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
• Generalized assignment problem: MTG, MTHG
• Bin packing problem: MTP
• Subset sum problem: MTSL

Documentation is available here.

Installation

pip install 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)

Generalized Assignment Problem

from mknapsack import solve_generalized_assignment

# Given seven item types with the following knapsack dependent profits:
profits = [[6, 9, 4, 2, 10, 3, 6],
           [4, 8, 9, 1, 7, 5, 4]]

# ...and the following knapsack dependent weights:
weights = [[4, 1, 2, 1, 4, 3, 8],
           [9, 9, 8, 1, 3, 8, 7]]

# ...and two knapsacks with the following capacities:
capacities = [11, 22]

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

Bin Packing Problem

from mknapsack import solve_bin_packing

# Given six items with the following weights:
weights = [4, 1, 8, 1, 4, 2]

# ...and bins with the following capacity:
capacity = 10

# Assign items into bins while minimizing the number of bins required
res = solve_bin_packing(weights, capacity)

Subset Sum Problem

from mknapsack import solve_subset_sum

# Given six items with the following weights:
weights = [4, 1, 8, 1, 4, 2]

# ...and a knapsack with the following capacity:
capacity = 10

# Choose items to fill the knapsack to the fullest
res = solve_subset_sum(weights, 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

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Jesse Myrberg (jesse.myrberg@gmail.com)