The specific ideas of BEF have been updated, and more ideas are in the business card at the end of the article
Ideas for Question A (Huawei Question): Super-resolution positioning in mobile scenes
Question A is a problem of positioning through signal waves in a mobile scene. Here we need to use frequency modulation continuous wave radar FMCW. Let me explain FMCW to you. Frequency modulation refers to the frequency of radar transmission signals changing with time, and continuous wave refers to radar transmission signals. The waveform is continuous in time.
principle
As shown in the figure above, the solid line represents the transmitted signal, and the dotted line represents the received signal.
B - Sweep range
Fb - beat frequency
τ - Delay of the echo
T- emission period
The composition of the radar
Question A is relatively difficult, requires a lot of mathematical formulas, requires strong mathematical skills, and novices do not consider
Ideas for Problem B (Huawei Problem): Batch Optimization of Square Parts
Sub-problem 1 :layout optimization problem. It is required to establish a mixed integer programming model to reduce the amount of plates as much as possible under the requirements of production orders and related constraints.
constraint:
- The width (or length) of product items (items) in the same stack (stack) should be the same;
- The product item resulting from the final cut is complete, not stitched.
This sub-problem requires programming, with data set A as input, and the output requirements are shown in Part V.
Ideas for sub-question 1:
First observe and analyze the data (A1-A4, A5 are deleted and not considered, the official has notified), the materials in each excel sheet are the same, and the goal is to give the cutting plan of the plate.
According to the assumption in Article 3, the layout method is accurate layout and the number of cutting segments does not exceed three. In the sub-problem, the width or height of the products in the same stack is also required to be the same, so it is easy to think of merging parts with the same length or width in the data , arranged into larger components combined as a stack, such as these three components:
| 224 |
397 |
| 224 |
378 |
| 224 |
378 |
They have the same width, combine it into a large block of 224*1153 as a stack, and then add some redundancy to this stack, such as 224*1160, pay attention to keep the width unchanged, and then merge similar different stack components Larger strips, so that the length of the strip is exactly the length or width of the board, and the different strips are combined again until they match the length and width of the raw material.
A total of three combinations can be added each time with appropriate redundancy, and finally the length and width of the raw material plate can be accurately matched. Such a division can meet the requirements of the topic. For the three-stage constrained nesting algorithm, there are two kinds of precise algorithms (such as linear programming, dynamic programming, integer programming and branch and bound method, etc.) Make a selection.
Then how to judge the excellence of this segmentation? It can be expressed by the effective utilization rate, which is the sum of the area of all components divided by the sum of the area of all raw materials used. The higher the better.
First determine the limit utilization rate, that is, the minimum number of plates required in theory. For example, the total area of all components in A1 is 2.84 million square meters, and 83.54 raw material plates of 2440*1220 are required, that is, at least 84 plates are required, and the limit utilization rate is 99.45%. , so the closer the utilization rate is to 99.45 after division, the better (it is impossible to exceed it in theory). Of course, the upper limit can be lowered. For example, there are 2418*58 parts in the A1 data. Components are available, so this component will inevitably have an area loss of 22*58 when placed in the version. If this situation is considered, the upper bound can be further reduced.
The bottom-level algorithm is a geometric algorithm, which can use the left bottom strategy to place components, and select the optimal component to place in a rectangle through different strategies.
The randomization method and the intelligent optimization algorithm need to deal with the order of the discharge rectangles, and can use various rules, such as sorting by area size, perimeter, width, height, synthesis, etc., and then organize and select search strategies. It is often necessary to quickly find a better solution in a local range, and then slowly search for a better global solution.
Take the genetic algorithm as an example:
First, group the components with the same length or width, and use the genetic algorithm to encode them in integers (the encoding method is not unique-for example: each component has a group number and a serial number within the group, positive numbers indicate horizontal placement, negative numbers indicate vertical placement, etc.), When decoding, combine adjacent parts into larger parts according to the order of integer arrangement, and then combine different parts to calculate the utilization rate and so on.
Sub-problem 2 :Order batching problem. It is required to establish a mixed integer programming model to group all the orders in the data set B, and then carry out independent layout for each batch, so as to make the amount of original plates as small as possible under the satisfaction of order requirements and related constraints.
Further requirements on the basis of satisfying the constraints of sub-problem 1:
- Each order if and only if it appears in one batch;
- The product items (items) of the same material in each batch can use the same original plate for nesting;
- In order to ensure the rapid flow of processing links, the total number of product items (items) in each batch cannot exceed the limit value;
- Due to factory capacity limitations, the total area of each batch of product items (item) cannot exceed the limit value;
This sub-question requires programming, with data set B as input, and the requirements for output results are shown in Part V.
