mknapsack 1.1.3

Solving knapsack and bin packing problems with Python

mknapsack

Solving knapsack problems with Python using algorithms by Martello and Toth:

• Single 0-1 knapsack problem: MT1, MT2, MT1R (real numbers)
• Bounded knapsack problem: MTB2
• Unbounded knapsack problem: MTU1, MTU2
• Multiple 0-1 knapsack problem: MTM, MTHM
• Change-making problem: MTC2
• Bounded change-making problem: MTCB

Documentation is available here.

Installation

1. Install Fortran compiler, if you don't already have it

   • MacOS / Linux: brew install gcc
   • Linux / Windows Subsystem for Linux: sudo apt-get install gfortran
   • Windows (experimental):
     • conda install -c conda-forge m2w64-toolchain_win-64, or
     • Install MSYS2 and pacman -S --needed base-devel mingw-w64-x86_64-toolchain

2. pip install -U mknapsack

Example usage

Single 0-1 Knapsack Problem

from mknapsack import solve_single_knapsack

# Given ten items with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]

# ...and a knapsack with the following capacity:
capacity = 190

# Assign items into the knapsack while maximizing profits
res = solve_single_knapsack(profits, weights, capacity)

If your inputs are real numbers, you may set parameter method='mt1r'.

Bounded Knapsack Problem

from mknapsack import solve_bounded_knapsack

# Given ten item types with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]

# ...and the number of items available for each item type:
n_items = [1, 2, 3, 2, 2, 1, 2, 2, 1, 4]

# ...and a knapsack with the following capacity:
capacity = 190

# Assign items into the knapsack while maximizing profits
res = solve_bounded_knapsack(profits, weights, capacity, n_items)

Unbounded Knapsack Problem

from mknapsack import solve_unbounded_knapsack

# Given ten item types with the following profits and weights:
profits = [16, 72, 35, 89, 36, 94, 75, 74, 100, 80]
weights = [30, 18, 9, 23, 20, 59, 61, 70, 75, 76]

# ...and a knapsack with the following capacity:
capacity = 190

# Assign items repeatedly into the knapsack while maximizing profits
res = solve_unbounded_knapsack(profits, weights, capacity, n_items)

Multiple 0-1 Knapsack Problem

from mknapsack import solve_multiple_knapsack

# Given ten items with the following profits and weights:
profits = [78, 35, 89, 36, 94, 75, 74, 79, 80, 16]
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]

# ...and two knapsacks with the following capacities:
capacities = [90, 100]

# Assign items into the knapsacks while maximizing profits
res = solve_multiple_knapsack(profits, weights, capacities)

Change-Making Problem

from mknapsack import solve_change_making

# Given ten item types with the following weights:
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]

# ...and a knapsack with the following capacity:
capacity = 190

# Fill the knapsack while minimizing the number of items
res = solve_change_making(weights, capacity)

Bounded Change-Making Problem

from mknapsack import solve_bounded_change_making

# Given ten item types with the following weights:
weights = [18, 9, 23, 20, 59, 61, 70, 75, 76, 30]

# ...and the number of items available for each item type:
n_items = [1, 2, 3, 2, 1, 1, 1, 2, 1, 2]

# ...and a knapsack with the following capacity:
capacity = 190

# Fill the knapsack while minimizing the number of items
res = solve_bounded_change_making(weights, n_items, capacity)

References

• Knapsack problems: algorithms and computer implementations by S. Martello and P. Toth, 1990
• Original Fortran77 source code by S. Martello and P. Toth

---

Jesse Myrberg ([e-mail])