generation, operation and maintenance costs, replacement costs and fuel costs [3]. The load power shortage rate indicator refers to the power supply performance of the microgrid, which reflects the ability of the microgrid to meet the load requirements of the microgrid in an independent state. Environmental protection indicator refers to the environmental benefits of microgrid operation. Through environmental protection indicators, the advantages of the environmental protection benefits of the microgrid can be measured. In addition, targets such as power loss minimisation and voltage profile improvement are also considered. Therefore, the optimal configuration of the microgrid is a multi-objective optimisation problem.
In the optimisation of capacity allocation, the economic requirement can be considered separately according to specific needs [4, 5]. In this situation, the allocation problem is a single objective optimisation problem. However, in most cases, multiple objectives should be considered. When optimising multiple objective functions, multiple objectives can be integrated according to certain weights and then solved by the single-objective optimisation method [6]. A multi-objective optimisation algorithm based on Pareto optimal solution can also be used to solve the problem [7]. In this process, the Pareto solution set of the problem to be optimised can be obtained by a single run. Compared with the weight method, the latter can get the solution set more comprehensively and efficiently. In fact, the weight method takes only a small part in solving multi-objective optimisation problems, and the rest employ the Pareto front method.
In the process of solving the multi-objective capacity allocation problem, many algorithms have been designed and applied. Compared with the basic intelligent algorithm, a hybrid intelligent algorithm has many outstanding advantages in solution quality, problem processing scale and convergence speed, and therefore it may be more suitable for solving such problems [8,9,10]. Meanwhile, the utility of agents for solving problems has aroused much concern these years. The concept of agents and their generation, which constructs a multi-agent system (MAS) and allows different search spaces to be explored simultaneously, thereby achieving solutions with more diversity and high quality [11].
In view of the advantages of hybrid intelligent algorithms and the multi-agent approaches, approaches with multi-agent technology are a good choice in the process of hybridisation [9]. In this study, a differential multi-agent multi-objective evolutionary algorithm (DMAMOEA) was designed by combining differential evolution strategy and multi-agent technology, which is used to solve the capacity optimisation problem of the microgrid including wind turbine, photovoltaic equipment and battery storage, considering the two objectives of economy and load outage rate.
Comparing the results with the classical multi-objective evolutionary algorithm – Non-dominated Sorting Genetic Algorithm II (NSGA-II), the quality of the final solution set and solution time of the designed algorithm is better than that of the classical algorithm. Subsequently, some representative solution in the solution set is analysed and the effectiveness of microgrid implementation is also illustrated.
In this work, the optimal allocation model of microgrid capacity includes three kinds of equipment: photo-voltaic power production facility, wind power production facility and storage battery. The output models of the three kinds of equipment are as follows.
The power output of the photovoltaic array can be described as follows as in Eq. (1) [12]:
The output power of a wind turbine fluctuates with the fluctuation of wind speed. Thus, the actual distribution of wind speed must be obtained to calculate the power output of the wind turbine. It can be pointed out that the wind speed distributed on the ground is different from the height of the measuring point. The real-time wind speed data provided by the Meteorological Bureau are generally measured near the altitude of 9 m. To get the actual output power of the wind turbine, the measured wind speed should be converted into the speed at the height of the rotating shaft of the wind turbine. The conversion can be roughly calculated by the following equation: [13, 14].
The remaining electricity of the battery at time
The residual electric quantity can be described as under when the battery discharges or charges [15].
The power outputted from wind turbines and solar photovoltaic power generation equipment is related to local weather conditions, which are random and cannot be adjusted artificially. Battery energy storage systems can be charged and discharged within a certain range and can supplement the difference between renewable energy (wind turbine and photovoltaic power generation) and load demand according to specific conditions. In addition, by connecting power lines, the microgrid can exchange energy with the main network, sell surplus power to the main network or purchase power from the main network to satisfy the load demand of the microgrid. In this work, the overall energy control strategy is to use the power of wind turbine and photovoltaic unit preferentially in the microgrid system, and the battery plays the role of energy buffer and system standby.
A year is divided into 8760 h. Assuming that the output power of wind turbine and photovoltaic remains constant within an hour, the difference between the system load demand and the total wind and photovoltaic power generation is calculated according to the mathematical model of each micro-source.
In this case, there are some operation principles with the microgrid. They are mentioned below:
If the power generated by renewable energy generation equipment equals the load demand of the microgrid, the batteries don’t charge or discharge, and no energy interacts between the microgrid and main network. If the power generated by the renewable energy equipment surplus the load demand in the microgrid, the batteries should be charged preferentially with the allowance state of the batteries. If there is still surplus power, it will be sold to the external power grid as far as possible within the power limit of tie-line backward transmission, and the remaining power will be the system energy spillover. If the net load is greater than zero, the renewable energy generation power is insufficient. Under the conditions of the batteries discharge power and the state are allowed, they are preferentially used to balance the load in a microgrid. When the power which is discharged by the batteries cannot meet the load demand, the left power is purchased from the main network to ensure power balance in the microgrid.
In the actual micro-grid operation process, it is necessary to consider not only the economics of the microgrid but also power supply reliability and environmental protection. In this work, the economy and power supply reliability are considered in the multi-objective planning and design of the microgrid, which is a two-objective optimisation problem. The optimised independent variables are the number of photovoltaic power generation equipment
The cost of Net Present Value (
The ability of microgrid to meet the load demand in microgrid independently is defined as the self-balancing rate of microgrid, that is, the proportion of annual power supply of microgrid equipment to the annual power consumption of load, which is shown as the equation below [3, 7].
Number of micro-sources constrain
Limitation of interaction ability with the external power grid
To prevent the influence on the stability of the external power grid, the power interaction limit between the microgrid and external power grid is set.
Power balance constrain be described below.
Battery charging and discharging power and depth constraint
Multi-agent search strategy has attracted much concern for its promising computational model in optimisation problems in these years. The agent can be seen as a physical or abstract entity, which has the perception, interaction and problem-solving ability [17]. Multiple agents compose the MAS. The MAS has remarkable features, such as autonomy, distribution, coordination, etc. By virtue of self-organisation ability, learning ability and reasoning ability, the multi-agent search strategy for optimisation problems achieved good results.
In this section, a DMAMOEA for a multi-objective microgrid allocation optimal problem is proposed based on the concept of the Pareto method. In this algorithm, several operators for a multi-objective problem are designed, such as neighbourhood Pareto preferred operator, neighbourhood differential evolution operator, mutation operator, etc. By these operators, the agents in MAS interact with each other and produce feasible solutions for the multi-objective microgrid allocation problem. The non-dominated solutions produced in each generation are kept in the archive set. To guarantee the uniformity of the archive set, the solutions with larger crowding distances are further optimised. The simulation results demonstrated the effectiveness of DMAMOEA.
In the structure of MAS, each agent stands for a feasible solution, which is a real-valued vector. All the agents are fixed on a squared network. The structure of the network is shown in Fig. 1. Each agent can only interact with the agent's neighbourhood.
Fig. 1
The structure of multi-agent system

