Traveling Salesman Problem Visualization

Visually compares Greedy, Local Search, and Simulated Annealing strategies for addressing the Traveling Salesman problem.
Thanks to the Discrete Optimization course on Coursera by Pascal Van Hentenryck for teaching me about this! www.coursera.org/learn/discre...
Read more in this blog post: popcyclical.com/2013/08/19/Tra...
Update:
PBS's NOVA features this animation in Einstein's Quantum Riddle. Watch at 34:35 www.pbs.org/wgbh/nova/video/e...
Sources:
City coordinates: www.geonames.org/export/
US Map: commons.wikimedia.org/wiki/Fil...
Music: / clearly-opaque

[@patanypang]

the background music make it looks extra cool

[@ComputerCurry]

Name?

[@Chris_t0]

Love how the music speeds up when the code is in action, it actually makes it enjoyable and not a bunch of boring moving lines.

[@Cscuile]

I always come back to this video due to the sheer amount of beauty it contains.

[@ghaith81981]

kzbin.info/www/bejne/nZ6Tf5ZqrLV9kKs

[@Kurchack]

I first watched it to understand methods of solving TSP. Then I watched it 4 more times because it's so optically pleasing.

[@ifudiscusswithmeurprobably7273]

+1

[@andrejpaluch648]

and then like 62345 times because of music lol

[@arshpreetsingh239]

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

[@ghaith81981]

kzbin.info/www/bejne/nZ6Tf5ZqrLV9kKs

[@sindorei]

I watched this 2 or 3 years ago. Now, I am here again. Great video! Visualization and your choice of music make me watch this over and over again.

[@astarothgr]

This is the absolute best TL;DW (too long, didn't watch) video for anybody looking for a quick intro into what is local search. Great work!

[@insaneviruss]

Finally a video that explains the core logic so easily, thanks a tonn!

[@Cscuile]

This is the most beautiful algorithm video I have seen on youtube.

[@philipwells7149]

Oh this is so beautiful. Thanks for making this video!

[@noxiouspro]

This isn't just a good visualization but also a good production video. Thus it's might invite more audience into the field.

[@bodenseeboys]

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

[@ziq1450]

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

[@ghaith81981]

kzbin.info/www/bejne/nZ6Tf5ZqrLV9kKs

[@nabilaabrak5738]

What an impressive approach of the problem. It's clear, and the video is so cool.

[@Playncooler]

Man, travelling salesmen are smarter nowadays...

[@decepticon1SB]

best visualization I've seen on TSP

[@ChairmanMo]

If you ever played Galactic Civilizations 3, you have to deal with this problem too when you start to set up your Hypergate networks. Thanks for the suggestions about moving the edges. That will help!

[@yogi799]

What a magnificent way of explaining these concepts, thank you!

[@_motho_]

the drums are like routes connecting and colliding with eachother. i like it

[@SirCutRy]

Awesome visualization!

[@JonDotExe]

Love it! These are the types of visualizations we need to get people into mathematics. So much easier to understand than a dude at a white board

[@freshdesignbe-to-ce3070]

Good visualization of the salesman problem. Thanks!

[@wahyuagungsugimartanto3340]

I loved the music, it just plain awesome

[@billpetrak]

I can't believe my ears! Is this post rock music in an algorithm video I hear? Had to watch multiple times. It made my day! Now if only every piece of information was accessible through a video like this. :/

[@ghaith81981]

Have a look if you like this video kzbin.info/www/bejne/q4aylWiaf7mFbac

[@therkoth]

Cool! Now do one on vertex cover focused on internet infrastructure! ;) I remember having a blast coding heuristics to find suboptimal solutions in the uni. Really enjoyed the video.

[@LEARNWITHPANDA]

very cool video on travelling salesman problem. Interesting visualization.

[@emperorlelouch5696]

Wow, it's so intense and difficult that there had to be epic music to accompany it

[@zhanglg921]

Awesome. Thanks for sharing the video.

[@yesamd3169]

love the music

[@fanz4088]

Thanks! Really appreciate your work! May I cite your work in my presentation? Please let me know how can I properly cite it!

[@notabailabe97]

Excelent video on an famous algorithm.

[@arctan-k]

One of the sub problems that i had in my dimploma project duting my bacholer's involed this problem. I solved it using two methods: integer programming and genetic algorithms. It was so fun and exciting. I'm so eager to learn more math during my master's.

[@arctan-k]

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

[@synony6]

So good. Very impressed

[@chasyen5945]

so beautiful. thank you

[@BubbaYoga]

Very well done!

