Multiple Constraint Knapsack Problem

Question

If there is more than one constraint (for example, both a volume limit and a weight limit, where the volume and weight of each item are not related), we get the multiply-con

Answer 1

Merge the constraints. Look at http://www.diku.dk/~pisinger/95-1.pdf chapter 1.3.1 called Merging the Constraints.

An example is say you have
variable , constraint1 , constraint2
1 , 43 , 66
2 , 65 , 54
3 , 34 , 49
4 , 99 , 32
5 , 2 , 88

Multiply the first constraint by some big number then add it to the second constraint.

So you have
variable , merged constraint
1 , 430066
2 , 650054
3 , 340049
4 , 990032
5 , 20088

From there do whatever algorithm you wanted to do with one constraint. The main limiter that comes to mind with this how many digits your variable can hold.