Table of contents
1. The modeling steps are as shown in the figure below:
2. The difference between subjective and objective evaluation issues
3. How to choose appropriate evaluation methods
1. Basic problem-solving steps for prediction competition questions
2. The difference between prediction problems
3. How to choose the appropriate prediction method
3. Optimization competition questions
1. Basic problem-solving steps for optimization competition questions
2. How to choose the appropriate optimization method
Generally speaking, the types of mathematical modeling competition questions are mainly divided into three types: evaluation, prediction and optimization. Among them, optimization is the most common type of competition, and it is
published in regional competitions or national competitions almost every year. Questions must be mastered and familiar with.
As shown in the following table: it is mainly divided into evaluation, prediction and optimization problems.
1. Evaluation issues
Comprehensive evaluation problems are a type of questions with relatively clear ideas among mathematical modeling problems. From comprehensive evaluations in each semester, selection of tourist attractions to selection of mobile phones, evaluation problems also exist everywhere in life.
1. The modeling steps are as shown in the figure below:
2. The difference between subjective and objective evaluation issues
●Subjective and objective concepts 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 comprehensively determine the weight.
●There is a certain degree of subjectivity in weight determination, and the weight distribution determined by different methods may not be consistent, which will lead to uncertainty in weight distribution and ultimately may lead to uncertainty in the evaluation results. Therefore, in actual work, no matter which method is used to determine weight distribution, it should rely on more reasonable professional explanations.
Generally speaking, the objective weighting method is more accurate, but it can be troublesome.
3. How to choose appropriate evaluation methods
In the analysis of evaluation problems, how to choose the appropriate evaluation method is the key factor that determines the quality of the evaluation results. Therefore, it is necessary to understand the
basic characteristics and usage conditions of each commonly used evaluation method in order to successfully answer the questions.
2. Prediction questions
1. Basic problem-solving steps for prediction competition questions
●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 types of prediction methods based on mathematical modeling, from the classic single consumption method, elastic coefficient method, statistical analysis method, to the current gray prediction method. When using corresponding forecasting methods to build forecasting models, we need to know the research characteristics, advantages, disadvantages and scope of application of some main forecasting methods.
2. The difference between prediction problems
●Prediction problems are divided into two categories:
●One type is a problem whose internal evolution mechanism cannot be described in mathematical language;
●The other type is a problem whose internal laws can be described through differential equations. We call this type of problem a mechanism modeling problem and solve it through differential equation modeling.
3. How to choose the appropriate prediction method
●In the analysis of prediction problems, different prediction methods may produce different results due to the limitations of prediction conditions (such as the size of the data, the relationship between variables, etc.), so the choice needs to be based on the actual situation.
3. Optimization competition questions
1. Basic problem-solving steps for optimization competition questions
●Optimization problems are to select the most reasonable solution from all possible solutions to achieve the optimal goal. In various scientific problems, engineering problems, production management, and social and economic problems, people always hope to obtain the maximum gain (such as insurance) at the lowest possible cost under limited resource conditions.
●The general steps for solving optimization problems are:
●(1) First determine the decision variables, which are the variables that need to be optimized;
●(2) Then determine the objective function, which is the purpose of optimization;
●(3) Finally determine the constraints. When the decision variables reach the optimal state, they are subject to those objective limitations.
2. How to choose the appropriate optimization method
Mathematical models and solution 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.