Ideas for sub-question 2:
The amount of data in sub-problem 2 reaches 109,218. What we need to do is to complete the batching according to the requirements of the topic. The batching needs to meet the following restrictions:
The upper limit of the total number of single batch product items (item) max_ itemn_ _num = 1000
The upper limit of the total area of a single batch product item (item) max_ item_ area = 250 (m2)
According to a rough estimate of the number of product items, at least 110 batches are required.
We are looking for the batching principles to be followed. It is mentioned in the background of the topic: if the batch size is too small, the material utilization rate is low, and the production efficiency is low; if the batch size is too large, the material utilization rate will increase, but the delivery date of the order cannot be guaranteed, and order sorting is difficult increase, and decrease production efficiency.
Assume that we already have a grouping strategy and need to build a model that can quantify the rationality of batching. We can use the number of product items in a batch/the upper limit of the total number of product items in a single batch and the product area in a batch/single batch The two indicators, the upper limit of the total area of product items, are evaluated.
Then how to generate the batch strategy, you can establish an integer programming model, and use heuristic algorithms, such as genetic algorithms, to solve the problem on the basis of data processing (summarizing items according to the same material and size).
You can try a variety of batching strategies, calculate the number of original plates used, and select the smallest as the optimal solution.
Ideas for Question C: Scheduling optimization problem of automobile manufacturing painting-assembly cache scheduling area
Question C is an optimal scheduling problem. Due to the different constraints of each workshop, the production scheduling cannot be continuously produced in the same sequence. Different constraints and related time data are given in the title. The scheduling optimization problem is due to the equation or inequality Finding the performance index constraints under the constraint conditions is an NP-complete problem in terms of calculation amount. As the scale of the problem increases, the calculation amount for solving the optimization increases exponentially.
For this question, we can simplify it into a mathematical programming model, collect data by running simulation programs, focus on the description of the logical relationship running in the system, and compare and evaluate production scheduling.
Algorithms such as queuing network model, simulated annealing algorithm, and heuristic graph search method can also be considered for solution analysis. The overall difficulty is easier than AD questions, and beginners can also consider it appropriately.
Ideas for Question D (ZTE Question): PISA Architecture Chip Resource Arrangement Problem
Question D belongs to the arrangement of chips. If you are a professional in communication and chips, you can consider it. The overall question is more difficult, and novices are not recommended to consider it.
Ideas for Question E : Research on Grassland Grazing Strategies
Question 1. From the perspective of mechanism analysis, establish a mathematical model of the impact of different grazing strategies (grazing methods and grazing intensity) on the soil physical properties (mainly soil moisture) and vegetation biomass of the Xilin Gol Grassland.
Question 1 can be simplified as the effects of grazing methods and grazing intensity on soil moisture and vegetation biomass.
The independent variables of the model we want to build are:
1. Grazing methods: According to the question, there are five types: continuous grazing throughout the year, grazing prohibition, selective grazing rotation, light grazing, and rest grazing during the growing season. Among them, the two meanings of grazing prohibition and light grazing overlap with grazing intensity. Therefore, no additional consideration is required; in addition, the impact of the strategy on the grassland emphasizes the impact on time, and the impact on space is reflected in the inherent nature of the grassland . Therefore, in fact, only two grazing methods need to be considered as independent variables: all Annual continuous grazing and time-sharing grazing. In order to simplify the model, this variable can be reflected in the model as a proportional coefficient.
2. Grazing intensity: This variable can be expressed directly by a constant S , and S is the number of sheep per square meter. Note that the "sheep" here is just a livestock unit. Cows, horses, and camels = 6 sheep, cubs of cows, horses, and camels = 3 sheep, and lambs = 0.5 sheep.
The dependent variable of the model is:
1. The change of soil humidity dh/dt: where h represents humidity, and what we output as a model is the change of h with time, so it is necessary to differentiate with time, and the amount of vegetation is the same.
2. Change of vegetation biomass dw/dt: where w represents vegetation biomass. Note: Vegetation biomass data are dry weights in Annex 15, not to be confused with data in Annexes 5, 6, and 10.
For the impact of grazing intensity on vegetation change, the formula in the extended reading can be directly applied:
For the impact of grazing intensity on soil moisture, it can be combined with the soil moisture in Annex 3, the soil evaporation data in Annex 4, the precipitation in Annex 8, and the data in Annex. Since the only factors affecting soil moisture are soil evaporation, precipitation, and grazing conditions, after removing the effects of soil evaporation and precipitation (these two items are known from the appendix), what remains is the impact of grazing conditions on soil moisture.
From the vegetation biomass data in Appendix 15 combined with the relationship between the aspects just mentioned and plant growth, the grazing situation can be inversely deduced. From this, we can get the impact of grazing situation on the allowable humidity.
Considering time-sharing grazing, we can finally add a proportional coefficient to the model output.
