One Hull of A Rain ForestGreen Computing

Computer ScienceNeil GordonJanuary 14 2011

The Travelling Salesman problem

What is it?

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• 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

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Beverley

Tickton

York

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The Problem

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• 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?

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• 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

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• 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

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• 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

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Beverley Tickton

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Tickton

York

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Beverley Paull

How many possibilities are there?

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• 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

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• 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

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• 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

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• 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?

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• 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

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• 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.