knapsack

The Knapsack problem is an example of the combinational optimization problem. This problem is also commonly known as the “Rucksack Problem“. The name of the problem is defined from the maximization problem as mentioned below:Given a bag with maximum weight capacity of W and a set of items, each having a weight and a value associated with it. Decide the number of each item to take in a collection such that the total weight is less than the capacity and the total value is maximized.Types of Knapsack Problem:The knapsack…

How to solve an optimization problem using quantum computing, compared to a traditional solutionThere are many problems that require finding the maximum or minimum of a function, called the objective function, that depends on several (or many) variables; certain constraints may or may not need to be applied to the variables. The variables could be binary, integer, elements in sets, floating point, etc. The constraints may apply to variables individually, or could be more complex.Specifically, these problems could offer…

What is Knapsack Problem?Suppose you have been given a knapsack or bag with a limited weight capacity, and each item has some weight and value. The problem here is that “Which item is to be placed in the knapsack such that the weight limit does not exceed and the total value of the items is as large as possible?”.Consider the real-life example. Suppose there is a thief and he enters the museum. The thief contains a knapsack, or we can say a bag that has limited weight capacity. The museum contains various items of…

Learn how to solve optimization problems in Python using scipy and pyomoPhoto by Denisse Leon on UnsplashThe knapsack problem is probably one of the first problems one faces when studying integer programming, optimization, or operations research. In this problem, from a given set of items, one must choose the most valuable combination to fit in a knapsack of a certain capacity (weight, volume, or both).Throughout this article, we will implement the knapsack problem in a relaxed form using scipy and in an integer form…