Question 2. Based on the soil moisture data in Annex 3, the soil evaporation data in Annex 4, and the precipitation data in Annex 8, please establish a model to predict the soil moisture at different depths in 2022 and 2023 while keeping the current grazing strategy unchanged, and complete The following table.
It can be known from Question 1 that the current grazing strategy can be deduced from the vegetation biomass, and the impact of grazing strategy on soil moisture has been obtained in Question 1, so the model in Question 1 can be directly applied.
Be careful not to be affected by the complicated formulas in the extended reading when doing this question:
We only need to take E(α) as a whole as a known quantity.
Question 3. From the perspective of mechanism analysis, establish a mathematical model of the influence of different grazing strategies (grazing methods and grazing intensity) on the soil chemical properties of Xilin Gol Grassland. Please combine the data in Appendix 14 to predict the values of soil organic carbon, inorganic carbon, total N, and soil C/N ratio in the Xilin Gol Grassland monitoring plots (12 grazing plots) under different grazing intensities in the same period in 2022, and complete the table below.
This small question is relatively simple, just use the data in Appendix 14 to apply the regression model. A separate regression model was designed for each chemical property, and the parameters were adjusted separately. Due to the limited amount of data and features, it is recommended to use the decision tree model here.
Question 4. Use the desertification degree index prediction model and the data provided by the attachment (including the data collected by yourself) to determine the desertification degree index value of the monitoring points under different grazing intensities. And please try to give a quantitative definition of soil compaction. On the basis of establishing a reasonable soil compaction model, combined with question 3, give a grazing strategy model to minimize the desertification degree index and compaction degree.
Question 4 is divided into two sub-questions. The desertification prediction model for the first sub-question has been given in detail in Article 3 of the extended reading and will not be analyzed further. Now look at question 2.
The known compaction formula is:
B = f（W,C,O）
The lower the soil moisture w, the larger the bulk density c, the lower the organic matter content O, and the more serious the degree of soil compaction B. Among them, the soil moisture data is in Appendix 3, the organic matter content is in Appendix 14, and the bulk density is in Appendix 7 (it is a constant). The model can be specifically expressed as:
Here, the ratio between the three coefficients is mainly determined according to the degree of influence of the three factors. The data given in the question does not measure the obvious characteristics of this indicator, so the determination of the coefficient is justified.
Combined with the impact of grazing strategy on O in question 3, the influence of grazing strategy on B can be further obtained, and combined with the desertification degree prediction model, the optimal grazing strategy can be obtained.
Ideas for Question F: Scientific management of living materials during the COVID-19 epidemic
Question 1: The impact of the large-scale flow of various living materials on the epidemic
The epidemic in many cities could not be quickly controlled in a short period of time. Reflecting on the reasons, there is a view that the development or control of the epidemic is related to the distribution of living supplies. Please combine the data on the number of people infected with the virus during the COVID-19 epidemic in Changchun City and other data in attachments provided in Appendix 1 or the data you can collect to identify and analyze the effect before and after the distribution of vegetable packages in Changchun City, so as to facilitate future prevention and control Work.
Analysis of ideas: first of all, question 1, mainly to analyze the impact of the distribution of vegetable packages on the epidemic control in Changchun City, the data of vegetable packages is in Appendix 4, but when the vegetable packages will start to be distributed, earlier data needs to be consulted, if It is really impossible to find the data in Appendix 4. At this time, the data on the number of infected people in the epidemic is divided into data before and after the distribution of vegetable packages, and then displayed. If it shows an inverted V shape, it means that the distribution of vegetable packages has a great impact on suppressing the epidemic. Development works well. Note here that it includes two parts: the discussion of the districts and the data discussion of the entire Changchun City. If you need to build a model, you can build a relational expression between the distribution data of vegetable packages and the number of people infected by the epidemic.
Question 2: The number and location of distribution points for daily necessities
At the beginning of the outbreak of the epidemic, Changchun City's daily necessities were mainly distributed through several distribution points. Considering that in the early stage of the epidemic, a large number of human resources are required while at the same time minimizing the movement and contact of people, the number of delivery points is particularly important. Attachment 2 provides the distribution results of the number of distribution points in different areas of Changchun City at that time. Please combine the relevant data in Annex 3 and Annex 4 to discuss the rationality of the number of delivery points, and conduct appropriate optimization through mathematical modeling. In addition, please fully consider special events such as future epidemics and natural disasters, make reasonable plans for the location and quantity scale of government stockpiles and large-scale material sorting sites, and propose the optimal number, scale and potential spare sites for site selection Location.
