Numeric optimization of maritime flows - Cartographic application & Theorerical prospection

Presentation

This projects takes part in the final grading of the nationwide examination for the entrance to the French Grandes Écoles (specialized engineering schools).

The main objective is to determine an optimal solution able to find the most relevant (in term of cost) route for a commercial vessel.

The final report (released under slides format) is available here.

Table of contents

1. Problem's introduction & Main goals
2. Introduction to graph theory
3. Naive approach: relational track using fundamental graph theory with Dijkstra's algorithm (Shortest Path Problem)
4. Complexity (spatial and time) discussion and theorems results related to
5. A refinement: Optimal geometrical approah using a grid system and new approximate heuristics using A-star algorithms
6. Discussion on the navigation systems: 4-directions, 8-directions and 360-system (respectively: Manhattan, Tchebychev and Euclidian distances)
7. Practical implementation of a cartographic application using the final weighted A-star algorithm (PA*)
8. Study of the spheric coordinates projections operators
9. Conclusion
10. Appendices

Results

Here are some screenshots of final results of the application developed in the third section of this project.

Other examples are avaiable in docs/slides/img.

Fig. 1 : Example of final result • Simulation based on specified parameters

Fig. 2 : Example of final result • Simulation based on specified parameters

Fig. 3 : Example of final result • Simulation based on specified parameters

License

Lucas RODRIGUEZ • lcsrodriguez.github.io

Academic work - April 2019 - May 2020. All rights reserved