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Chapter 6: Problem 19

List three more applications of the branch-andbound design strategy.

Short Answer

Expert verified
Three additional applications of branch-and-bound design strategy are: Traveling Salesman Problem (TSP), the Knapsack Problem, and the Assignment Problem.

Step by step solution

01

Understanding the Technique

Understand that the branch-and-bound strategy is a tree-based algorithm used to solve optimization problems such as assignment, travel, and scheduling.
02

First Application

One application is in the Traveling Salesman Problem (TSP). Here, the strategy is used to find the shortest possible route that includes a specified set of cities, and returns to the origin city.
03

Second Application

A second application is in the Knapsack Problem where outputs are restricted of certain constraints. Here, the branch-and-bound strategy helps in maximizing the total value of items chosen, without exceeding the weight capacity of the knapsack.
04

Third Application

The strategy can also be applied in the Assignment Problem, where the objective is to assign tasks to workers in a way that minimizes the total cost, time, or distance. The branch-and-bound strategy helps in finding the most efficient assignment.

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Most popular questions from this chapter

Use Algorithm 6.1 (The Breadth-First-Search with Branch-and-Bound Pruning algorithm for the \(0-1\) Knapsack problem) to maximize the profit for the following problem instance. Show the actions step by step. $$\begin{array}{llll} i & p_{i} & w_{i} & \frac{p_{i}}{w_{i}} \\ 1 & \$ 20 & 2 & 10 \\ 2 & \$ 30 & 5 & 6 \\ 3 & \$ 35 & 7 & 5 \\ 4 & \$ 12 & 3 & 4 \\ 5 & \$ 3 & 1 & 3 \end{array}$$ w=13
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