1. Project Presentation by Eddie Smolyansky & Shilo Abramovitch Supervisor: David Erdos

2.  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.  Vehicle Routing Problem  With Time Windows  Assumptions  Complication: No Fly Zones  Complex combinatorial optimization problem.

4.  Background  Greedy  Genetic Algorithms  Simulated Annealing  Taboo Search  combinations

5.  Main code written in C++  Graphical output using MATLAB  Input, output and interface between programs in form of text files

6.  It has been proven reliable  Simple and understandable concept  Easy to modify and improve

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

8.  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.  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.  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

14.  Taboo search  A greedy search  Stop upon reaching local minima

15.  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.  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.  Difficulties with assessing results Instance# WaypointsCapacityRun- Time# UAVsBenchmark r10110020055 sec19 c1011002003 sec10 rc101100200100 sec1514 r206100100050sec33 c2011007007 sec33 c10810020011 sec10

21.  Versatile algorithm  Very fast  Quality results  Surpassed expectations

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

23.  Graphical User Interface  Soft time windows  Improved coding (object oriented)

24.  Questions?