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Problem: An Example Of The 0-1 Knapsack Problem

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CHAPTER 1
INTRODUCTION
1.1 0-1 Knapsack problem
The 0-1 Knapsack Problem is an example of a combinatorial optimization problem, which seeks for a best solution from among many other solutions. It is concerned with a knapsack that has positive integer volume (or capacity) V. There are n distinct items that may potentially be placed in the knapsack. An item i have a positive integer, volume Vi and positive integer benefit Bi. In addition, there are Qi copies of the item i available, where quantity Qi is a positive integer satisfying 1 ≤ Qi ≤∞.
Let Xi determines how many copies of item i are to be placed into the knapsack. The goal is to:
Maximize
N
∑ Bi Xi i = 1

Subject to the constraints
N
∑ Vi Xi ≤V i = 1

And
0 ≤ Xi ≤ Qi
If one or more …show more content…

• Cutting stock: In industrial application of cutting stock, optimization methods are carefully programmed for each new task. ATLBO algorithm could be used to give better suggestions.
• Budget control: For large scale budget management it is difficult to handle lots of computerized data and need rapidly of optimization, there is ATLBO algorithm able to play a very important part in managing the budget of long time.
• Financial management: Financial management is the basic need for all types of organization so there is various technologies for monitoring and maintaining money, proposed ATLBO algorithm could be suggest better management results.
1.6 Structure of the Thesis
This dissertation consists of seven chapters. The first chapter provides a general introduction and overview of the area of research, including a general introduction of 0-1 knapsack problem, Teaching learning based optimization (TLBO) and problem definition. The motivation is discussed along with the scope of the study and

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