Lec-24 Traveling Salesman Problem(TSP)

Lecture series on Advanced Operations Research by Prof. G.Srinivasan, Department of Management Studies, IIT Madras. For more details on NPTEL visit nptel.iitm.ac.in

[@guicarboneti]

I spent hours looking for some explanation for the reason of choosing the shortest subtours to eliminate and then comes this old video and this great professor explains everything! Thank you very much!

[@paramshah1349]

What is the explanation that you found, can you explain pls?

[@jagdishtilokani2531]

He is a professor from department of management studies and still explained the algorithm far better than most of the cse professors.

[@maker72460]

Management people use optimization methods a lot!

[@zhuoyunjin4476]

Best explanation I found online. Thanks, Professor!

[@stevenson720]

Yep. This guys great.

[@noorulsaba9179]

Totally agree.

[@yashthedreamer]

Best and most lucid lecture on TSP ... something I have been searching for 3 days. Thank you very much !

[@sumithaswar490]

Awesomeness level over 9000. You Sir are too good, explanation much better than the one done by my Prof. at Cal. State University

[@yshasft]

The entire series of OR is simply fabulous. Easily understandable even by a layman. Thank you so much sir.

[@davidhand8337]

Great video, especially from 30:00 onward. Went through every step, with no skipping. Perfect for learning this algorithm.

[@Joshmaradomx]

Well done Sir! I have on 2 weeks a Freight Logistics Exam and this vid helped me so much on my preparation, keep going with this magnificent job!! Greets from the Technical University of Munich.

[@mosyemessy]

I really really like Prof. G.Srinivasan. He enunciates well, provides good examples and he is very accurate. He is also very much talented in teaching. Thanks.

[@amiththomas3884]

Loving this tutorial :) Came here just to learn the algorithm. Ended up really interested in the whole concept.

[@kelvinkoiser]

12 year video sorting my issues today, thank you Prof. I have been struggling to understand these theorems for the last 1 week.

[@SanjayKonaecar]

Glad to understand now in 2024 from a video which was posted 14 years ago which such proper explanation. Thank you sir from Germany 🙏🙏🙏

[@مصطفىالربيعي-ت8غ]

Most of the lectures on this problem were just talking without real results but this one is totaly different thank you for ur offerts

[@Dave-lr2wo]

I know next to nothing about math and found this perfectly clear. Wish I had teachers like you when I was in school -- then I probably would know more than nothing about math now.

[@clloydmathison995]

This guy is a good instructor...he makes a complex mathematical problem seems easy.

[@productionnet2242]

The Ui - Uj constraint corresponds to the formulation proposed by Tucker and Miller in 1960. It is defined for i,j >=2....n, and ij. A small mistake, but this guy is awesome.

[@ROHITGR72]

I never took a book to study or. Your lectures are more than enough to us....... Thank you sir.....

[@janicklasralphjames9179]

Hey, he is just trying to find the best paths, he goes in order because it will be easier to work with the table, u will get the same solution if u go 1 to 5 and choose 5 to 2, then 2 to 4 ...... overall u just find the paths the best solution should contain in any order. Hope this answered ur question. Very good video, good job sir.

[@Mbc43m276]

IIT has the best minds in india. very good lecture

[@lohitchinthala7886]

30:40 if any one looking for diff. branch and bound methods for TSP

[@MaxammedBile]

thank you for the effort you put on this video. it really is gonna help me alot to perform well in the upcoming exams. I liked the way you clarified the algorithm and you made it look easy.

[@zaacymay]

Excellent summary of the TSP and B&B algorithm. Extremely helpful.

[@divyanshujhawar3671]

26:40 How come professor wrote "U5 - U4 + 5

[@rohitkalra9981]

yeah, same ques

[@noorulsaba9179]

Really good explanation. I am really impressed by his lecture style, very simple and easy to understand.

[@datdang5042]

Do you know how to work it out in excel ?

[@vijeta268]

@24:34 can anyone explain what is 'u_i/j' exactly, in the modified constraint?

[@brucenguyen5264]

Thank you sir, from Australia

[@elishaayoo3689]

That's my Don! Enjoying much your lectures.

[@siddhartharao1484]

Too Good!! Superbly taught! Thank you sOOO much sir!

[@keerthanaashok6884]

Really an excellent lecture Sir. thank you so much . the lecture helped me a lot.

[@crazypanther1]

Just one word sir ... Brilliant!!!

[@md.sabbirahmed9029]

Obviously best lecture. Explanation is very clear. Thank you sir.

[@PremRajasekaran]

salute you Sir, you are far far far far better than English profs.

[@TheFusEE]

Absolutely BRILLIANT and GREAT!! So well explained and described!

[@galluer]

@Sampath Krishnan yes you can do that. But you would have to solve all other branches for solution/elimination anyways. Essentially, you fix one path and find the shortest path based on the remainder matrix. In this respect, the node you start off for evaluation of the remainder matrix is your choice.

