Huawei Cup Mathematical Modeling Competition Experience Sharing

In about a week, the 20th Huawei Cup Mathematical Modeling Competition will start, so today I would like to share my experience in the personal mathematical modeling competition.

Today I would like to share with you an experience sharing about the Huawei Cup Mathematical Modeling Competition. I will explain it from the following three aspects:

(1) How to prepare for a mathematical modeling competition?

(2) How to choose appropriate competition topics for modeling?

(3) How to improve your chances of winning?

1. How to prepare for a mathematical modeling competition?

Completing a high-quality entry in a short period of time requires the full cooperation of everyone in the team, so team formation is particularly important. Teams are generally composed of modelers, programmers, and essay writers. Newbies who participate in a modeling competition for the first time may think that modelers are only responsible for modeling, programmers are only responsible for programming, and essay writers are only responsible for writing papers. In fact, it is a wrong perception. The modeler needs to inform the programmer of the idea of the established mathematical model to facilitate its programming implementation. Secondly, it is also necessary to inform the thesis author of the modeling ideas and communicate with them the entire modeling framework and ideas to facilitate the writing of subsequent papers. Finally, the programmer and thesis writer also need to communicate about the presentation and analysis of thesis results. Participants need to master basic tools, including programming tools (matlab, python), writing tools (word) and drawing tools (origin). Therefore, mastering the above tools is essential. In addition, it is important that we understand what mathematical modeling is. For modelers, they need to understand what mathematical modeling is and master the modeling methods of common problems in mathematical modeling competitions. This requires modelers to read more relevant excellent papers. In addition, they also need to master relevant programming. Base. For programmers, they must learn programming software, and use codes related to intelligent algorithms, machine learning, and deep learning flexibly. In addition, they must also read relevant excellent papers and have a certain degree of understanding of modeling ideas for relevant competition questions. learn. For writers, writing tools and drawing tools must be mastered. They need to read a lot of relevant excellent papers, learn the writing framework of excellent papers, and form their own set of writing ideas. In addition, they must have certain knowledge of mathematical modeling. No one of the modelers, programmers, and writers is responsible for only one thing, but their focus is different. Modelers and programmers need to communicate with each other to select competition topics, and communicate with each other during the competition to determine the establishment of the model. In addition, after the experimental results are completed, the modeler needs to communicate with the writer about writing ideas and complete the paper writing.

2. How to choose appropriate competition questions

Mathematical modeling competitions are generally divided into four categories: optimization, prediction, evaluation and mechanism analysis. Generally speaking, prediction is the simplest and optimization is the most difficult. If you encounter prediction questions, you can give priority to prediction questions. The following is a brief summary of the four types of competition questions.

A. Optimization category

It refers to establishing a corresponding objective function to achieve the optimal (maximum or minimum) objective function under certain constraints. Such as the common traveling salesman problem. Optimization problems require three important factors based on problem analysis: objective function, decision variables and constraints. This type of questions is generally difficult and is not recommended for beginners.

The general steps to solve this type of problem are:

1. Determine optimization goals

2. Determine decision variables

3. Construct the objective function

4. Analyze the problem and construct constraints

5. Choose a suitable method to solve the objective function

6. Solve the results

Recommended software MATLAB, Python

Solving method: intelligent algorithm (particle swarm optimization algorithm, etc.), solver solution (cplex, gurobi)

B. Prediction type

It refers to the process of finding the inherent development laws based on existing data or phenomena, and then making predictions about future situations. Common load forecasting, population forecasting, stock forecasting, time series classification forecasting, etc. This type of question is easy to learn, but the accuracy of the predicted indicators directly determines whether you win the prize.

General steps for solving prediction competition questions

1. Analyze and determine forecast targets

2. Perform data cleaning on historical data (complete missing data, raise abnormal data, normalize processing, etc.)

3. Choose appropriate forecasting methods for forecasting

4. Get prediction results

5. Use evaluation indicators to analyze prediction results

Recommended prediction methods include BP neural network, support vector machine, random forest, LSTM, etc.

C. Evaluation category

Refers to the process of classifying the development or current situation of things according to certain standards. Mathematical modeling can be reflected in the evaluation of ecological environment and program strategies. The key to solving such problems is to construct a suitable evaluation index system and appropriate evaluation methods.

General steps for solving evaluation competition questions

1. Clarify the purpose of evaluation

2. Clarify the evaluation objects

3. Establish an evaluation system

4. Determine the weight coefficient corresponding to each evaluation index

5. Select or construct a comprehensive evaluation model

6. Calculate the comprehensive evaluation value of the system and provide the analysis results.

Recommended methods include data envelopment analysis, gray relational analysis, principal component analysis and fuzzy comprehensive evaluation method.

D. Mechanism analysis

It refers to analyzing the causal relationship and finding out the laws of internal mechanisms based on the understanding of the characteristics of real objects. When solving problems, analyze the physics, chemistry and other related knowledge of the object, and then make reasonable assumptions about the known data or phenomenon analysis, and on this basis, construct appropriate equations or mathematical relationships to mathematically express its internal laws. Mechanism analysis questions are difficult and require a lot of knowledge to solve, such as aerodynamics, fluid mechanics, etc.

In general, if you encounter prediction-type questions, you should give priority to prediction-type questions. Then in your daily preparation, you can read more related excellent papers and learn machine learning and deep learning codes so that you can use them flexibly in competitions, such as supporting For learning codes such as vector machines, random forests, BP neural networks, LSTM, and CNN, the more you prepare, the easier it will be to start the questions.

3. How to improve your chances of winning

During the competition everything will be presented on the paper, so the writing of the paper is crucial. While completing the competition questions as much as possible, ensuring the readability and presentation of the paper is a necessary condition for winning the award. Here, writers are required to read excellent papers on related types of competition topics in advance and imitate the writing framework of excellent papers. After the competition topic is determined, you can discuss with your teammates in advance to put together the framework of the paper. Secondly, when writing about each problem, it is recommended to draw a block diagram of ideas at the beginning. Through the block diagram, we can show our thinking on this problem, what key technologies we used, and what results we obtained. Secondly, the presentation of experimental results should be as diverse as possible, using tables, drawings and other methods to present the results to avoid simplification. The more important data in the table can be bolded. Secondly, since the last few questions in the competition are generally more difficult, try your best to complete the questions. Then when you encounter a more difficult question, you can appropriately simplify the question requirements, make some reasonable assumptions and then go to the problem to solve it. For example, if we encounter a large-scale optimization problem, we will first face problems such as modeling difficulties and insufficient solution time. We can try to break the big problem into small problems, or simplify the constraints as much as possible. It is also possible to make a relatively simple model and present it in other ways.

Here is an example to share with writers. The following is an excellent paper from National One. We can see that they have made a technical route during the analysis of the problem, so that the review experts can know your thinking on this problem from the beginning, which is a plus point. I suggest that during the competition, you can add a technical route or flow chart after each problem analysis. The technical route or flow chart here needs to be provided by modeling hands and programming hands.