Questions tagged [knapsack]

For questions related to the knapsack problem that seeks to find the number of each item to include in a limited container (in an integer knapsack or whether to include an item in a binary knapsack), given each item's weight and value, with the goal of maximizing the total value.

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5
votes
1answer
76 views

NP-hardness of a special case of multiple choice knapsack problem

Let us consider the following problem: \begin{align} \max &\quad\sum_{i=1}^n\sum_{j=1}^m v_{i,j}\cdot x_{i,j} \\ \text{s.t.}&\quad \sum_{i=1}^n x_{i,j} =1 &\forall j =1,\dots,m \\ &\...
7
votes
0answers
89 views

Estimate lagrangian multiplier based on instance characteristics

Assume we have a simple resource allocation problem, where all players have the same cost, but a different utility $a_s$. The resources assigned to a certain player must be between $L$ and $M$. ...
0
votes
1answer
158 views

Solving weekday and weekend fare movies

Thinking if it is a Knapsack problem. Here is the scenario: Michael and his daughter (7 year old kid) enjoy going to cinema for movies. ...
5
votes
1answer
116 views

0-1 knapsack with non-linear objective function

There's efficient algorithms for solving the 0-1 knapsack problems when the objective function is just a sum of profits. I am dealing with the following problem with non-linear objective function: $$\...
2
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1answer
81 views

Looking for a similar optimization problem

I want to know if there is any already defined problem that could give me a hint on how should I approach the following task. There are N tasks that should be accomplished, each task requires ...
4
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3answers
133 views

Is there a knapsack problem which allows 'out-of-capacity'?

I wonder if there is an option in the knapsack problem which has a huge cost for 'out-of-capacity' instead of strictly limiting the constraint.
3
votes
1answer
85 views

A variant of maximum sum subarray problem?

This is related to the foillowing Q on Cross Validated https://stats.stackexchange.com/questions/483002/experimental-design-problem-with-goofy-constraints which I am trying to answer, but the ...
5
votes
0answers
52 views

What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money $m$ to spend over $r$ different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
8
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2answers
356 views

knapsack problem with non-linear constraint

I have a basic knapsack problem where I need to fit the most weight possible in a bin: ...
3
votes
1answer
132 views

Multiple Knapsacks with splitting

I am trying to solve a problem that I believe is a variation of the multiple knapsacks. Like the classical multiple knapsacks problem, I have a set of items, each one with a weight and a value and I ...
0
votes
1answer
610 views

How to solve knapsack problem with simulated annealing?

I was going through the course contents of Optimization with Metaheuristics in Python in udemy , where they have solved a quadratic assignment problem using Simulated annealing in python , i was ...
2
votes
1answer
168 views

Does this problem fall into any common problem definition…Knapsack maybe?

I am struggling to find a representative problem formulation for this optimization challenge. I have implemented a MILP in Matlab, but the run time is taking more then a day. My goal is to see if it ...
5
votes
1answer
223 views

Solving a variant of multiple knapsack problem/ generalized assignment problem

Consider $m$ knapsack and $n$ items. With each knapsack $j$ associated a capacity $c(j)$ and with each item $i$ associated a profit $p(i,j)$ (that depends on the knapsack, so it's not exactly the ...
17
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3answers
3k views

Solving a knapsack problem with a lot of items

I am wondering what are the fastest ways(faster than classical dynamic programming) to solve the knapsack problem (to optimality) with $n$ items when $n$ is nearly equal to $10000$ ? Apart from ...
7
votes
1answer
129 views

How to convert 3D bin packing problem to 2D bin packing approximation?

I'm trying to approximately solve a 3D container loading problem. Is it possible to use 2D bin packing algorithms? If so, how do we make the transformation? What are the conditions needed to make the ...
12
votes
1answer
198 views

Looking for books in the same style as Hans Kellerer 2004, Knapsack Problems

I really enjoyed reading Hans Kellerer, David Pisinger, Ulrich Pferschy 2004 book Knapsack Problems. Can anybody recommend books in a similar style, about some other classes of problems / optimisation?...
7
votes
1answer
223 views

Shipments consolidation - how to model mutually exclusive items with OR-Tools CP Solver in Python (multi-knapsack, updated)

I am implementing a solution for packages consolidation (basing on Nurse Problem solution) with OR-Tools CP Solver. There is a factory that manufactures some small Packages that need to be ...
12
votes
3answers
1k views

Allocating credit card points

I’m interested in the idea behind this in general, so I thought this would be the best place to post, though I have a practical and semi-urgent need of allocating the points on my credit card towards ...
16
votes
1answer
884 views

Prove that these linear programming problems are bounded by $O(k^{1/2})$

Prove that these linear programming problems are bounded by $O(k^{1/2})$ Conjecturally the expanded partial sums of the Möbius transform of the Harmonic numbers have two out of three properties in ...