[@st1ry1ntz]

I'd never be able to graduate without his help. Thanks :D!

[@aayushkapadia4491]

Best Explanation of TSP problem.

[@romzen]

Thank you, Professor. This helped me a lot in my B.Sc. thesis!

[@geraldomouramoura2781]

romzen 🐬

[@shikhar2811]

At 47:00 won't we be also cancelling out value for 3-->1 (8) since 1-->3 is already travelled? If yes then this node will give value 34 and not 33.

[@santanubanerjee5479]

Correct!!

[@Lostpanda123]

The greatest techer of all time!

[@TheViniArya]

@chandrataken No, because we have to return to the initial node at the end. So if we start from node1, we have to come back to the same node and hence, 3-1 is not considered as a subtour. Its basically completing the cycle. I hope u got it :)

[@johnward9255]

What an excellent explanation. Thank you so much!!!

[@ArunDevKaushik]

46:30 why it is 33. X13 has assigned than why he consider X31? It must be 34.

[@shikhar2811]

You are right i also had the same doubt.

[@milenavuk]

Thank you so much for this lecture Professor. Really helpful.

[@olgapawlowicz6232]

And the another question is about 49:00. Why there are considered only two edges: 3 - 2 and 3 - 5, whereas 3-4 does not create a subtour? There are made edges: 1-3 and 2-4 Adding edge 3-2 leads to 1-3-2-4, which is ok, adding edge 3-5 leads to 1-3-5, 2-4 which is also ok, adding edge 3-4 leads to 1-3-4-2

[@Devina0514]

Dear Prof., I show my respect to you!

[@happinin]

this guy is BETTER than the english lecturer i have at my university in the algorithms subject and he explains it so damn well. professor you are brilliant and anyone who doesnt understand you is fucking illiterate. this is coming from an aussie!

[@kakorckaact07]

Yay! Thank you. This is very helpful since I'm not learning anything from my Algorithm prof...

[@lucellenaidoo7194]

this lecture helped me a lot in my research of TSP

[@datdang5042]

Do you know how to work it out in excel ?

[@kagisomokena7140]

Thank you very much sir, you have saved me a lot of time in explaining the TSP

[@raziebe]

According to the wiki of TSP en.wikipedia.org/wiki/Travelling_salesman_problem . In the subtours elimination the i starts from 2. The professor wrote it correectly so now I am able to understand this constraints.

[@VishnuBJanga]

Thank you so much Sir! You're teaching methodology is awesome ! Regards.

[@lechiman01]

thankyou keep up the good work sure it is helping loads of people

[@dhanashreenemade3009]

This video was very helpful... thank you...!

[@jack76781]

@bbbarhas these lectures were given in Indian universities we're lucky they lecture in english

[@timpanitimptim]

At 26:08, what are these u1 and u2 and u3 and so forth defined as? 28:26, he says its always possible to find u1 and u5 to make that inequality satisfied.

[@KiloWhiskay]

How come around 40:00 we go from X15 to X23? Doesn't that imply that the path is 1-5-2-3? Shouldn't we be checking X53 instead?

[@henrikl218]

Kenneth Worden, this method does not directly analyze the steps taken in a given order. instead it analyzes the options possible when one arc between two nodes has already been used. so each new section of branches represents a new node starting from the lowest number and increasing. so when for example the arc between node 1 and 5 is chosen it doesnt mean that we are currently in node 5, its simply means that arc x15 is the arc from node 1 with the lowest cost, therefore we'll choose this one and analyze what other options are left now starting from node 2.

[@KiloWhiskay]

Thank you

[@johnyepthomi892]

awesome.. keep it going.learning a lot.

[@stevenson720]

Thank you from Ireland

[@samkris6089]

Can someone explain this - after branching off for example from X15 (with cost 31), how is he forming branches to X21, X23, X24? Since X15 is already fixed, shouldn't the next path only be from point 5 which is the destination reached? So the child branches from X15 should only be X52, X53, X54? Similar for X32 and others?

[@chandrataken]

I think when you go through this, you are missing some of the subtour eliminations. For example when 1 - 3 is set, and then 2 - 4 is set, you include 3 -1 in the row minimum summation. But wouldn't 1 - 3, then 3 - 1 be a subtour??

[@pushkar------4920]

Hiii

[@Andr3wco7]

Lec-24 Traveling Salesman Problem(TSP)

[@daizybhadresha5167]

Perfecttttt for any learner!!!!!!

[@alexantosh]

Daizy Bhadresha hi, what does U stand for in the Ui -Uj + nXij

[@mittijoshi]

best to learn TSP ,,,thanX for posting this video..

[@troff15]

@jack76781 FYI, this lecture was given in one of the IITs, and all lectures in all the IITs are given in English.

