Multiple UAV Waypoint Ordering with Time Windows

1. Project Presentation by Eddie Smolyansky & Shilo Abramovitch Supervisor: David Erdos Multiple UAV Waypoint Ordering with Time Windows

2. Presentation Structure • Project definition • Previous solutions • Work environment & interface • Our solution • Finding shortest paths • Building initial solution • Moving in solution space • Taboo search • Results & Discussion • Summary • Improvements & Future work

3. Project Definition • Vehicle Routing Problem • With Time Windows • Assumptions • Complication: No Fly Zones • Complex combinatorial optimization problem.

4. Previous Solutions • Background • Greedy • Genetic Algorithms • Simulated Annealing • Taboo Search • combinations

5. Work Environment & Interface • Main code written in C++ • Graphical output using MATLAB • Input, output and interface between programs in form of text files

6. Why we chose Taboo search • It has been proven reliable • Simple and understandable concept • Easy to modify and improve

7. Stages of the algorithm • Finding the shortest paths between points and their “costs” • Finding an initial solution to the problem • Trying to improve that solution

8. Finding the shortest paths using the Floyd–Warshallalgorithm • Finding the cost of going directly between all two points (including NFZ polygon points) • Allowing to pass through one more NFZ polygon points in each iteration • Along the way saving all the minimum costs (time/distance) and the shortest paths in a matrix

9. Initial solution – Solomon algorithm • Start with an empty route and add waypoints as long as possible • The waypoints we chose are those that maximize the time difference • Then we start with a fresh route until we finish with all the way points

10. Minimizing vehicle number • Discarding all empty routes • Trying to insert all the way-points of a route to the others • Upon success in discarding a route we start from the beginning of the stage

11. Single route changes

12. Double route changes

13. Triple route changes

14. The search algorithm • Taboo search • A greedy search • Stop upon reaching local minima

15. The break-out • Reversing the optimizing direction • Restarting the search upon reaching a local maximum • A fast break out but does not guarantee finding a new local minimum

16. No fly zones • As many points as needed in each polygon • Any kind of polygons, convex or not • Any kind of combination of polygons, overlapping or not

17. VRPTW Results – Solomon Instances • Difficulties with assessing results

18. Clustered Formation – Low Vs. High Capacity

19. 100 Nodes - Random Formation

20. No Fly Zones

21. Results Discussion • Versatile algorithm • Very fast • Quality results • Surpassed expectations

22. Summary • The problem • Finding shortest paths • Building initial solution • Moving in solution space • Taboo search • Results & capabilities

23. Future Work & Improvements • Graphical User Interface • Soft time windows • Improved coding (object oriented)

24. Thank You For Listening! • Questions?