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 19

c101 100 200 3 sec 10 10

rc101 100 200 100 sec 15 14

r206 100 1000 50sec 3 3

c201 100 700 7 sec 3 3

c108 100 200 11 sec 10 10

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Clustered Formation – Low Vs. High Capacity

100 Nodes - Random Formation

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No Fly Zones

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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?

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