Table of contents
1. The modeling steps are shown in the figure below:
2. The difference between subjective and objective evaluation problems
3. How to choose the appropriate evaluation method
1. Basic problem-solving steps for forecasting competitions
2. The difference between prediction problems
3. How to choose the appropriate forecasting method
1. Basic problem-solving steps for optimization competition problems
2. How to choose the appropriate optimization method
Generally speaking, the types of mathematical modeling competitions are mainly divided into three types: evaluation, prediction and optimization. Among them, optimization is the most common type of competition, and almost every year there are
regional competitions or national competitions. The problem must be mastered and familiarized with.
As shown in the table below: It is mainly divided into evaluation, prediction and optimization problems.
1. Evaluation questions
Comprehensive evaluation questions are relatively clear-cut questions in mathematical modeling. From the comprehensive evaluation of each semester, the selection of tourist attractions to the selection of mobile phones, evaluation problems exist everywhere in life.
1. The modeling steps are shown in the figure below:
2. The difference between subjective and objective evaluation problems
●The concepts of subjectivity and objectivity are mainly divided when determining the weight of indicators. The difference between subjective evaluation and objective evaluation is that the subjective evaluation algorithm is mainly based on the subjective experience of the judge when determining the weight, while the objective evaluation is mainly based on the basic characteristics of the measurement data to determine the weight comprehensively.
●The determination of weights has a certain degree of subjectivity, and the weight distribution determined by different methods may not be consistent, which will lead to the uncertainty of weight distribution, and may eventually lead to the uncertainty of evaluation results. Therefore, in actual work, no matter which method is used to determine the weight distribution, it should rely on a more reasonable professional explanation.
Generally speaking, the objective weight method is more accurate, but it will be troublesome.
3. How to choose the appropriate evaluation method
In the analysis of evaluation problems, how to choose an appropriate evaluation method is the key factor that determines the quality of the evaluation results. Therefore, it is necessary to have insight into the
basic characteristics and conditions of use of each commonly used evaluation method in order to answer the questions smoothly.
2. Forecasting questions
1. Basic problem-solving steps for forecasting competitions
●Forecasting is to estimate and predict the future based on the past and present. Statistical forecasting belongs to the research category of forecasting methods, that is, how to use scientific statistical methods to make quantitative predictions about the future development of things
●There are many kinds of prediction methods based on mathematical modeling, from classic single consumption method, elastic coefficient method, statistical analysis method to the current gray prediction method. When using the corresponding forecasting method to establish a forecasting model, we need to know the research characteristics, advantages and disadvantages and scope of application of some main forecasting methods
2. The difference between prediction problems
●Forecasting problems are divided into two categories:
●One type is the problem whose internal evolution mechanism cannot be described by mathematical language;
●The other type is that the internal law can be described by differential equation. We call this type of problem mechanism modeling problem and solve it through differential equation modeling.
3. How to choose the appropriate forecasting method
●In the analysis of forecasting problems, it is also limited by the forecasting conditions (such as the size of the data, the relationship between variables, etc.) Different forecasting methods may produce different results, so it needs to be selected according to the actual situation.
3. Optimization questions
1. Basic problem-solving steps for optimization competition problems
●The optimization problem is to choose the most reasonable plan from all possible plans to achieve the optimal goal. In various scientific issues, engineering issues, production management, and social and economic issues, people always hope to obtain the greatest gains (such as insurance) at the lowest possible cost under limited resource conditions.
●The general problem-solving steps for optimization problems are as follows:
●(1) First determine the decision variable, which is the variable to be optimized;
●(2) Then determine the objective function, which is the purpose of optimization;
●(3) Finally determine the constraint conditions, when the decision variable reaches the optimal state, it is subject to those objective limitations.
2. How to choose the appropriate optimization method
Mathematical models and solving algorithms commonly used in optimization problems, including linear programming, nonlinear programming, integer programming, multi-objective programming,
etc. In model solving, for convex optimization models, gradient-based solving algorithms can be used; for non-convex optimization models,
intelligent optimization algorithms can be used.