2023 Mathematical Modeling National Competition Preparation Must-See

0. What needs to be prepared before the game

1. Division of labor and cooperation, choose the direction of the problem - three cobblers, top Zhuge Liang
2. Study excellent papers - modeling, algorithms, writing
3. Making a Writing Template - Good Writing is Half the Battle
4. Learning excellent algorithms - complex models, difficult solutions, high computing power requirements
5. Learn to consult the latest literature - traditional algorithm + latest algorithm + self-created algorithm

1. Excellent papers in national competitions over the years

The password in the comment area: "Xiaoyun who loves Mathematics" , come and get the excellent papers of the previous national competitions from 2004 to 2021!

2. Summary of commonly used models and algorithms (the most complete in the whole network)

problem/model	common algorithm	illustrate
Linear Programming	Simplex Method	The optimal solution under linear constraints is found by iteratively optimizing the value of the objective function.
Integer Programming	Branch and Bound	Break down the problem into smaller subproblems and use bounds to prune the search tree to find the optimal solution subject to integer constraints.
Graph Theory	Shortest path algorithm (Dijkstra algorithm, Bellman-Ford algorithm)	Find the shortest path between two nodes in the graph.
Discrete Event Simulation	Event-driven Simulation	Process events in chronological order and update the system state, simulating the discrete-event behavior of the system.
Data fitting (Curve Fitting)	Least Squares Method	Choose an appropriate function form, and find the optimal fitting curve by minimizing the sum of squared residuals between the observed value and the fitting curve.
Dynamic Programming	Knapsack Problem algorithm (Knapsack Problem)	Split the problem into sub-problems and build a dynamic programming table to find the optimal solution.
Stochastic Models	Markov Chains	Modeling a system with randomness, the future state is only related to the current state, can be used to simulate and predict random processes.
Genetic Algorithms	Genetic Algorithm	Based on the principle of biogenetics, the optimal solution to the optimization problem is found through the evolution of the population and genetic operations (selection, crossover, mutation).
Particle Swarm Optimization	Particle Swarm Optimization	Simulate the behavior of a flock of birds or fish, and search for the optimal solution by optimizing the position and velocity of particles.
Support Vector Machine (Support Vector Machine)	Support Vector Machine (Support Vector Machine)	Classification and regression tasks are achieved by finding optimal hyperplanes in high-dimensional spaces.
Neural Networks	Backpropagation algorithm (Backpropagation)	Based on the structure of multi-layer neurons, tasks such as pattern recognition, classification and regression are realized by backpropagating error signals and adjusting weights.
Deep Learning	Deep Neural Networks	The deep learning model based on multi-layer neural network learns feature representation and solves complex pattern recognition problems through multiple iterations of forward propagation and back propagation.
Markov Decision Processes	Q-Learning, Value Iteration	Model sequential decision-making problems, and find the optimal strategy by learning the value function or Q-value function.
Mixed Integer Programming	Branch and Bound and Cutting Plane Method	The problem is decomposed into integer programming and linear programming subproblems, and the optimal integer solution is found by branch and bound and adding cutting plane constraints.
Reinforcement Learning	Deep Q-Network, Policy Gradient, etc.	Through the interaction between the agent and the environment, the optimal strategy is learned based on the reward signal, which is used to solve the sequential decision-making problem.

3. Programming and computing software

software	illustrate
MATLAB	A high-level technical computing and programming environment for numerical computation, data analysis, and visualization. It provides a rich set of mathematical functions and toolboxes that can be used to solve various problems in mathematical modeling.
Python	A general-purpose programming language with powerful scientific computing libraries and data processing capabilities. In mathematical modeling competitions, Python is often used in model building, data analysis, algorithm implementation and visualization.
R	A programming language specialized for statistical computing and data analysis. R has a rich statistical library and plotting functions, and is suitable for tasks such as statistical modeling, data visualization, and inferential analysis in mathematical modeling.
Microsoft Excel	A widely used spreadsheet software for data manipulation, modeling, and visualization. Excel has powerful calculation functions and charting tools for simple mathematical modeling and data analysis tasks.
Wolfram Mathematica	A comprehensive technical computing software that provides a wide range of mathematical, scientific and engineering computing functions. Mathematica supports symbolic computation, numerical computation, and visualization, and is suitable for a variety of mathematical modeling and simulation tasks.
IBM SPSS	A professional statistical analysis software for data preprocessing, statistical modeling and predictive analysis. SPSS has a friendly user interface and rich statistical functions, and is suitable for tasks such as data analysis and model verification in mathematical modeling.
GAMS	A software system dedicated to modeling and solving optimization problems. GAMS supports a wide range of mathematical programming and optimization models, which can be used to solve linear programming, integer programming and nonlinear programming problems in mathematical modeling competitions.
AMPL	A high-level modeling language and environment for mathematical modeling and optimization problems. AMPL provides a flexible modeling syntax and a powerful solver interface, which can be used to describe and solve various mathematical modeling problems.

4. Writing software

software	illustrate
Microsoft Word	A commonly used word processing software used for writing reports, theses, and technical documents. Word has rich typesetting and formatting functions, which are suitable for document editing and typesetting in mathematical modeling competitions.
Microsoft Visio	It is often used to draw flowcharts, block diagrams, network topology diagrams, etc., to show the design ideas, system structure, and data flow of models and algorithms. It provides a rich graphics library and editing tools, making the creation and editing of graphics easy and intuitive. Visio's visualization and professionalism make it one of the commonly used graphics drawing tools in mathematical modeling competitions.
LaTeX	A professional typesetting system for producing high-quality scientific documents and mathematical formulas. LaTeX is commonly used in mathematical modeling competitions for writing reports, papers and presentations, and for inserting mathematical symbols and formulas.
Overleaf	An online LaTeX editor and collaboration platform for multi-person collaborative writing of scientific and technical documents. Overleaf provides functions such as real-time preview, version control, and collaborative editing, which facilitate teamwork to complete the writing and editing of mathematical modeling competition reports.