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Project Presentation by Eddie Smolyansky & Shilo Abramovitch Supervisor: David Erdos. Multiple UAV Waypoint Ordering with Time Windows. Presentation Structure. Project definition Previous solutions Work environment & interface Our solution Finding shortest paths - PowerPoint PPT Presentation
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Multiple UAV Waypoint Ordering with Time Windows
Project Presentation by Eddie Smolyansky & Shilo AbramovitchSupervisor: David Erdos
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
Project Definition
Vehicle Routing Problem
With Time Windows
Assumptions
Complication: No Fly Zones
Complex combinatorial optimization problem.
Previous Solutions Background
Greedy
Genetic Algorithms
Simulated Annealing
Taboo Search
combinations
Work Environment & Interface Main code written in C++
Graphical output using MATLAB
Input, output and interface between programs in form of text files
Why we chose Taboo search It has been proven reliable
Simple and understandable concept
Easy to modify and improve
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
Finding the shortest paths using the Floyd–Warshall algorithm
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
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
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
Single route changes
Double route changes
Triple route changes
The search algorithm
Taboo search
A greedy search
Stop upon reaching local minima
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
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
VRPTW Results – Solomon Instances Difficulties with assessing results
Instance
# Waypoint
s
Capacity Run- Time
# UAVs
Benchmark
r101 100 200 55 sec 19 19c101 100 200 3 sec 10 10rc101 100 200 100 sec 15 14r206 100 1000 50sec 3 3c201 100 700 7 sec 3 3c108 100 200 11 sec 10 10
-10 0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90Final Plan: 10 Vehicles
X [m]
Y [m
]
-10 0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90Final Plan: 3 Vehicles
X [m]
Y [m
]
Clustered Formation – Low Vs. High Capacity
100 Nodes - Random Formation
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80Final Plan: 18 Vehicles
X [m]
Y [m
]
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80Final Plan: 19 Vehicles
X [m]
Y [m
]
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70Final Plan: 8 Vehicles
X [m]
Y [m
]
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70Final Plan: 8 Vehicles
X [m]
Y [m
]
No Fly Zones
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70Final Plan: 8 Vehicles
X [m]
Y [m
]
Results Discussion
Versatile algorithm
Very fast
Quality results
Surpassed expectations
Summary The problem
Finding shortest paths
Building initial solution
Moving in solution space
Taboo search
Results & capabilities
Future Work & Improvements Graphical User Interface
Soft time windows
Improved coding (object oriented)
Thank You For Listening!
Questions?
-10 0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90Final Plan: 10 Vehicles
X [m]
Y [m
]