The neighbourhood of Agent Local Env
The neighbourhood Pareto preferred operator is designed to determine the dominance relations among the individuals in the local environment of agent
Randomly select three solutions in the neighbourhood agent
In the mutation process, if
After the mutation operation, the crossover operation is executed. This operation can be described in the equation below. In this equation,
To further maintain the distribution of the population, the mutation operation is performed on all the variables of agents in the lattice with mutation probability
To maintain the distribution of the solution in the archive set, crowding distance is introduced to estimate the crowding degree of the solutions, as shown in Fig. 2. Taking the
Fig. 2
Calculation of crowding distance

The procedure of DMAMOEA can be summarised as follows:
Step 1: Let Step 2: Distribute all the individuals on a
Step 3: If the iteration number reaches the set value ( Step 4: Implement the neighbourhood Pareto preferred operator on the agents on the lattice sequentially, and the best solution Step 5: Implement the neighbourhood differential evolution operator on each agent; Step 6: Implement the mutation operator on Q( Step 7: Calculate the crowding distance of all the solutions in
If the iteration number is less than the set value, go back to Step 3.
This procedure is shown in Fig. 3.
Fig. 3
Calculation procedure of DMAMOEA

Take a certain year in a certain region as an example, its power consumption load, wind speed, sunlight intensity and the price of electricity are shown in Figs 4–7.
Fig. 4
One year power load demand

Fig. 5
Annual average wind speed at a certain place

Fig. 6
Annual light intensity

Fig. 7
24-Hour electricity price

The capacity of the fan is 30 kW, the capacity of the photovoltaic equipment is 1 kW, and the single battery capacity is 50 kW h. The value of initially installing cost, operating and maintaining cost, the replacement cost of each item of equipment is shown in Table 1. The upper and lower limit of battery power is 0.3 and 0.8, and the default initial power is 0.5. The interactive power consumption with the grid is 10% of the maximum power consumption in the period.
Calculation of the cost of decigrams
Unit price | 8870 $/kW | 8790 $/kW | 1200 $/kW |
Operation and maintenance cost | 7.7 $/kW h | 5.5 $/kW h | 7 $/kW h |
Replacement cost | 0 $/KW | 0 $/KW | 1200/set |
Compared with other multi-objective optimisation algorithms, the NSGA-II algorithm has some advantages in solution efficiency and result division [18]. Therefore, the classical NSGA-II algorithm and the algorithm proposed in this article are used to optimise the problem.
In this study, the running CPU is Core i5-6300 CPU, the memory is 8 Gb, and MATLAB software is also used. In terms of parameter setting, the DMAMOEA is set to 16 agents, the archive set scale is 200 and the number of iterations is 100; the population number of NSGA-II is 200, and the number of iterations is 70. The simulation result is shown in Fig. 8.
Fig. 8
The simulation results of the DMAMOEA and NSGA-II

