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Questions tagged [branch-and-bound]

30 questions
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3 answers

What is the difference between bounding and pruning in branch-and-bound algorithms?

Could anybody please explain what the difference between "bounding" and "pruning" in branch and bound algorithms is? I'd also appreciate references (preferably books), where this distinction is made clear.
Martin Thoma
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Branch and Bound explanation

I have a test about the branch and bound algorithm. I understand theoretically how this algorithm works but I couldn't find examples that illustrates how this algorithm can be implemented practically. I found some examples such as this one but I'm…
MR.NASS
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Branch and bound for minimum linear arrangement

I am trying to solve this branch and bound problem but I could not come up with any approximate cost function which is better than the cost. Let's say $G$ is a graph of $n$ nodes $\{1, 2, 3, \ldots , n\}$. For a permutation $f$ of the nodes of $G$,…
Bibek Bhattarai
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1 answer

Making a branch-and-bound algorithm more efficient for a large input

I am trying to implement the branch and bound algorithm to solve the knapsack problem (in the Coursera discrete optimisation course). I tried implementing dynamic programming first, and that worked fine, but ran into memory issues with larger…
guskenny83
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3
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1 answer

Branch and Bound - Transform a into b

I'm trying to design an algorithm which will accept two natural numbers: a and b. Its purpose is to get b from a by making the following operations: *3 and /2. For example, if a = 10 and b = 7, then: 10/2*3/2 = 7 I decided to use branch and bound,…
fergaral
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Branch and Bound running time and golden ratio

This is a follow up question to When does Branch and Bound exactly stop giving solutions for the bin packing problem After testing many instances I found out that when r = V / Vtotal <= ϕ (Golden Ratio) the algorithm takes a lot of time to printout…
AIri
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Trying to understand the Gilmore-Lawler lower bound

For a class project we're developing a software that solves a common optimisation problem. After some research we've found out that our problem is called QAP (Quadratic Asssignment Problem) and the algorithm that is commonly used is Branch and…
Setzer22
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Backtracking vs Branch-and-Bound

I'm getting a bit confused about the three terms and their differences: Depth-First-Search (DFS), Backtracking, and Branch-and-Bound. What confuses me: Stack Overflow: Difference between 'backtracking' and 'branch and bound', Abhishek Dey:…
Martin Thoma
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3
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2 answers

Examples of Analysis of Branch and Bound Method

I am solving a graph problem, which can be formulated as an integer programme. Based on computer experiments, it seems that the branch and bound method works well. I would like to analyse the running time, and wonder whether there have been other…
Hung H
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1 answer

Branch & Bound: Avoiding equivalent solutions

There is a certain family of typical branch & bound problems in which we have to put $n$ objects into $m$ indistinguishable bags. Usually solutions are represented by $n$-size vectors in which $V[i]$ means that the $i$-th element is in the $V[i]$-th…
Álvaro G. Tenorio
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How to find the Branch factor of 8 Puzzle

I would like to know how to find the average branching factor for 8 puzzle.While referring Artificial Intelligence by George F Luger it says that: Suppose,for example we wish to establish the branching factor of the 8-puzzle.We calculate the total…
justin
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Can the effective branching factor be negative?

I've implemented A* algorithm in Python, after that I calculated the effective branching factor $ B^* $ $$ T+1=1+B^*+(B^*)^2+\dots +(B^*)^L$$ where $T$ is the number of expanded nodes. My question is: is it possible in theory that the effective…
sdrabb
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1 answer

Traveling Salesman: how to use a lower bound?

Let me preface this question by giving some helpful background material. I'm trying to solve the traveling salesman problem using branch and bound. Concretely, for a partial solution, I'm using the solution the algorithm would attain by making…
rookie
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What are all linear extensions of the product order of $\{1, \dots, M\} \times \{1, \dots, N\}$?

Note: I have read somewhere that finding all linear extensions of a partial order is in general a #P-complete problem (which apparently means difficult, and thus no closed form expression), but just because the general problem is difficult does not…
hasManyStupidQuestions
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How to prune branches in a branch-and-bound solution for Flow Shop Scheduling?

I am implementing a Branch-and-Bound algorithm to find the optimal solution for the Flowshop Scheduling Problem, but I am stuck on the optimization phase, here is a rundown of the problem and what I go so far. (I am sorry for my English, not a…
Victor Capone
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