The knapsack problem is a classic optimization problem in computer science and operations research.
The problem is defined as: Given a set of items, each with a weight and a value, determine the items to include in a collection (or "knapsack") so that the total weight does not exceed a given limit and the total value is maximized.
The code implements:
- Knapsack Problem
- Duality Problem
More realistic application of Knapsack Problem:
- Transportation planning: The knapsack problem can be used in transportation planning to optimize the loading of goods into vehicles, such as trucks or planes, to maximize the total value of the goods transported.
- Portfolio optimization: The knapsack problem can be used to optimize investment portfolios by selecting the best combination of assets that maximize return while staying within budget constraints.
- Resource allocation: The knapsack problem can be used to determine the optimal allocation of resources, such as staff, equipment, or budget, to achieve a certain objective or goal.