Every County Town in Britain

[bobb]

Just a thought about a potential tour (that would probably take some time!) I might do one day. The rules are I have to visit every county town in every county in mainlnd GB. Also, administrative areas have to be passed through.

This has to be done in one hit. ie every mile must be cycled continuously. No going home, then getting a train and starting it up again.

What do you reckon is the most efficient way of doing this would be?

I'd start from Chelmsford (which is where I live) so that ticks one off before I even get started. But what should I do next? I could head south and knock off a few counties or just go straight north and pick them off up the east coast. But then I'd have to come back down and do a lot of wiggling around.

This may well have been done before, but a (brief) Google has been fruitless.

I reckon the collective wisdom of yacf could build a decent GPX route to do this.

So how would I tackle the area in which you live? Or indeed the entire country?

[Canardly]

Thats a big ask. I make it 39 (traditional) county towns in England alone.

[Cudzoziemiec]

It's an interesting project. You might need to first define your county towns. Good luck with it and be sure to post photos.

[Rod Marton]

Mathematically, it is a travelling salesman problem, and there is no way to find a globally optimum solution.

Before that you will have to define a county town. In England several counties have alternatives, and I think the situation is even more complicated in Scotland.

Beyond that, the only advice I can give is to start in Truro and finish in Thurso. Unless, of course, you want to do a closed loop and finish at your start point, in which case it is irrelevant. But a closed loop will be significantly longer.

[mattc]

Beyond that, the only advice I can give is to start in Truro and finish in Thurso. Unless, of course, you want to do a closed loop and finish at your start point, in which case it is irrelevant. But a closed loop will be significantly longer.

Is there a proof of that?

[psyclist]

There are 2 ways that I would approach this, and I would do both and see how they compare.

Firstly, having defined all the points to visit, I would use scheduling software to determine an efficient route for visiting all points (ie minimising distance). This would then need to be refined to route via nice cycling roads in the order suggested by the software.

Secondly, I would visually plot the points on a map, and work out the most logical entry and exit points for the extremes of the map, such as the south west corner, then work with the remaining points to determine what visually would appear to be an efficient route.

I suspect the former approach will yield the better result.

This does assume that by efficient you mean in terms of shortest distance.

[clarion]

This is the sort of pointless but interesting plan which appeals to me.  Hope you do get to realise it, bobbers!

[Canardly]

May be useful for initial planning

https://www.freemaptools.com/how-far-is-it-between.htm

[Oaky]

Beyond that, the only advice I can give is to start in Truro and finish in Thurso. Unless, of course, you want to do a closed loop and finish at your start point, in which case it is irrelevant. But a closed loop will be significantly longer.

Is there a proof of that?

Not sure about "significantly", but you can easily show that for any closed loop visiting all towns, there are many shorter, non-closed paths through the same towns.  (just take the closed loop through all towns and delete any link between two adjacent towns on the path:- voila - a shorter, non-closed path that still visits all the same towns).

[RichForrest]

Beyond that, the only advice I can give is to start in Truro and finish in Thurso. Unless, of course, you want to do a closed loop and finish at your start point, in which case it is irrelevant. But a closed loop will be significantly longer.

Is there a proof of that?

Starting in Truro and coming north would only mean you go through Cornwall and Devon once instead of having to retrace your journey back up country if started elsewhere.

[Ruthie]

What a superbly bonkers idea.

[Wowbagger]

There is a chess equivalent - the Knight's Tour.

https://en.wikipedia.org/wiki/Knight%27s_tour

It's possible to waste hours on this. Great idea, though, bobb!

[JennyB]

There are 2 ways that I would approach this, and I would do both and see how they compare.

Firstly, having defined all the points to visit, I would use scheduling software to determine an efficient route for visiting all points (ie minimising distance). This would then need to be refined to route via nice cycling roads in the order suggested by the software.

Secondly, I would visually plot the points on a map, and work out the most logical entry and exit points for the extremes of the map, such as the south west corner, then work with the remaining points to determine what visually would appear to be an efficient route.

I suspect the former approach will yield the better result.

This does assume that by efficient you mean in terms of shortest distance.

This is one of the classic 'intractable problems' in computer science, the 'travelling salesman' problem. if you were to check all possible paths at a million paths per second, it would take several billion years to find the shortest route between 25 points.¹

Fortunately there is a shorter way, devised by Shen Lin of Bell Telephone Labs:

Draw a random circular route, visiting all the towns. 
Pick three links you don't like the look of, eliminate them, and see if you can link the remaining sections into a shorter route.
Repeat until satisfied.