[@SM-fb4qb]

26:50 how does the second constraint exist? because i=1 to n-1 i.e 1 to 4 ; so u5 should not be possible.... someone clarify?

[@ChitStarkid94]

Thank you, Professor. Very helpful!

[@jacobli2676]

Great tutorial for learners, thanks

[@kousarmuskan4979]

Appreciated Sir .. Thank You . great explanation.

[@WeslleyCXS]

"i" is the vertical position in a table and "j" is the horizontal position

[@abhaymathur5342]

in a 5 city problem, there are 4 possible types of sub-tours(st) : loop of 4 cities, 3 cities 2 cities & 1 city. a problem is only completed if all of the cities are visited. so if there is a ST of 4 cities there has to be an ST of 1 city. so by eliminating 1 city ST, the 4-city ST is automatically eliminated. similarly for 3 city ST there has to be 2 single city ST or one 2-city ST.......hence for 5 city prob. eliminating 1 & 2 city ST can ensure elimination of all STs

[@datdang5042]

Do you know how to work it out in excel ?

[@DOMINICTSONGO]

This is really interesting.

[@blackmajor93]

25:35 ..why it's not defined j=1 X31? if there is the connection between 3 and 1

[@ChiragRajputS]

They way it's done, it's hard to implement programmatically

[@himanshujhamb]

Why we need to eliminate subtours ? In the problem if we are starting from some vertex then we have to reach to that vertex so why we need to eliminate subtours ?

[@yasminebenlefki2880]

Because you have to visit all the cities once and only once

[@olgapawlowicz6232]

@TheViniArya- it does not make sens. When we already have 1-3 and we added tour 3 - 1 we create subtour, because every vertex have only one enterance and one exit, It means the tpur 1-3-1 is closed and does not have connection to other vertex. I can't get this. Once we consider about subtour once not.

[@ankurmishra5463]

Thank you sir this video is very help full to me

[@shubhamthapliyal988]

Brilliant teacher

[@ahbarahad3203]

great recording quality i can almost see the pixels

[@CamiloSanchez1979]

why are all this videos about algorithms and stuff like that all from India?

[@tppt3987]

Wdym??

[@islamamaize6298]

@@tppt3987 why are you so butthurt abt it?

[@stevenson720]

Because the indians are big into stem and realized how useful, especially in a poor country teaching this way is. No university campus required.

[@AkshayKumar-wu8fc]

@@stevenson720 Do you know what the population of our students in colleges or school may be double or triple of your total population.

[@AkshayKumar-wu8fc]

@@stevenson720 there were over 2.6 million primary school teachers in India. Then you think about it how many students are in India.

[@geniusvincy]

helped in ca final operations research...thank you :)

[@sagnik1991]

true. am using this video as well. same is not available in sanjay agarwals video.

[@adg764]

whoa !! awesome !! great material !

[@TheGrizzFul]

I think since the travel costs do not depend on the direction we take around the tour, we should divide the number of feasible solutions by 2 to get (n-1)!/2. ?

[@parthaghosh975]

Awesome explanation, too good!!

[@neferiusnexus]

Looking at this video enables me to properly appreciate just how inefficient our methods of communication are when it comes to abstract concepts. Using basic verbal, written and visual encryptions, the lecturer is barely able to explain a single concept within the timeframe of one hour, allthewhile retracing and reiterating his arguments in order to increase resolution. I'm afraid this method of propagating knowledge is completely inadequate for today's high volume of available information.

[@chadboy5385]

Branch And Bound Algo at 29:30

[@ANAYKhairatkar]

salute sir...u are the best

[@programm.r]

Very helpful. Thank you!

[@alexantosh]

int the inequality: Ui -Uj + nXij

[@nickyouyang3723]

alexantosh it's an artificial variable

[@9japrince642]

Lovely lecture. What is the name of the branch and bound algorithm used in this lecture?

[@vitoriaheliane7238]

Awesome!!! Thanks a lot!!!

[@Psycheoflame]

Thank you Professor.

[@chinthaladivyasree4816]

Tqq sir I like u r teaching

[@isaacpemberthy507]

Regards, great explanation, thank you for that. But I have two questions, first the significance of the variable U, and second as I can include inequality constraint that a program that handles linear models, for example Excel Solver. Thanks, again

[@OscarZhang1990]

Can someone tell me, near 25:00 what is Ui and Uj ？

[@yinengwu8927]

very helpful, thanks!

[@gkthakral]

thannks a lot sir..!! that was reaalllyy helpful for me :) :)

[@chandrataken]

@TheViniArya But if 1-3 is already set - then wouldn't 3-1 be a subtour?? Amy

[@bobbeeez]

excellent.......................!!

[@lukekreung]

Great lecture, but is it not true that the number of Hamiltonian cycles in a complete graph is (1/2)(n-1)! because you can reverse the order of the cycles?

[@anjalian6314]

How can we find the value of u1,u2 in subtour elimination