At the same time, you can test the correctness of your model through simulation, which is a necessary method in the competition)
2, data fitting, parameter estimation, interpolation and other data processing algorithms (usually meet a large number of data needs in the competition.
Processing, and the key to processing data lies in these algorithms, usually using Matlab as a tool)
3, linear programming, integer programming, multivariate programming, quadratic programming and other planning problems (most of the problems in modeling competition
Belong to the optimization problem, many times these problems can be described by mathematical programming algorithm, usually with Lindo,
Argot software implementation)
4, graph theory algorithm (this kind of algorithm can be divided into many kinds, including the shortest path, network flow, bipartite graph and other algorithms, involving
Problems related to graph theory can be solved by these methods and need careful preparation)
5, dynamic programming, backtracking search, divide and conquer algorithm, branch and bound computer algorithm (these algorithms are algorithm design.
More commonly used methods can be used in many occasions in the competition)
6. Three non-classical algorithms of optimization theory: simulated annealing method, neural network and genetic algorithm (these problems are
The algorithm used to solve some difficult optimization problems is very helpful to some problems, but the algorithm is true.
It is more difficult now, so it needs to be used with caution)
7, grid algorithm and exhaustive method (grid algorithm and exhaustive method are the best algorithms for violent search, in many competitions.
There are applications in the topic. When we focus on the model itself and despise the algorithm, we can use this violent scheme, preferably.
Use some high-level languages as programming tools)
8, some continuous discretization methods (many problems are practical, data can be continuous, only computers have.
It recognizes discrete data, so it is very important to discretize it, replace differential with difference, and replace summation with integral. )
9, numerical analysis algorithm (if you use high-level language programming in the game, that some numerical analysis often.
The algorithms used, such as solving equations, matrix operations, function integration, etc., need to write extra library functions to call)
10, image processing algorithm (there is a kind of problem related to graphics in the competition, even if it has nothing to do with graphics, the paper should be
When applying mathematics to solve various practical problems, it is a very crucial and difficult step to establish a mathematical model. The process of establishing teaching model is the process of simplifying and abstracting complex practical problems into reasonable mathematical structures. Through investigation and data collection, observe and study the internal characteristics and laws of actual objects, grasp the main contradictions of problems, establish quantitative relations reflecting actual problems, and then analyze and solve problems by using mathematical theories and methods. This requires a deep and solid mathematical foundation, keen insight and imagination, strong interest in practical problems and extensive knowledge. Mathematical modeling is the bridge between mathematics and practical problems, the medium through which mathematics is widely used in various weapons, and the main way to transform mathematical science and technology. The important role of mathematical modeling in the development of science and technology has been paid more and more attention by the mathematical and engineering circles, and it has become one of the necessary abilities of modern scientific and technological workers.