1. Common question types in mathematical modeling
2. Evaluation questions
Comprehensive evaluation is a common problem in mathematical modeling. It often appears in national competitions and American competitions, such as the comprehensive evaluation of the Yangtze River water quality in the national competition in 2005, the quantitative evaluation of the influence of the 2010 Shanghai World Expo, and the 2014 American competition. The question of "the best college coach" and the allocation of taxi resources in the "Internet +" era in 2015 are all comprehensive evaluation questions.
Comprehensive evaluation is a common problem in mathematical modeling. It often appears in national competitions and American competitions, such as the comprehensive evaluation of the Yangtze River water quality in the national competition in 2005, the quantitative evaluation of the influence of the 2010 Shanghai World Expo, and the 2014 American competition. The question of "the best college coach" and the allocation of taxi resources in the "Internet +" era in 2015 are all comprehensive evaluation questions.
2. The difference between subjective and objective evaluation questions
●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 comprehensively determine the weight.
●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.
3. How to choose the appropriate evaluation method
●In the analysis of evaluation problems, how to choose the appropriate evaluation method is the key factor to determine the quality of the evaluation results. Therefore, it is necessary to have insight into the basic characteristics and conditions of use of the commonly used evaluation methods in order to answer the questions smoothly!
3. Forecasting questions
1 Basic problem-solving steps for forecasting competitions
●Forecasting is to estimate the future 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 Differences in prediction problems
●Forecasting problems are divided into two categories:
● One category is the problems whose internal evolution mechanism cannot be described by mathematical language;
●The other type can describe its internal laws through differential equations, which we call mechanism modeling problems, and solve them 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 problems
1 Basic problem-solving steps of 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:
●(1) First determine the decision variables, that is, the variables that need to be optimized;
(2) Then determine the objective function, which is the purpose of optimization;
●(3) Finalize the constraint conditions, the decision variables are subject to those objective restrictions when they reach the optimal state.
2 Solutions to some optimization problems in national competitions
●In the issue of reasonable arrangement of ophthalmic beds in the 2008 national competition,
●The objective function is the highest utilization rate of hospital beds;
The decision variable is the service strategy: first-come-first-served patients, first-patient emergency patients, or first-occupied patients, etc.;
●Constraints may include the maximum waiting time limit for patients, patients with different symptoms in different rooms, etc.;
●In the 10-year national competition traffic police service platform setting and scheduling issues,
●The decision variable is the location coordinates of the service platform;
●The objective function is the shortest time for the traffic police car to reach the accident site, and the shortest time for the traffic police to block the traffic arteries;
●Constraints may include the latest arrival time of the traffic police after the accident, the minimum number of service platforms in a certain area, etc.
3 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 The optimization model can adopt intelligent optimization algorithm .
