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?

@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 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.

@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.

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 is not ok? Why? The branch 2-5 and 5-1 can't be added?

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

For students of Integer Constraints Programming there is an awesome app on Android Play store https://play.google.com/store/apps/details?id=in.co.boilerplate.solver . It provides a SCARTCH like programming environment to model constraints. I am the author.

sir good but i have a doubt at starting point you are saying that sum of i=1 to n but actually it is i=1 to n-1 because (n-1)! possible ways.since each city visit only once so sum of i=1 to n-1 xij value is equal to 0 where i not equal to j and j =1,2,3,….n

hello… how to write programs using HEAPSORT to solve Travelling Salesman Problem – TSP on programming language C … and I need code 🙁 im form Viet Nam…thanks

Would appreciate help: Minute 26, subtour elimination, i is from 1 to n-1 (=5-1=4), but he uses U5… If he would have done it according to i=1…n-1, j=2…n, the second subtour would be one equation that satisfies U4-U5+5<=4 + I read that U stands for sequence in the tour, is that right???

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.

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

According to the wiki of TSP https://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.

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 ?

26:40 How come professor wrote "U5 – U4 + 5 <= 4". As according to the condition "i" can only take values from 1 to n-1 and here U5 indicate that i has been taken as 5.

They are really smart ppl xD

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

how can the matrix be anti-symmetric? the way the matrix be built guarantees the matrix must be symmetric

it seems that symmetric and anti-symmtric don't conflict. check the definition in any discrete math text book.

Do you also teach chemistry? If so do they give out free helium in the staff lounge?

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

Better than the lecture on my university. Shame on our "elite" professors.

Isn't i should be the rows and j be the columns?

Is the same thing.

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?

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

mathematicals!

THANK YOU!!

@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 sir,

from Australia

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.

Thank you Professor.

Best explanation I found online. Thanks, Professor!

Lec-24 Traveling Salesman Problem(TSP)

thanks you sir. Kudos.

Just one word sir … Brilliant!!!

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

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

thumbs up sir 🙂

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

Regards.

@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.

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 is not ok? Why? The branch 2-5 and 5-1 can't be added?

Explained masterfully.

thanks sir

Perfecttttt for any learner!!!!!!

int the inequality: Ui -Uj + nXij <= n-1 , what does U stand for?

does anyone know who proposed this method of branch and bound?

Loving this tutorial 🙂

Came here just to learn the algorithm. Ended up really interested in the whole concept.

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

For students of Integer Constraints Programming there is an awesome app on Android Play store https://play.google.com/store/apps/details?id=in.co.boilerplate.solver . It provides a SCARTCH like programming environment to model constraints. I am the author.

sir good but i have a doubt at starting point you are saying that sum of i=1 to n but actually it is i=1 to n-1 because (n-1)! possible ways.since each city visit only once so sum of i=1 to n-1 xij value is equal to 0 where i not equal to j and j =1,2,3,….n

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

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

greattings from Egypt

Hi, I think I solved this in a nice way. I would love some feedback, thanks. the answer is on my youtube page

This is really interesting.

This video was very helpful… thank you…!

Very helpful. Thank you!

Thank you sir this video is very help full to me

I executed a code implementing the same algorithm. It gives the answer as 41.

he pronounced n as "yan" ?

hello…

how to write programs using HEAPSORT to

solve Travelling Salesman Problem – TSP on programming language C …

and I need code 🙁

im form Viet Nam…thanks

Well Explained!!!

Really an excellent lecture Sir.

thank you so much . the lecture helped me a lot.

helped in ca final operations research…thank you 🙂

Would appreciate help: Minute 26, subtour elimination, i is from 1 to n-1 (=5-1=4), but he uses U5…

If he would have done it according to i=1…n-1, j=2…n, the second subtour would be one equation that satisfies U4-U5+5<=4

+ I read that U stands for sequence in the tour, is that right???

Thank you, Professor. Very helpful!

this lecture helped me a lot in my research of TSP

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.

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

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

IIT has the best minds in india. very good lecture

1:36 Illuminati Confirmed

marvellous

Thnk u sir…

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

Could someone explain what the U variable refers to around 27 minutes?

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?

Thanks sir

use digital boards, not on green boards its getting confusion

According to the wiki of TSP https://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.

great explaination

Great tutorial for learners, thanks

How 31 came?

Appreciated Sir .. Thank You . great explanation.

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

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 ?

Great 🙄

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

That's my Don! Enjoying much your lectures.

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

That Awsome

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

Tqq sir I like u r teaching

great lecture.

Thanks

shit, i found it 35 just by looking at it

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

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

Thank you sir

26:40 How come professor wrote "U5 – U4 + 5 <= 4".

As according to the condition "i" can only take values from 1 to n-1 and here U5 indicate that i has been taken as 5.

Branch And Bound Algo at 29:30

Best Explanation of TSP problem.

👌👌👌👌

very helpful, thanks!

he is a god

How is the cost calculated Sir?

7:40

I have the same doubt as that of arun kaushik

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

Brilliant teacher

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

I absolutely understood by listenning to the lecture. Thank you, and so much!

You are great!!!