How to solve an Integer Linear Programming Problem Using Branch and Bound
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- เผยแพร่เมื่อ 24 ส.ค. 2024
- In this video, first, we give a brief introduction about the difference between the linear programming problem and Integer linear programming problem. Then, we learn the Branch and Bound method to solve integer linear programming problems. Please carefully watch 8:20-10:00. In this part, we show that solution 27 is the optimal solution. I continue branching for the sake of understanding, in case someone started off by the right branch before starting on the left branch.
You wouldn’t normally need to investigate further branches under the first right branch (X2 >= 3) is that correct? The objective value in the relaxed subproblem (26.75) is less than the current best (27) therefore no further branch can possibly yield anything better.
yes, I mention that in the video, and if you don't skip you will hear that as well. Thanks!
Must have missed it. Thank you very much
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@@bazingazeroni
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Thanks for the feedback!
That's amazing cause i had spent about 3 hours to re-learn this section in the classroom but you have just helped me to tackle it just in 17 mins. Thanks so much!
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This is fantastic! I learned branch and bound in like 10 minutes because of you. I really thought it was hard but my lecture notes are just so unclear..
I wish, there was more Integer Programming videos, that you made. Thanks Professor.
Thanks for the detailed description of the branch and bound algorithm. I just would like to make a small note for the given problem. Since the objective function is the result of summing up the multiplications of the integer decision variables by integer coefficients, the optimal objective function value must be an integer. Since the optimal LP relaxation solution at the root node (subproblem1) is 27.67, so we can claim that 27 is an upper bound. Since the solution of the subproblem at the first branch is found to be 27, we can stop without the need to explore the other branches. This is a detailed description of the previous comment by Lekshman Ramesh.
Thank you and that is correct! I went through the whole branches for learning purposes and also in cases where the order of solving subproblems are so that one goes through the right branch before going to the left ones.
Thanks I was looking for confirmation
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glad that it was helpful!
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Your explanation is very clear and the problem is simple enough to follow. Thanks a ton!!! I really appreciate this.
It is my first time working on this popular algorithm and from your video, I feel like I understand it so well. Thank you.
thank god i've found your video! i was getting frustrated but now.....FINALLY i understand what i must do in just 10minutes! didn't even know that it was this easy! your explanations are so clear !
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I was searching for a video about Branch & Bound Method and finally got here. It was the best of all. Simple and easy to understand. Thank you :)
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I think there is a mistake @ 11:10, when you have found z= 26.75 for x1=1.75 and x2=3; you don't need to proceed further down since all the sub-problems of this branch will give solution z
Lol! My OR teacher need to see this.
Thank you mam.
Not sure why textbooks can't be this clear, but thanks, that was amazing. Almost like they don't want you to know or something.
@3:25. for your optimal function. where did the 15 come from?
To be able to find a point that maximizes our objective function, we started by putting the objective function equal to some arbitrary number.This arbitrary number is 15. You can put this function equal to any number that you would like.
@@mervesafaarkan32 thanks Merve!
A very clear explanation with additional subtitle that really helped a lot. Thank you very much!
thank you so much for this video 🙏🏼 loved how you always put the graphics next to the branches and explained it so well and understandable 🙏🏼 thank you for your effort 😊
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You got a sweet voice that makes learning quicker
your explanation is quite clear, thanks mirzaei!
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Thanks very much. Very clear explanation and really helped to answer this method in my exam.
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واقعا مفید و کمک کننده بود. ممنون👏🏻❤️
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Thank you!
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Many thanks for sharing this. Very clear and concise.
how do you know which constraint to use, to replace the x values? because in some cases shes using constraint 2 and in the first case she used constraint 1
خیلی ممنون سرکار خانم میرزایی ^^ بسیار عالی بود
Love the way you teach...Hats off
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Thank you for such a great explanation of this problem. 🙂
Thanks! It`s very useful!
a very clear explanation ... thank you so much
I believe you mentioned that the optimum has to be at a vertex because it's a convex set, at 2:18, but I think that you have to require a concave objective function for that to be true.
Best! Thanks a lot Shokoufeh Mirzaei!!!
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Great explanation. Thanks!
In 15:47, x2>=4 while x1 = 1 is already the previous constraint, how can you get another branch with x1=0 and x2 = 4? I believe it is not fathomed, it is already infeasible.
That was really clear and you made it so much easy to understand. Thank you for helping us to understand this topic very well 🙋🏼♂️
How did you get to make the objective function equal to 15 at 3:14
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I do not understand how you put x1=3 for the objective function value? As in your "How to Solve a Linear Programming Problem Using the Graphical Method" lecture, you said the optimal solution will be an intersection of constraint 1 and constraint 2. why not in this case? why we don't use a value of x1 = 7/3 and x2 8/3, for objective function value as you do in your Graphical method lecture?
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خیلی ممنونم :)
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Thanks! likewise :)
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This was an excellent explanation! I am taking Operations Research at the University of Maine at Augusta and I sure wish you were an instructor there. This is much more straightforward than our instructors' lectures! Fantastic right before an exam, thank you!
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Thank you!
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Well made, thanks Shokoufeh. :)