[@yilmazaliyy]

great job, thanks for sharing

[@hartake6667]

This woke me up - literally :D

[@Chaosfury50]

I thought this would be another foreign indian common chintzy explanation but the visualization actually really hit home for me and I immediately left my life, my marriage, even my chemo treatments and now reside in a corner of the Atlantic ocean in a perfectly cubed and sealed floating room, bobbing with the waves. People are free to continue visiting me with well wishes and to see all the progress I've made and get a copy of the book I have written until now (I do enjoy the challenge of having to completely rewrite it back to get to my spot and continue).

[@WhiteDragon103]

An idea I had for the travelling salesman problem (when the points are in some euclidean space): 1) Enclose the smallest possible convex hull around all of the points. 2) For each point not on the edge of the current hull, pick the one that is closest to the hull (or, that would increase the length of the path the least if inserted into the closest hull edge). 3) Bend the hull to include that point. The point would be inserted between the two points already in the hull forming the edge that it is closest to. 4) Go to step 2 until there are no points left not part of the hull. For added precision, you could enumerate through all of the first N possible vertex insertions and use the combination of insertions that results in the shortest path. The above algorithm assumes N == 1. I just tried doing this manually in MS Paint and it seems to work pretty well. I got almost the same result you did at 1:17 (though I did eyeball it).

[@poprhythm]

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

[@WhiteDragon103]

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

[@likeyou3317]

Love the visualization

[@MRlinkinpark12]

I love it man!

[@user-is1jt8jt7f]

I agree with the others...I'm a techie and route planning solver...this helps me when explaining to customers

[@toussaintbamporiki8850]

This was very nice. Thanks

[@MiguelBacaoco]

great music!

[@DaRKtWiSTeR1000]

This video is very fascinating. I appreciate it because on a real simple way, i.e. visualization, it provides the core of the TSP. But it contains a little mistake though. If the quantity of possible routes is calculated with (n-1)! with n:= number of cities then for 304 the solution should be about 8,43*10^(621) ____________________________________________________________ "Wenn Null besonders groß ist, ist es beinahe so groß wie ein bisschen Eins. Tadeln ist leicht, deshalb tun es so viele; mit Verstand loben ist schwer, darum versuchen es so wenige." (Anselm Feuerbach)

[@Randomperson-by1eg]

2.3*10^624 possibility? That is 10^544 times more than atoms in observable universe

[@thomaselder4076]

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

[@dorukayhanwastaken]

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.

[@connorskudlarek8598]

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.

[@MrAntiKnowledge]

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

[@apostolismoschopoulos1876]

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

[@vector8934]

In what computer science course do we learn about the Traveling Salesman Problem, the Post Correspondence Problem, etc..?

[@SURYATEJA96]

how were you able to make the simulation? can you tell us what software/application you have used for the same?

[@taFBackwards]

Hey there, this is a very interesting algorythm; I just would like to ask what background music are you using for this video?

[@poprhythm]

+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

[@mrkinetic]

Would it be more accurate to use a brute force algorithm? Iterate over each possible route, and throw away the previous route if the the current one is shorter?

[@poprhythm]

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

[@Chaoswarrior3489]

As a CS nerd, I love the visualisation. Any way I can purchase a copy of the song?

[@poprhythm]

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

[@hyperrealhank]

fantastic!

[@linowmik]

very nice video

[@weichenghe]

It helps a lot, thanks

[@alan2here]

More visualising algorithms videos please :) How about 2D sorts, these are on a 2D grid and the numbers must decrease downwards as well as rightwards.

[@ghaith81981]

kzbin.info/www/bejne/nZ6Tf5ZqrLV9kKs

[@ThiNguyen-gd9ny]

hello... how to write programs using HEAPSORT to solve Travelling Salesman Problem - TSP on programming language ... and I need code :( im form Viet Nam...thanks

[@rajenderkumar5351]

its awesome

[@poprhythm]

Thank you!

[@reymicroc]

It always end up choosing the outline made by the points, why search then?

[@Nidhichirania02]

How did you get the visual representation?

[@dillonl6324]

What if you split the area into quadrants and then connected them? You could also use a rotating axis that finds the 4 most optimal quadrants and then it syncs them. This 2-opt swap just ends up making a giant trace around the outside of the area; no more clever than connect the dots.

[@poprhythm]

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!

[@deeplearningpartnership]

Fantastic.

[@ghaith81981]

Have a look if you like this video kzbin.info/www/bejne/q4aylWiaf7mFbac

[@maxniebs2174]

I love the little 7!

[@weeva6390]

I Luv the channel name

[@willjadsonevania9787]

teacher I developed a heuristic and would like to share it. My heuristic uses topology and concentric circles. What do you think?.

[@sanyamjain7229]

Hey. What softwares did it take to build such kind of beautiful simulation ?