Analysis of ideas: Question 2 is mainly divided into two sub-questions. The former is to discuss the rationality of the quantity. The key to the rationality is whether the quantity can guarantee the material security of the population in the quarantine area. The configuration and the proportion of materials at the delivery point every day, so we only need to simply discuss the quantity; the division of the quantity is mainly related to factors such as the number of people in the isolation area, the density of the road network, and the number of communities. This is because theoretically the denser the road network The greater the possibility of causing traffic congestion, the more delivery points need to be set at this time; the more the number of communities, the more responsible it is to find, and more delivery points should be set, so the problem is transformed into the need to establish the number of delivery points and road According to the analysis in Question 1, we can first find out which areas have the most obvious reduction in the number of infected people after the delivery of vegetable packages, and then establish the relationship between the number of delivery points and the number of communities based on this data. For the equation between the three, it is enough to solve and optimize the remaining area based on the equation. The following small question is a site selection problem. There are many similar methods. The main thing is to establish a suitable optimization model. Here, you can privately contact the seniors to provide a similar site selection modeling method. The optimization model mainly includes three parts, decision variables , objective function and constraint conditions, where the decision variable is the location coordinate information and the minimum quantity of the location, so it can be regarded as a multi-objective optimization problem; the objective function is the shortest distance to each area, etc.
Note: Please be sure to place the relevant results in the text in the form of a table . The main parameters include the location of the site and the area it belongs to, the radius of the site the number of communities under the jurisdiction, and the population within the jurisdiction. Key information should be reflected in the table .
Question 3: Scientific distribution of living materials
During the distribution of living materials during the epidemic, vegetables are a special product that people urgently need and have a short shelf life, and the distribution effect is more important. After a period of exploration, Changchun City found that the form of vegetable packages not only reduced the number and workload of volunteers in the city, but also reduced personnel's contact with vegetables. Please analyze the vegetable bag demand and distribution pattern according to Appendix 5, and evaluate and adjust the vegetable bag supply plan from April 10 to April 15 according to the location and population information of each community in Appendix 3.
Analysis of ideas: Question 3 is mainly to analyze the rules through Annex 5 first, and then adjust the data from April 10 to 15. First of all, you should first determine the relationship between the purchase volume and the distribution volume. This relationship cannot be constructed by simple regression analysis. This is because the two are not in a one-to-one relationship (there is an inventory relationship). The real logical relationship between the two needs to be dynamically analyzed. First, the daily purchase volume and distribution data of each region are sorted out, and then the prediction models for the purchase volume and distribution volume are respectively established. Gray prediction is not recommended for the prediction model here. This is because the data does not show a monotonic relationship, and the quadratic exponential smoothing orARMAalgorithm can be used to predict the data from April 10th to 15th after predicting the law. After the prediction is completed, it can be dynamically adjusted in conjunction with the data in Appendix 3.
Question 4: Make a plan for the orderly distribution of residents' living materials in the case of large-scale lockdown in Changchun City
Although the epidemic situation in Changchun City in March was extinguished safely, you should take precautions. Please, on the basis of the second and third questions, combined with the table of Changchun City streets and communities given in Appendix 3, make a plan to ensure the supply of residents’ daily necessities during special periods. Detailed scenario (ordered network diagram). The upstream of the network is the source of various materials (choose a location for each district, and the participating teams can choose by themselves according to the coordinates), the middle reaches are the distribution centers of various materials (the number of distribution centers can be selected by themselves, you can first set according to Attachment 2, and then adjust and optimize), the network Downstream are all residential areas in Changchun City. Logistics is the quantity of various daily necessities transported through each edge of the network on each day in a cycle (only vegetables can be considered at the beginning, and different varieties of vegetables can be sent on different days to increase the variety of vegetables for residents). At the beginning, each edge of the network may not use real streets, and it is considered that the two points are connected by the shortest path. Later, you can choose a few administrative districts to choose routes according to real streets, up to the whole city. Since it is a special period, saving manpower (the workload is calculated by the product of the transportation mileage and the number of residents in the community) is the most important indicator. At the same time, it is hoped to reduce direct and indirect contact of personnel. After completing the ordered network diagram, please further consider using trucks to transport materials. Each large truck can hold 10 tons, and each small truck can hold 4 tons. Observe whether there is any significant difference in the plan.
Note: Please condense the relevant results in the main text in the form of graphs or tables, and analyze and evaluate the advantages of the distribution plan you gave against the indicators.
Question 4 is mainly to give a systematic plan based on the various models established above. This mainly includes selecting a material concentration place for each region, and selecting and optimizing the location of the midstream living material delivery point, so this problem is still an optimization. The problem is that you can first optimize the delivery point of the midstream material, the quantity can use the data in Appendix 2, and the location needs to be selected according to the road network information and community data. There are many options for the model here. After the selection of the delivery point is completed, select the material The idea of selecting the location of the source is the same, as long as the distance from the location to each delivery point is the shortest.
Note: Please condense the relevant results in the main text in the form of graphs or tables, and analyze and evaluate the advantages of the distribution plan you gave against the indicators.
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