Question D: Mobile Communication Network Site Planning and Regional Clustering Problems
This year, there are many people who should choose D question, which is a typical target optimization question. The difficulty of this question is simpler. It is estimated that many students will choose this question. Of course, winning the prize will be a little more difficult. Clustering algorithms can be used, and there are many classic algorithms.
The main work of question D is to cover a certain area of a city with base station signals, and grid this area (and only consider the center point). The data structures are grid coordinates and traffic. On the base station, one is a macro base station, which has a large coverage (30), and the other is a micro base station, which has a small coverage and low cost.
content
background statement
The rapid development of mobile communication technology and the growing scale of operations have resulted in more and more complex communication networks. With the development of 5G, the bandwidth of communication is getting larger and larger, but the coverage area of base stations is getting smaller and smaller, so that covering the same area requires more base stations. In addition, the types of base stations and antennas have also increased. This makes the planning of the communication network, especially the problem of site selection, more and more complicated. The problem of site selection is: according to the coverage of the existing network antenna, select a certain number of points for the weak coverage area of the existing network, so that after the new base station is built on these points, the coverage problem of the weak coverage area of the existing network can be solved. For example, the figure below shows the coverage of the existing network in a certain area of a city, where the red area represents a weak coverage area. In actual network planning, considering the construction cost of the base station and some other factors, sometimes it may not be possible to solve all the weak coverage areas. At this time, you need to consider the factors of traffic volume, and try to give priority to the weak coverage areas with high traffic volume. In order to facilitate the calculation, the given area is divided into small grids, and only the center point of each grid is considered, that is, any given area can be divided into a limited number of points. Each point has some attribute values, including: coordinates, whether it is a weak coverage point, traffic volume, etc. The station site can also only select the point within the area 2. Whether a point is covered by the planned base station can be judged as follows: set the coverage range of the selected base station as d, and the coordinates of the point planned by the base station as: , otherwise it is considered that the point is not covered by the base station. At the same time, a constraint condition also needs to be considered in practice, that is, the distance between the new sites and between the new sites and the existing sites cannot be less than or equal to a given threshold.
Question 1
describe
The size of the given area is 2500×2500 grids or 2500×2500 points, where the abscissa ranges from 0 to 2499 and the ordinate ranges from 0 to 2499. In Annex 1 is the information to filter out the weak coverage points in this area, including the coordinates and traffic volume of each point. Given 2 kinds of base stations,
They are:
Macro Base Station (Coverage 30, Cost 10)
Micro base station (coverage 10, cost 1)
The coordinate points of the existing network base stations are also given in Annex 2, and the threshold of the distance between the new sites and the distance between the new sites and the existing sites is 10. According to the given information and data in the attachment, site planning is carried out, so that 90% of the total traffic volume of weak coverage points is covered by the planned base station. The coordinates of the selected site and the type of base station selected for each site are given. The coordinates of the site can only be selected from 2500×2500 points within a given area.
Problem solving ideas
The first question gives 2500x2500 points, as well as the grid coordinates and traffic volume of the points to be covered, which can actually be abstracted into an integer programming problem. There are three situations for each point: no base station, macro base station and micro base station. The Solver problem requires an objective function and constraints.
Objective function: You can combine cost and coverage according to your needs (up to 90)
Constraints:
the distance between the existing base station and the future base station is less than 10 The distance between the
base station and the weak coverage point is less than 10/30
- To solve this kind of problem, you can use heuristic algorithms such as genetic algorithm, simulated annealing, particle swarm, etc.
in terms of methods, and you can use spsspro (planning solver module) and lingo (a software dedicated to solving planning solver problems) in software.
Question 2
describe
Further consideration, in practice, each station is not completely circular coverage, but each station has 3 sectors, each sector pointing in one direction. Each sector has the largest coverage in the main direction (30 for the macro base station and 10 for the micro base station), which can be covered within 60 degrees left and right of the main direction, and the coverage is gradually reduced linearly. At 60 degrees, the coverage Half of the coverage in the main direction. Above 60 degrees, it cannot be covered by the sector.
Considering that the angle between the main directions of any two sectors of each station cannot be less than 45 degrees, while still considering other conditions such as the cost of the base station in the previous question, under the conditions of the optimal site location and sector angle , whether the new station can cover 90% of the total traffic volume of weak coverage points. If yes, give the results of the optimal site and sector angle; otherwise, give the results of the optimal site and sector angle, and give the proportion of the total traffic of the weak coverage points that can be covered at most.
Problem solving ideas
Ideas: The second question is basically similar to the first question, but a restriction needs to be added, which is more inclined to the method of signal propagation in practice. Three sectors are manually selected on the base station, each sector covers a range of 60 degrees, and the coverage is gradually reduced.
It can be considered that the coverage area is a diamond, and the coverage area of a base station becomes similar to the Mitsubishi icon, and two constraints can be added on the basis of the above.
Objective function: You can combine cost and coverage according to your needs (up to 90).
Restrictions:
- The distance between the existing base station and the future base station is less than 10.
- The distance between the base station and the weak coverage point is less than 10/30.
- The included angle of the main direction is less than 45 degrees
- Signals in non-dominant directions are gradually attenuated.
Question 3
describe
In practical work, in order to better solve the problem of weak coverage, it is necessary to perform regional clustering on weak coverage points, and group the weak coverage points with close distances into one category to obtain weak coverage areas, so that different weak coverage areas can be managed separately. This makes it possible to better solve the weak coverage problem.
If the distance between the two weakly covered points is not greater than 20, the two weakly covered points should be clustered into one class, and the clustering property is considered transitive, that is, if point A and point B are of a class, point B and point C is a class, then points A, B, and C are all a class. Try to cluster all weak coverage points, and the total time complexity of the method used for clustering is required to be as low as possible.
Problem solving ideas
Ideas: Go to the third question to directly use the clustering method for clustering.
Such as K-means/DBSCAN, you can use SPSSPRO's clustering module (K-means) or python/matlab programming language for clustering.
Epilogue
"If you are undecided, you can ask the spring breeze, and if the spring breeze does not speak, you will follow your heart" means: if you are hesitant about something, ask the spring breeze how to do it. . "If you are undecided, you can ask the spring breeze. If the spring breeze does not speak, you will follow your heart." The sentence comes from the "Jianlai" written by the Internet writer "Fenghuo Opera Princes". The original text is: "If you are undecided, you can ask the spring breeze. Follow your heart".