¹ This and Shen's solution is from a fascinating book Spatial Organization - The Geographer's View of the World  Abler Adams and Gould 1971

[Ham]

¹ This and Shen's solution is from a fascinating book Spatial Organization - The Geographer's View of the World  Abler Adams and Gould 1971

Ooo look - available as a pdf download https://www.e-education.psu.edu/geog571/sites/www.e-education.psu.edu.geog571/files/documents/Spatial%20Organization_The%20Geographer%27s%20View%20of%20the%20World_Abler%20Adams%20and%20Gould_1971_SCANNED%20COPY.pdf

[bikepacker]

There is a book by a guy with a similar idea only he wanted cycle to and climb to the highest point in each county. It is called Heights of Madness https://heightsofmadness.com/jonny-muir/

[Kim]

This is one of the classic 'intractable problems' in computer science, the 'travelling salesman' problem. if you were to check all possible paths at a million paths per second, it would take several billion years to find the shortest route between 25 points.¹

And remember that for a real world route, the graph encompasses every road and junction that might be used to route between two destinations, not just the straight-line distance between them...

[Tigerbiten]

Nice problem .......... 

I'd start with a big map, pins and some cotton.
Stick a pin in each county town.
This will give you a good visual of where each one is.
Then wrap a length of cotton between all the pins.
Measure the length and try a different order of pin.
It's a quick visual method of getting at least a first approximation of a route.
Plus you cannot miss a town by mistake.

If I was doing a closed loop .....
I'd probably start in the east where it's flatter, so I could cycle myself fitter before the hilly parts.
I'd also try to avoid the scottish highlands in midge season ..... 

[Wascally Weasel]

Nice idea Bobb, I like it.

At some point I'm going to do a tour of the whole of the UK coast. No idea when I'll have the spare time but I do fancy it.

[bobb]

Thanks for the replies 

Perhaps I shouldn't have used the word "Efficient" as many people (understandably) took that to mean the shortest distance. I'm not so bothered about that, rather the most logical way to get between the towns without doubling back - I want it to be a loop that anybody could do, no matter where you start from. Of course, the far South West (and other areas of the country) is going to cause problems, but if it's unavoidable, so be it.

I need to set some rules. I'm working on them 

Edit: I'd also rather take the scenic route (if available) rather than blasting down some horrible A road...

[Kim]

Perhaps I shouldn't have used the word "Efficient" as many people (understandably) took that to mean the shortest distance.

I don't think we did, except in the abstract mathematical sense.  It's perfectly normal for graph algorithms used in the real world to weight routes according to all sorts of factors, be it network bandwidth or prevalence of Silly Sustrans Gates.

Map-based heuristics are a good starting point, but as ever, a quality real-world route is going to involve some human input and hopefully local knowledge.

[Cudzoziemiec]

As you live in one county town, Chelmsford, it would be silly not to start there. From there I'd head to the next nearest one along what looked like a decent cycling route, and from there to the next one and so on. I'm sure there'd be lots of doubling back and it would take about a year and a day, but it would be rather fun. Mostly. Definitely more fun that not. Even if it's not efficient.

[Tigerbiten]

I need to set some rules. I'm working on them 

Silly rule .....
 
There a watershed that runs from the channel to the scottish border.
You only cross it once .........   
IE:- starting in the west -> up the west -> around scotland -> down the east -> cross the watershed -> finish any towns in the west.
That makes it a "nice" circular tour and not just a random zigzag ..... 

The odd crossing there and back may be allowed for "Efficiency" if a town very close to the wrong side of the watershed.
Or maybe not.

[mrcharly-YHT]

I think it should be a point of honour never to retrace your route at any time, even if that adds tons of miles.

[Cudzoziemiec]

You need a small ceremony to carry out in each county town. Not just a photo of you + bike in town, but something like a tandem ride with the mayor, leaving a YACF item (badge, sticker, whatever) on the county hall or presenting the leader of the town council with a petition for more bike parking/cycle routes/etc and threatening them with a sharpened chainring to the throat getting forumites to write until they enact it, etc etc.

[Canardly]

 A chair leg baton could be taken on the journey?