Enumerating all possible solutions of Knapsack problem

[Tomas_Pevny]

Dear All,

I would like to ask, if anyone has experimented with an algorithm to enumerate all possible solutions of the knapsack problem. I have seen scientific papers solving this problem and would like to know, if someone has tackled this.

Thank you very much in advance.

Tomas

[odow]

all possible solutions

All possible optimal solutions?

This came up a few days ago:

Right solver for JuMP to find every solution of a linear system of equations with integer solutions

No problem. While it’s fresh in my mind, here is a more general solution for future reference: ## Packages using JuMP using Gurobi function example_big_sum(rowsum, colsum; verbose::Bool = true) ## Model: model = Model(Gurobi.Optimizer) @assert length(rowsum) == length(colsum) N = length(rowsum) INDEX = 1:N @variable(model, y[INDEX,INDEX] >= 0, Int) @constraint(model, rowCons[i=INDEX], sum(y[i,j] for j in INDEX) == rowsum[i]) @constraint(model, colCons[j=INDEX…

See the JuMP documentation:

Solutions · JuMP

[ccoffrin]

I will also note if you would like to roll your own algorithm to do this the following online course can provide some good ideas for how to approach it.

Discrete Optimization

[Tomas_Pevny]

Thank you very much both. I would not kind to follow the course, but there are many things I need to follow. But the course looks amazing.

Tomas

I knew that this forum will not let me down.