[@poprhythm]

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

[@adnanbehrem9651]

More videos pls

[@gredangeo]

The general consensus I'm getting is, travel in a circle that makes your last point nearest to your starting point, and don't cross lines.

[@changlife7581]

Thats really cool!!!!

[@SantiagoGonzalez-wy4vx]

So cool!

[@ahmidahmid9303]

this video is motivating

[@vibe_wit_y]

amazing

[@Blacksoul444]

0:16, greedy-algo is taking the next closest point? but as he connects the first 8 points, the 7th is more far away from the 6th than the 8th from the 6th, isn't it? :D Aynway, really cool video!

[@poprhythm]

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!

[@Centauri902]

Curvature of the earth plays with flat maps a bit.

[@Twas-RightHere]

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

[@No3xx]

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

[@zaidalmahmoud4272]

Awesome work! Thank you.

[@user-sb5mz8gk9f]

Which programme used??

[@osamarizwan1635]

How did you make this video

[@doomiesa2830]

Could genetic algorithms be implemented? I would like to see that.

[@ghaith81981]

kzbin.info/www/bejne/nZ6Tf5ZqrLV9kKs

[@yongamer]

What if there is several salesmen?

[@TSPxEclipse]

This is fine and all, but what if the name of the salesman is Crowley?

[@user-xr6lu8fb1e]

How difficult is it to draw a circle?

[@MrDavePed]

I have an idea for finding the optimal route consistently, a new approach, a new algorithm. How would I get it to work like your video? I'm not a programmer. Is there software to do this? If not would you be willing to consider writing it if I describe it to you? Thank you. ..

[@poprhythm]

+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/

[@MrDavePed]

+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.

[@samuelwallace-dr.universal]

I'm thinking a sequence of pi should be rendered around the travel area. Then the program extrapolates the rout to the perimeter of the travel area. Once the outline is created, the remaining locations could run greedy sequence. The key is starting with a circle and working from there, wish I could write code or I'd try it haha.

[@alkestos]

Why Pi though?

[@thetruereality2]

Why do you choose different vertices in different algorithms?

[@poprhythm]

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.

[@markjoe664]

Ill use it to visit US thank you

[@shivakumarcd]

this music while solving Rubik's cube would be more thrilling ... ;-)

[@SGuy157]

Why is this so lit

[@StephenCurry-ff4zc]

Practically speaking, what is this information used for in practical life

[@grossteilfahrer]

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.

[@alexanderstrada2933]

Doesn't the order of the swapping affect the outcome? You say to select edges at random for the swap, but I'm assuming you're actually comparing every edge to every other edge once, right? (Otherwise, how do you know when to stop?) So, if you go through the whole thing once, wouldn't going through it again produce further changes? As other parts of the route switch around, the changed distance between each edge also varies, no?

[@poprhythm]

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.

[@grossteilfahrer]

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

[@dsc5085]

Simulated annealing seems like it would make a good approximation algorithm

[@lenlen8099]

Is this a minimum spanning tree problem?

[@poprhythm]

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

[@subratapaul061325]

awesome

[@georgeraafat1329]

Guys, I think I found the solution to reduce the time as much as possible. But what can I do with the solution?

[@lyan2759]

uhm... isn't it (n-1)!/2 ?

[@rajenderkumar5351]

thanx

[@amruthaloveusweetheartamma1653]

Can I get the source code

[@amruthaloveusweetheartamma1653]

Please sent the source code to this email. [e-mail]

[@florianreichelt]

cool!:)

[@lenlen8099]

I have a feeling you need to make a shape with the smallest area

[@climbercarmich]

What software did you make this in? Looks like R?

[@poprhythm]

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

[@sciencestruck9698]

nice

[@WondrousSky]

neato!😄

[@OliverJoshuaJacob]

this was flabbergasting.

[@alperkalamanoglu4660]

lol I can literally just watch this for the music. Mmy favourite part starts at 1:43, watched for 4 times.

[@quaxk]

please, next time, make the background music louder, I feel I could still discern some notes through the distortion, also choose it more randomly, I feel it wasn't a 100% inappropriate

[@bhavanasrinivasravipati1996]

can you please share the code

[@poprhythm]

My code isn't in a state that'd be appropriate to share - however, here are some of my notes: popcyclical.com/2013/08/19/TravelingSalesmanProblemVisualization.aspx Also, here's some java code implementing many of the same ideas: www.theprojectspot.com/tutorial-post/simulated-annealing-algorithm-for-beginners/6 And another: toddwschneider.com/posts/traveling-salesman-with-simulated-annealing-r-and-shiny/

[@bhavanasrinivasravipati1996]

@@poprhythm thankuuuuu