0/1 knapsack with dependent item weight?

Question

The standard 0/1 knapsack requires that the weight of every item is independent to others. Then DP is a efficient algorithm towards the solution. But now I met a similar but

Answer 1

This is a very interesting problem and I have been working on this for a while. The first thing to consider is that binary knapsack problem with dependent item weights/value is not trivial at all. You may consider using Bayesian networks, Markov models, and other similar techniques for solving this problem. Nonetheless, any practical approach to this problem has to make some assumptions either about the optimization model or its input. Here is an example of formulating the binary knapsack problem with value-dependent items. https://arxiv.org/pdf/1702.06662.pdf

In this work, authors have proposed modeling the input (value-related dependencies) using fuzzy graphs and then using the proposed integer linear programming model to solve the optimization problem. An extended version of the work has been accepted for publication and will be soon available online.

Please do not hesitate to contact me if you needed further information. I can also provide you with the source code of the model if needed.