具有多重约束的背包（例如重量、体积等）

Question

Ive successfully written algorithms in C++ to obtain optimal solutions for integer knapsacks, fractional knapsacks, and a mixed-type knapsack, all with or without bounds to how many of each item is allowed to be taken.

These have only dealt with items with singular a constraint, which is weight. If I wanted to solve a knapsack that could have 2+ constraints, would I pull from other code Ive already written or need to write a whole new algorithm?

The integer and mixed type knapsacks were written solved dynamic programming, while the fractional used greedy.

Ex. Given two integer items and one fractional item.

Respective values are (9, 8, 3)

Respective weights are (2, 3, 1) max Weight =24

Respective volumes are (3, 2, 2) max Volume=23

Find the optimal solution and sum.

I believe I've calculated this sum to be 77.5

Answer 1

As soon as you have multiple constraints you enter the realm of linear (if all your variables can be fractional) or mixed integer linear (if some need to be integer) programming, and your best bet is to use an MILP solver. There are several commercial (cplex, gurobi, xpress) and open source solvers (clp/cbc, glpk).