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2 Recommended structure of thesis table of contents
3 Introduction to the concepts of model establishment and solution
3.1 Model establishment
Model building is to abstract the original problem into an expression in mathematical language.
Model buildingIt must be based on previous problem analysis and model assumptions.Earned.When using a model that has been established by others, be sure to closely combine the questions asked in the question with the model., be careful not to apply models arbitrarily.
Innovations and Highlights of the Paper:
(1) Improve or optimize a certain aspect of an existing model.
(2) Establish different models to solve the same problem.
3.2 Solution of the model
Model solving is to reduce the actual problem to a certain mathematical model and then use the mathematical model to solve the proposed practical problem.
- Commonly used software:
- Matlab
- Spss – Statistical Questions
- Lingo – Planning Problems
- Excel
- Stata
- Python – Machine Learning
After the solution is completed, we getThe solution results should be standardized, accurate and eye-catching,likeThe solution result is too long, it is best to include it in the appendix.. (Note: IfIf you use intelligent optimization algorithms (such as simulated annealing algorithms, etc.) or numerical calculation methods to solve the problem, you need to briefly explain the calculation steps of the algorithm. )
4 Requirements for model establishment
After clarifying the meaning of the question,Briefly describe the basic ideas。
(1) First of all,Briefly introduce the basic principles and basic ideas of utilization
(2) againBuild a basic model, such as mathematical expressions, algorithm flow charts, etc., toClearly explain the thoughts and ideas for solving the problem, it is logical, reasonable and feasible, and needs to be fully described.
(3) The basic model can also be improved and perfected in combination with actual problems so that it can solve problems effectively and practically.
Three requirements:
(1)A mathematical model is necessary: That is, a set of mathematical structures composed of mathematical formulas, or a set of mathematical solutions, etc.;
(2) The model must be expressed completely, correctly and concisely;
(3) The model must be practical and can be solved to be able to Problem solving is the principle.
Quoted from "Guide to College Students' Mathematical Modeling Competition" edited by Xiao Huayong
5. Establishment of different types of problem models
5.1 Physics problems
Physics problems rely on physical knowledge due to their strong professional knowledge.It is necessary to write down the corresponding physical knowledge and physical formulas used to solve the problem。
5.2 Optimization problems
Establishment of optimization problem modelsThe objective function and constraints need to be written, and the constraints also need to be explained.。
5.3 Using an already established model
Use established models to solve problems,Must be closely related to the problem. (Related terms of the established model plus title)
When introducing the established model, you canUse flowcharts(Process flow chart of how the model solves the problem) can make the introduction more intuitive and prevent duplication.
6. Solution to the model
6.1 Things to note when solving the model
(1) Optimization problems often occur in national competitions. If you useheuristic algorithmIf you want to find a solution,The algorithm steps must be briefly described, and the calculation ideas must be clarified based on specific problems.。
(2) The solution results should be prominently displayed in the paper, questions with specific answers are relatively simple, just put the numerical calculation results; ifopen questionsif,Be sure to clarify and explain the results, and it would be better if you can add beautiful and neat charts.。
（3）What does the question ask and what does it answer?
7 Analysis and testing of the model
If this part only has the analysis of the model, the title of the thesis module can be: Analysis of the model; if there is only the test of the model, the title of the thesis module can be: Test of the model.
Or directly: model checking
The content of model analysis and verification can be placed in the model establishment and solution part.It can also be extracted separately for explanation. This part is often a bonus point for the paper.。
7.1 Analysis of the model
There are two main types of model analysis in modeling competitions, one is sensitivity analysis and the other is error analysis.
7.1.1 Sensitivity analysis
Sensitivity analysis is a method of studying and analyzing the sensitivity of changes in the state or output of a system (or model) to changes in system parameters or surrounding conditions.
ThatGeneral stepsYes: Controlling other parameters unchanged,Change the value of an important parameter in the model, and then observe the changes in the model results.
The analysis of the model requires corresponding explanations and conclusions.。
7.1.2 Error analysis
Error analysis refers to analyzing the sources of errors in the model, or estimating the errors existing in the model.Generally used for prediction problems or numerical calculation problems。
Error analysis can provide relevant explanations and explanations.
7.2 Model testing
Model testing can be divided into two types
One isChecks that should be done before using the model, such as the consistency test in the analytic hierarchy process, the test of quasi-exponential law in gray prediction,This part should be placed in the model establishment part。
7.2.1 Stability test
The other isAfter using the model, test the results of the model, the most common in digital analog isStability test。
