Traveling Salesman Problem Visualization 

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gm0Nc4wPJZI.html

hello

+1

and then like 62345 times because of music lol

Not just "optically", it's "optimally" pleasing too ; )

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gm0Nc4wPJZI.html

'Thus it's might invite' - that gave me cancer

I like science, so you are correct in saying it might invite more people into the field, because it worked for me.

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gm0Nc4wPJZI.html

Have a look if you like this video ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uUOd5dJTR7E.html

This seems like a good optimization for these kind of special cases - perhaps very similar to this: www.sciencedirect.com/science/article/abs/pii/0020019096001251?via%3Dihub

@@poprhythm Thanks, I'll have to read it ::}

Also, I researched local neighborhood search and big neighborhood search. I was also thinking about applying neural networks, but it was too difficult for me

+Oktay So, like....a lot?

Random Person That there is why combinatorics is hard - not because the algorithms and formulas are complex but because the resulting numbers are so large you can't store them in any naïve format.

Thomas, Well, if you took every particle in the universe (about 10^80), made a quadrillion duplicates, then duplicated all of your new particles and old particles a quadrillion times, and did it again, and again, and again, and again, and again, and again, you still wouldn't have even close to that number (you'd have 10^200). You wouldn't even be in the ballpark. But this doesn't even remotely compare to all the possible arrangements of every particle in the universe, which is absolutely monstrously large. If you duplicated every particle in the universe a quadrillion times every second until the universe died, you would not have reached a number of particles that was even close to the number of possible arrangements of every particle in our universe. Every arrangement is something like 10^(10^80), that is 10 to the power of 1 followed by 10^80 zeroes. The number you'd get duplicating particles a quadrillion times per second to the end of the universe is a mere 10^(10^20) if you assume the universe will live for 100 trillion years.

Can't explain/calculate something with 100% accuracy? Goddidit

Thta's why we have to find a new algorthim that shortens the avaible routes

Thank you!

+Fatbackwards I agree, it's really interesting to think about optimizations for large problem sizes such as this! I wrote the music using software synthesizers and lots of arpeggiators :) Here is a link to the soundcloud of the song soundcloud.com/poprhythm/clearly-opaque

Have a look if you like this video ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uUOd5dJTR7E.html

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gm0Nc4wPJZI.html

+Chaoswarrior3489 Thank you very much! I've enabled downloads for the song here soundcloud.com/poprhythm/clearly-opaque

+Sanyam Jain Hey thanks! Here's a blog article on how I made it popcyclical.com/2013/08/19/TravelingSalesmanProblemVisualization.aspx

I think you're right! I had chosen the top 8 locations from the population data I had found. The distances were calculated naively based on their lat/long coordinates. Either the calculations for Chicago->New York and Chicago->Philadelphia somehow put them opposite closeness, or I fudged it somehow . Not sure now, but Philadelphia is definitely a little closer!

Curvature of the earth plays with flat maps a bit.

I would guess the points are closer in reality, but the flat projection of the US makes it appear different.

It would be easier if the edges show their weights/distances.

Certainly! This will work fine for a small number of cities to test. However, as the number of cities grows, the number of possible solutions increases with a factorial amount - the time needed to check all of these grows from hours to days to years. There are optimizations (for instance, branch and bound - don't even consider a set of solutions unlikely to yield better result), but even then, the possible considered solutions can be quite large. Read more here: en.wikipedia.org/wiki/Travelling_salesman_problem#Exact_algorithms

Yes! If you have prior knowledge about likely patterns in your data then you can potentially reduce the problem size by many factors. This visualization only demonstrates for the generic case. If this problem were being addressed for real, a likely optimization would be to cluster all the metropolitan areas together and solve those discretely, then add them back into the complete solution by removing the "interior" nodes. These problems are fun to think about - especially how additional/alternate optimizations might make make it faster!

Why Pi though?

+Dave Ped There exist some toolkits for tinkering with optimization algorithms such as this. I'm not very familiar with them - this one came up in a google search, and it contains a TSP function optalgtoolkit.sourceforge.net/

+poprhythm Thank you. I need a nerd to check out my idea. I'm not nerd enough to do this. I just come up with ideas. I understand most people's ideas are not worth pursuing so if you want me to describe it in detail first, no obligations, fine I can do that. Thanks.

Hi! You might be interested in reading this more detailed look into the 2-opt swap mechanism : en.wikipedia.org/wiki/2-opt . You've hinted at the underlying problem - how do you know when to stop? For non-trivial optimization problems, you're often faced with accepting a "very good" solution as opposed to the optimal - simply because the search space for larger problems becomes astronomically large. Like hundreds of years on modern hardware large. So using a heuristic-based search to find good solutions in a reasonable amount of time is currently our best bet.

...which is why sometimes your car navigator will take a different route between the same adresses.

R is a great tool, but no, this was made in C#. Here's an article about creating it: popcyclical.com/2013/08/19/TravelingSalesmanProblemVisualization.aspx

Good question. Each set of vertices is a subset of the next - they're US cities sorted by population in descending order. I used the different numbers of these cities to illustrate the strengths (and weaknesses) of the techniques. For instance, it'd be harder to visually see the local minimum demonstrated in the local search section with the 300 vertices used in the simulated annealing section. Likewise, the apparent chaos resolving to a solution in simulated annealing wouldn't be quite as captivating with the 30 vertices used in local search.

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-gm0Nc4wPJZI.html

Maybe it's shorter, I could run it according to my algorithm

Your car GPS does a small bit of this every time you put in an address to go to. It will not find the BEST solution but one that is as good at is can find in the time before you lose patience and reboot it thinking it's crashed.

They're both distance-on-a-graph problems, but not quite the same! - here's a short discussion: stackoverflow.com/a/3838791/99492

Thank you! I've enabled the Community Contributions for closed captioning, I think. Let me know if you have any problem with it.

I've just submitted the subtitles. Thanks for enabling Community Contributions. It's a great video.