Table of contents
3 Common model classification of common digital modeling problems
1. Asia-Pacific Mathematical Modeling ABC Problem Idea Model: 9 After the competition starts, it will be updated as soon as possible and you can get the business card at the end of the article.
2. Competition time: Starts on November 23, 2023
3 Common model classification of common digital modeling problems
Optimization model
Predictive model
Evaluation model
3.1 Classification problem
Discriminant analysis:
Also known as the "discrimination method", it is a multi-variable statistical analysis method that determines the type of a research object based on various characteristic values under the conditions of determined classification.
The basic principle is to establish one or more discriminant functions according to certain discriminant criteria; use a large amount of data on the research object to determine the undetermined coefficients in the discriminant function, and calculate the discriminant index; based on this, it is possible to determine what category a certain sample belongs to. When a new sample data is obtained, it is necessary to determine which category of known types the sample belongs to. This type of problem belongs to the discriminant analysis problem.
Cluster analysis:
Cluster analysis or clustering is to divide similar objects into different groups or more subsets through static classification methods, so that member objects in the same subset have similar attributes, commonly included in the coordinate system medium and shorter spatial distances, etc.
Cluster analysis itself is not a specific algorithm, but a general task that needs to be solved. It can be achieved by different algorithms that vary greatly in terms of understanding what clusters are made of and how to find them efficiently.
Neural network classification:
BP neural network is a neural network learning algorithm. It is a hierarchical neural network composed of an input layer, an intermediate layer, and an output layer. The intermediate layer can be expanded into multiple layers. RBF (Radial Basis Function) neural network: The radial basis function (RBF-Radial Basis Function) neural network is a three-layer feedforward network with a single hidden layer. It simulates the structure of neural networks in the human brain that adjust locally and cover each other's receptive fields. Perceptron neural network: It is a neural network with a single layer of computational neurons, and the transfer function of the network is a linear threshold unit. It is mainly used to simulate the perceptual characteristics of the human brain. Linear neural network: It is a relatively simple neural network, consisting of one or more linear neurons. A linear function is used as the transfer function, so the output can be any value. Self-organizing neural network: Self-organizing neural network includes self-organizing competition network, self-organizing feature mapping network, learning vector quantification and other network structure forms. K nearest neighbor algorithm: K nearest neighbor classification algorithm is a theoretically mature method and one of the simplest machine learning algorithms.
3.2 Optimization problem
Linear programming:
Mathematical theory and method for studying the extreme value problem of linear objective function under linear constraints. English abbreviation LP. It is an important branch of operations research and is widely used in military operations, economic analysis, business management, and engineering technology. Modeling method: list the constraints and objective function; draw the feasible region represented by the constraints; find the optimal solution and optimal value of the objective function within the feasible region.
Nonlinear programming:
Nonlinear programming is mathematical programming with nonlinear constraints or objective functions, and is an important branch of operations research. Nonlinear programming studies the extreme value problem of an n-element real function under a set of constraints of equality or inequality, and at least one of the objective function and the constraints is a nonlinear function of an unknown quantity. The situation where the objective function and constraints are both linear functions belongs to linear programming.
Integer programming:
A program in which the variables (wholly or partially) are restricted to integers is called an integer program. If the variables in a linear model are restricted to integers, it is called integer linear programming. Currently popular methods for solving integer programming are often only applicable to integer linear programming. A type of mathematical programming that requires all or some of the variables in the solution to be integers. From the composition of constraints, it can be subdivided into linear, quadratic and nonlinear integer programming.
Dynamic programming:
Including knapsack problems, production and operation problems, fund management problems, resource allocation problems, shortest path problems and complex system reliability problems, etc.
Dynamic programming is mainly used to solve optimization problems of dynamic processes divided into stages by time. However, some static programming that has nothing to do with time (such as linear programming and nonlinear programming) can be regarded as a multi-stage decision-making process as long as the time factor is artificially introduced. , can also be easily solved using dynamic programming methods.
Multi-objective planning:
Multi-objective programming is a branch of mathematical programming. Study the optimization of more than one objective function over a given region. Any multi-objective programming problem consists of two basic parts: