knapsack | A module for resource allocation | Learning library

I am trying to solve this problem: There are n customers queuing at post office to wait to send parcels. a[0], a[1], ..., a[n-1] is the list of shipping costs of n customers from the 1st to the nth person. It takes exactly a minute for the postal worker to complete the information needed for a customer to send a parcel. However, all customers are too busy to wait for more than a certain period of time. t[0], t[1], ..., t[n-1] is the list of minutes each of n customers can spend at the post office. Help the postal worker to find a way to serve customers so that the post office can get the largest amount of money, knowing that the staff is allowed to refuse to serve some customers for the profitable reason.)

Example:

• For a = [10, 20, 5, 12], t = [2, 3, 3, 1], the output should be 42. Explanation: The order of the customers is: the 4th person -> the 1st person -> the 2nd person (1-based indexing)
• For a = [5, 1, 3, 2], t = [3, 1, 2, 2], the output should be 10. Explanation: Although the 2nd person can wait only 1 minute, this person has to pay the smallest cost. Therefore, the postal worker will not serve this customer. The order of the customers is: the 3rd person -> the 4th person -> the 1st person.

I think it is a variant of the knapsack problem, I can solve it by using brute force but only for small input. Can someone help me to solve this problem? Thanks.

I am trying to create an array using a struct in c++ which takes two variables i.e value and weight. So I created an array which will have value and weight in one element like this Arr[]={{1,2},{3,4}}...and i want that if i called Arr[0].value and Arr[0].weight then it should return 1 and 2 respectively but I think I'm doing something wrong because im getting many errors

KNAPSACK problem is old, but this has some differences:

At a store that has n items, each item has weight W[i] and value V[i]. A bag can include maximum weight W. Choose some items, which total have max values. And an item can be chosen more than one time.

I only can finish if an item can be chosen one time but more than one time is hard for me. So can you help me!

Trying to use GEKKO to solve knapsack optimization problem, but can't reach a satisfactory result. I have input data:

I am working on my version of a genetic algorithm to solve the knapsack problem in C++. I have a map of string to vector like

I have a very simple knapsack problem listed below.

The sample of the df looks like this:

I am trying to do a 0-1 knapsack optimization with constraint on the source of items. I took the example from the ortools website (ortool example) and try to add a constraint to only be able to pick one item from each owner in the knapsack.

I have a list of items with associated weights (data['weights']), values (data['values']) and source (data['owns']). I would like to find the best combination of items to put in knapsack knowing that only one item per source can go in the knapsack.

I am not sure how to write the constraint.

If you look at the code below and have 1 knapsack, then the optimal solution should be to take at most 1 item from owner 0, one from owner 1 and one from owner 2 which follows the weight constraint and the uniqueness of item picked (weight below 100).

Here is the code I use (taken from the ortool multiple knapsack example):

I have a problem and I feel like there should be a well-known algorithm for solving it that's better than just brute force, but I can't think of one, so I'm asking here.

The problem is as follows: given n sorted (from low to high) lists containing m probabilities, choose one index for each list such that the sum of the chosen indexes is less than m. Then, for each list, we flip a coin, where the chance of it landing heads is equal to the probability at the chosen index for that list. Maximize the chance of the coin landing heads at least once.

Are there any algorithms for solving this problem that are better than just brute force?

This problem seems most similar to the knapsack problem, except the value of the items in the knapsack isn't merely a sum of the items in the knapsack. (Written in Python, instead of sum(p for p in chosen_probabilities) it's 1 - math.prod([1 - p for p in chosen_probabilities])) And, there's restrictions on what items you can add given what items are already in the knapsack. For example, if the index = 3 item for a particular list is already in the knapsack, then adding in the item with index = 2 for that same list isn't allowed (since you can only pick one index for each list). So there are certain items that can and can't be added to the knapsack based on what items are already in it.

Linear optimization won't work because the values in the lists don't increase linearly, the final coin probability isn't linear with respect to the chosen probabilities, and our constraint is on the sum of the indexes, rather than the values in the lists themselves. As David has pointed out, linear optimization will work if you use binary variables to pick out the indexes and a logarithm to deal with the non-linearity.

EDIT:

I've found that explaining the motivation behind this problem can be helpful for understanding it. Imagine you have 10 seconds to solve a problem, and three different ways to solve it. You have models of how likely it is that each method will solve the problem, given how many seconds you try that method for, but if you switch methods, you lose all progress on the one you were previously trying. What methods should you try and for how long?

I have a program (knapsack, optimized for returning the highest value solution with the least weight) for which I want to use external files for the typedef and struct data.

But I can't get it working, somewhere I am messing up with the pointers. I get an 'multiple definition' error or when I change it, I get an 'xxx not declared' error...

/tmp/ccMy5Yw0.o:(.data+0x0): multiple definition of `item1'

Any help on pointing out my thinking mistake in greatly appreciated. (I compiled online @ https://www.onlinegdb.com/)

It did work when I had everything in one file, but after splitting it in different files I can't get it working...