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
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!
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.
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.
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.
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.
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.
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.
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.
@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.
@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 :)
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
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!
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?
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.
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??
Thank you so much for this! You are so much better than my professor at NU who doesn't give a fuck about people who fall behind. Basically, the class asked me go fuck myself, but with your material and all the great wonders of open source, I will jump back. Thanks for giving me the help to get back in the game. Yeah, and I agree with st1ry1ntz...I will be graduating now !!! Hahaa~
@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.
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
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?
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
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. ?
I have the same doubt. And I still can't figure out why he chose 2. Maybe because it's an arbitrary choice or maybe because 2 is the next number after 1. Still no concrete reason though.
He is a professor from department of management studies and still explained the algorithm far better than most of the cse professors.
Management people use optimization methods a lot!
Best explanation I found online. Thanks, Professor!
Yep. This guys great.
Totally agree.
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!
What is the explanation that you found, can you explain pls?
Awesomeness level over 9000. You Sir are too good, explanation much better than the one done by my Prof. at Cal. State University
Best and most lucid lecture on TSP ... something I have been
searching for 3 days.
Thank you very much !
Loving this tutorial :)
Came here just to learn the algorithm. Ended up really interested in the whole concept.
The entire series of OR is simply fabulous. Easily understandable even by a layman. Thank you so much sir.
Glad to understand now in 2024 from a video which was posted 14 years ago which such proper explanation. Thank you sir from Germany 🙏🙏🙏
Great video, especially from 30:00 onward. Went through every step, with no skipping. Perfect for learning this algorithm.
Most of the lectures on this problem were just talking without real results but this one is totaly different thank you for ur offerts
12 year video sorting my issues today, thank you Prof. I have been struggling to understand these theorems for the last 1 week.
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.
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.
This guy is a good instructor...he makes a complex mathematical problem seems easy.
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.
Thank you sir,
from Australia
IIT has the best minds in india. very good lecture
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.
Really an excellent lecture Sir.
thank you so much . the lecture helped me a lot.
Too Good!! Superbly taught! Thank you sOOO much sir!
30:40 if any one looking for diff. branch and bound methods for TSP
I never took a book to study or.
Your lectures are more than enough to us.......
Thank you sir.....
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.
Excellent summary of the TSP and B&B algorithm. Extremely helpful.
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.
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.
Obviously best lecture. Explanation is very clear. Thank you sir.
That's my Don! Enjoying much your lectures.
@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.
Thank you from Ireland
Absolutely BRILLIANT and GREAT!! So well explained and described!
26:40 How come professor wrote "U5 - U4 + 5
yeah, same ques
Really good explanation. I am really impressed by his lecture style, very simple and easy to understand.
Do you know how to work it out in excel ?
Just one word sir ... Brilliant!!!
@24:34 can anyone explain what is 'u_i/j' exactly, in the modified constraint?
@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 :)
What an excellent explanation. Thank you so much!!!
salute you Sir, you are far far far far better than English profs.
The greatest techer of all time!
Best Explanation of TSP problem.
This video was very helpful... thank you...!
Articulate to the max. Straight G of the teaching world.
Thank you so much for this lecture Professor. Really helpful.
Thank you very much sir, you have saved me a lot of time in explaining the TSP
Thank you, Professor. This helped me a lot in my B.Sc. thesis!
romzen 🐬
Dear Prof., I show my respect to you!
Yay! Thank you. This is very helpful since I'm not learning anything from my Algorithm prof...
I'd never be able to graduate without his help. Thanks :D!
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
Thank you so much Sir! You're teaching methodology is awesome !
Regards.
@bbbarhas these lectures were given in Indian universities we're lucky they lecture in english
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!
46:30 why it is 33. X13 has assigned than why he consider X31? It must be 34.
You are right i also had the same doubt.
this lecture helped me a lot in my research of TSP
Do you know how to work it out in excel ?
thankyou keep up the good work sure it is helping loads of people
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?
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.
Perfecttttt for any learner!!!!!!
Daizy Bhadresha hi, what does U stand for in the Ui -Uj + nXij
Brilliant teacher
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??
Hiii
best to learn TSP ,,,thanX for posting this video..
awesome.. keep it going.learning a lot.
Appreciated Sir .. Thank You . great explanation.
Thank you, Professor. Very helpful!
Thank you sir this video is very help full to me
Thank you so much for this! You are so much better than my professor at NU who doesn't give a fuck about people who fall behind. Basically, the class asked me go fuck myself, but with your material and all the great wonders of open source, I will jump back. Thanks for giving me the help to get back in the game. Yeah, and I agree with st1ry1ntz...I will be graduating now !!! Hahaa~
They way it's done, it's hard to implement programmatically
salute sir...u are the best
Great tutorial for learners, thanks
Awesome!!! Thanks a lot!!!
whoa !! awesome !! great material !
Awesome explanation, too good!!
This is really interesting.
int the inequality: Ui -Uj + nXij
alexantosh it's an artificial variable
@jack76781 FYI, this lecture was given in one of the IITs, and all lectures in all the IITs are given in English.
"i" is the vertical position in a table and "j" is the horizontal position
Thank you Professor.
Very helpful. Thank you!
@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.
helped in ca final operations research...thank you :)
true. am using this video as well. same is not available in sanjay agarwals video.
hats off sir...u are damn brilliant
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
Do you know how to work it out in excel ?
Tqq sir I like u r teaching
thannks a lot sir..!! that was reaalllyy helpful for me :) :)
You are great!!!
excellent.......................!!
What to do when the matrix is not symmetric?
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?
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
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. ?
very helpful, thanks!
Can someone tell me, near 25:00 what is Ui and Uj ？
Thank you professor!!!!
brilliant. thank you very much.
it seems that symmetric and anti-symmtric don't conflict. check the definition in any discrete math text book.
thanks you sir. Kudos.
Excellent!!!!
why are all this videos about algorithms and stuff like that all from India?
Wdym??
@@tppt3987 why are you so butthurt abt it?
Because the indians are big into stem and realized how useful, especially in a poor country teaching this way is. No university campus required.
@@stevenson720 Do you know what the population of our students in colleges or school may be double or triple of your total population.
@@stevenson720 there were over 2.6 million primary school teachers in India. Then you think about it how many students are in India.
thank you so much for the class
I have the same doubt. And I still can't figure out why he chose 2. Maybe because it's an arbitrary choice or maybe because 2 is the next number after 1. Still no concrete reason though.