Once again this year, the university campus has been severely affected by heat waves. Fortunately, existing trees and green spaces have helped users better withstand the high temperatures. To further mitigate these effects, the university would like to strategically plant additional trees so that all frequently used areas benefit from their cooling effect. However, trees cannot be planted on paved or concrete surfaces, where they must instead be replaced with parasols, which are less effective. Paved areas also reflect heat, which reduces the spread of cooling.
The project will be organized in several stages:
- formal modeling of the problem;
- algorithmic implementations (brute force, etc.);
- proposed extensions and improvements.
- Work in groups of 3–4 students.
- The final submission is due before the Christmas holidays; oral defenses will take place in January.
- Intermediate deliverables will be required.
The main problem is as follows:
How can trees be positioned so that all functional areas of the campus (e.g., sidewalks) are shaded? What is the minimum number of trees required to achieve complete coverage?
In a second stage, you will extend the model to account for parasols and for variations in shade distance depending on the type of terrain.
You may also propose your own variants of the problem, provided that you justify their relevance.
Results should be presented graphically to facilitate understanding and interpretation.
To complete the project, you will need cartographic data for the campus. These can be obtained from OpenStreetMap, for example using Overpass queries. You may also rely on other open data sources. The Python library osmnx could also be useful if you choose to implement your project in Python.
Each group will prepare a short presentation outlining their chosen modeling approach, as well as the tools they plan to use for implementation.