WHAT IS BRANCH AND BOUND ?
Branch and bound is a method for solving optimization problems, particularly those in which the solution is an integer or a binary value. The method starts by creating a tree of all possible solutions, with each node representing a possible solution. The algorithm then "branches" out from each node, creating new nodes that represent different choices or possibilities. As the tree is explored, the algorithm "bounds" the search by eliminating branches that cannot lead to a better solution than what has already been found. This allows the algorithm to efficiently explore the solution space and find the optimal solution in a reasonable amount of time.
EXAMPLE OF BRANCH AND BOUND PROBLEM:
KNAPSACK PROBLEM:
The knapsack problem is a classic problem in combinatorial optimization. Given a set of items, each with a weight and a value, the goal is to determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
Here is an example of the knapsack problem:
Imagine you are going on a camping trip and can only carry a certain weight in your backpack. You have the following items to choose from:
A tent (weighs 20 lbs, worth $100)
A sleeping bag (weighs 10 lbs, worth $75)
A cooking stove (weighs 2 lbs, worth $20)
A Firestick (weighs 1 lb, worth $10)
The maximum weight you can carry in your backpack is 25 lbs.
The knapsack problem can be represented using a diagram called a table. Here is an example of such a table for this problem:
Weight | Value | |
Tent | 20 | 100 |
Sleeping Bag | 10 | 75 |
Cooking Stove | 2 | 20 |
Firestick | 1 | 10 |
The columns represent the weight and value of each item, and the rows represent the different items. The goal is to fill the backpack with a combination of items that maximizes the total value, while not exceeding the maximum weight of 25 lbs.
The knapsack problem can be solved using various algorithms such as dynamic programming, greedy algorithm, and branch and bound.
I hope you got a brief overview of branch and bound algorithm
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