One Hull of A Rain ForestGreen Computing

Computer ScienceNeil GordonJanuary 14 2011

The Travelling Salesman problem

What is it?

Change the way you think about Hull | 6 January 2011 | 3

• Suppose Bob the salesman has been given a list of towns to visit to try selling his new products

• He knows how far it is from one town to the next

• But wants to decide what is the best way to travel around them

4

5

7

Hull

Beverley

Tickton

York

48

36

33

?

The Problem

Change the way you think about Hull | 4

• Given a list of places (cities) with distances between, what is the shortest journey to travel to each location once only

• It is hard – we will see how hard as we go through

• It isn’t a new problem – it dates from the 1800s – when it was thought of by the mathematician William Hamilton – look him up on the Internet to find out more

• Since then, it has been studied by mathematicians, computer scientists and lots of others….

Why is Bob’s problem relevant to saving rainforests and your one hull of a Rainforest project?

Change the way you think about Hull | 5

• There are a number of reasons – try listing them in your groups. Describe the reason, and why it is relevant to rainforests

• Some of the reasons are:

• Shorter journeys which saves– Time – for someone's job so that saves money as

well– Fuel and resources – less travel means less petrol

(or other fuel). That saves money AND helps to reduce the output of fossil fuels

Transport and the environment

Change the way you think about Hull | 6 January 2011 | 6

• Rainforests play a key role in the Earth’s eco-systems – who can explain what these are?

• They provide habitats

• They are the lungs of the planet, converting carbon-dioxide to oxygen.

• However, rainforests face a number of challenges

• acid rain – caused by pollution

• climate change – the world seems to be getting hotter. Caused by pollution, especially transport…..

How could you attempt to solve it

Change the way you think about Hull | 7

• Given a simple example, try it in your groups using page 1 of the hand-outFirst for the maps with 3 towns

• Then for the map with 4towns

4

5

7

Hull

Beverley Tickton

4

5

7

Hull

Beverley

Tickton

York

48

3633

4

12

7

Hull

Beverley Paull

How many possibilities are there?

Change the way you think about Hull | | 8

• How many possible routes could there be?

• Suppose you have 2 places to visit

• Or 3 places

• Or 4 - In your groups, try to work this one out – do the routes for 5 places that is on the back of the handout

• The answer is:see the next slide

Some example solutions

Change the way you think about Hull | 6 January 2011 | 9

• As the numbers get big, it quickly becomes hard to solveIf N=2 there are 2 possible routesif N=3 there are 6if N=4 there are 24What do you think for 5 places to visit?

• if N=5 there are 120 different routesIf N=6 there would be 720 possible routesIt then gets much bigger very quickly….

• To visit the top 10 cities, there are 3628800 possible solutions. [This is assuming there is only 1 road between each city. If there were more, it gets harder to solve…]

• To find the shortest route to visit the top 20 visitor attractions you would have to check 2432902008176640000 different routes. Even for a computer that takes a long time.

Applications

Change the way you think about Hull | | 10

• Can you think of anything that needs to solve this type of problem a lot?

• If your parents/carers/family have a SatNAV in their car, then that does this in the case where you want to travel between two places, sometimes with a third place to travel through.

• This is still complicated – as there are lots of roads and they measure different things to find the best route

• What criteria do they use to decide the best route?

Solving the Travelling Salesman problem

Change the way you think about Hull | 12

• The only way to guarantee the best solution is to try all possible routes

• There are some different approaches to try to make it easier, for example

• Start by only searching the shortest distances

• Use tree searches and other approaches – if you do computing later in your studies you will meet these and learn how to go about solving these problems

What can you do to reduce your carbon footprint?

Change the way you think about Hull | 6 January 2011 | 14

• In your groups, identify 1 thing per person that you can do at school, at home or travelling between them to reduce your carbon footprint

• Carbon calculator: http://www.cooltheworld.co.uk/kidscarbonquiz.html

Summary

Change the way you think about Hull | 6 January 2011 | 15

• We have explored a few aspects of the Bob’s problem

• We have seen that this is related to reducing the production of carbon and to helping protect the rain forests

• We can use computers to help solve this sort of problem

• Computers can help and assist in dealing with other problems too that can help in understanding and protecting the environment.