Ten algorithms for Mathematical Modeling

1. the Monte Carlo algorithm (also known as the Random Simulation Algorithm) is an algorithm that solves the problem through computer simulation. At the same time, it can be used to verify the correctness of its model, is a required method during the competition)

2. Data processing algorithms such as data fitting, parameter estimation, and interpolation (a large amount of data needs to be processed during the competition, and the key to data processing lies in these algorithms. MATLAB is usually used as a Tool)

3. Linear Planning, integer planning, multi-dimensional planning, secondary planning, and other planning issues (most modeling competitions are optimization problems. In many cases, these problems can be described using mathematical programming algorithms, usually implemented using Lindo and Lingo software)

4. Graph Theory Algorithms (these algorithms can be divided into many types, including the shortest path, network flow, and bipartite graph algorithms. These algorithms can be used to solve graph theory problems. Therefore, we need to carefully prepare them)

5. computer algorithms such as dynamic planning, backtracing search, divide and conquer algorithms, and branch and demarcation algorithms (these algorithms are commonly used in algorithm design and can be used in competitions in many cases)

6. Three non-classical algorithms of Optimization Theory: Simulated Annealing, neural networks, and genetic algorithms (these algorithms are used to solve some difficult optimization problems, it is helpful for some problems, but it is difficult to implement the algorithm and must be used with caution)

7. Grid Algorithm and exhaustive method (grid algorithm and exhaustive method are the most advantageous algorithms for brute force search. They are applied in many competitions. When we focus on the model and despise the algorithm, you can use this brute-force solution. It is best to use some advanced languages as programming tools)

8. Some continuous discretization methods (many problems come from reality. data can be continuous, while computers only recognize discrete data, therefore, it is very important to consider the idea of using difference instead of differential and sum instead of integral after discretization)

9. Numerical Analysis Algorithms (if advanced programming languages are used in the competition, some algorithms commonly used in numerical analysis, such as equations, matrix operations, and function points, require additional library functions for calling)

10. image processing algorithms (there is a type of problem in the competition question that is related to graphics. Even if it is not related to graphics, there should be images in the paper. How to present and process these images is a problem to be solved, MATLAB is usually used for processing)