As can be seen from Fig. 8, the results of the two algorithms coincide. To evaluate the approximation degree of the results of the two algorithms to the real Pareto optimal solution, generation distance is used to evaluate the results of the two algorithms. The equation of generation distance is described as follows [18]:
In this study, the ideal solution set is represented by the non-dominated solution set of the two solution sets obtained by the two algorithms. Generation distance is the average value of the sum of the minimum distance of each solution in the solution set and the solution in the ideal solution set. The smaller the value is, the better the result is. Fig. 9 is a column comparison diagram of generation distance obtained by DMAMOEA and NSGA-II running 10 times respectively. In terms of the operation time, DMAMOEA takes an average of 52 s, while NSGA-II takes about 66 s. Therefore, the DMAMOEA is superior to the traditional NSGA-II in terms of operation time and the approximation of the final solution set.
Fig. 9
Comparison of Gd Distance DEMAMOME and NSGA-II

Table 2 shows some representative results of DMAMOEA algorithm. Taking Solution 1 as an example, using the Environmental Benefit Analysis Method [7], the representative results are obtained and the results are shown in Table 3.
Some representative results of DMAMOEA algorithm
Solution 1 | 260 | 41 | 241 | 6.585×106 | 0.01839 |
Solution 2 | 250 | 80 | 221 | 6.372×106 | 0.01867 |
Solution 3 | 237 | 55 | 231 | 6.059×106 | 0.01912 |
Solution 4 | 228 | 43 | 63 | 5.567×106 | 0.2413 |
Solution 5 | 216 | 31 | 16 | 5.197×106 | 0.2457 |
Environmental benefits of Solution 1
CO2 | CO | SO2 | NOx | Total | |
---|---|---|---|---|---|
Pollution reduction (103Kg) | 88,122 | 127.65 | 817.81 | 532.03 | 89,600 |
Cost saving of pollution treatment(103$) | 326.05 | 20.425 | 793.27 | 686.32 | 1826.1 |
From Tables 1 and 2, the following conclusions can be drawn:
In terms of Solution 1 and Solution 2, there is some difference in the number of micro sources. Between the two solutions, the number of wind turbines and batteries in Solution 1 is more than that in Solution 2, while the photovoltaic equipment is less than that in Solution 2. Therefore, although the investment increases, the dependence of microgrids on the external network is reduced. From Solution 3 and Solution 4, the number of wind turbines, photovoltaic equipment and batteries in Solution 3 is increased, especially the number of batteries is increased from 63 to 231. Therefore, the energy storage capacity of the microgrid is further enhanced, so that the microgrid can meet its load demand much better. Considering the environmental benefits, and taking Solution 1 as an example, the environmental benefits obtained are shown in Table 3. In this table, through the implementation of microgrids, the total emission of pollutants is reduced by 89,600 tons, the environmental protection cost is saved by US $1,826,100, and the environmental protection benefit is obvious, which fully reflects the benefit of the implementation.
In this article, a DMAMOEA was proposed to optimise the two objectives allocation of microgrid system with photovoltaic, wind power and battery. The two optimisation objectives are the economy index which including investment, maintenance and replacement of the micro sources and the rate of load power shortage index which reflects the degree of dependence on the external power grid. At the end of the article, the optimisation results of this proposed algorithm are compared with the classic algorithm NSGA-II, and the following conclusions are reached:
A DMAMOEA is designed by combining differential evolution strategy and multi-agent technology. In the capacity optimisation model of microgrid, two goals of economy and reliability are considered. The optimisation results of the designed algorithm are compared with that of the classic multi-objective evolutionary algorithm NSGA-II, which shows that DMAMOEA has a shorter solution time and a better solution set than the NSGA-II algorithm.
Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Calculation of the cost of decigrams
Unit price | 8870 $/kW | 8790 $/kW | 1200 $/kW |
Operation and maintenance cost | 7.7 $/kW h | 5.5 $/kW h | 7 $/kW h |
Replacement cost | 0 $/KW | 0 $/KW | 1200/set |
Environmental benefits of Solution 1
CO2 | CO | SO2 | NOx | Total | |
---|---|---|---|---|---|
Pollution reduction (103Kg) | 88,122 | 127.65 | 817.81 | 532.03 | 89,600 |
Cost saving of pollution treatment(103$) | 326.05 | 20.425 | 793.27 | 686.32 | 1826.1 |
Some representative results of DMAMOEA algorithm
Solution 1 | 260 | 41 | 241 | 6.585×106 | 0.01839 |
Solution 2 | 250 | 80 | 221 | 6.372×106 | 0.01867 |
Solution 3 | 237 | 55 | 231 | 6.059×106 | 0.01912 |
Solution 4 | 228 | 43 | 63 | 5.567×106 | 0.2413 |
Solution 5 | 216 | 31 | 16 | 5.197×106 | 0.2457 |
Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model The improvement of museum information flow based on paste functional mapping method Constraint effect of enterprise productivity based on constrained form variational computing The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Badminton players’ trajectory under numerical calculation method Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Visual positioning system for marine industrial robot assembly based on complex variable function Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Nonlinear Differential Equations in the Teaching Model of Educational Informatisation Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Mathematical model of transforming image elements to structured data based on BP neural network Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe80Si10Nb6B2Cu2 Educational reform informatisation based on fractional differential equation Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Design of Morlet wavelet neural network to solve the non-linear influenza disease system Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x p m −x +δ )s +ax p m +bx overF p 2m Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet