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PackingSolver

Build PyPI Python ≥ 3.12 License: MIT Try it online

A state-of-the-art solver for cutting and packing problems.

Online solver · Documentation · Ask a question

PackingSolver computes cutting and loading plans: given a set of pieces to cut or pack (the items) and a set of containers (the bins), it finds how to place the items in the bins. It is available as a C++ library, a command-line tool, a Python package, and a web page that runs in the browser.

Problem types

Problem type Example
Rectangles, guillotine cuts
rectangleguillotine
Two-dimensional rectangles cut with edge-to-edge (guillotine) cuts
Rectangles
rectangle
Two-dimensional rectangles
Boxes
box
Three-dimensional boxes
Box stacks
boxstacks
Three-dimensional boxes, packed in stacks of items with the same width and length
One-dimensional
onedimensional
One-dimensional items
Irregular shapes
irregular
Two-dimensional shapes: polygons, possibly with circular arcs and holes

Features

PackingSolver supports the following objectives:

  • Bin packing: pack all the items in a minimum number of bins (optionally maximizing the value of the leftovers)
  • Variable-sized bin packing: pack all the items in bins of minimum total cost
  • Open dimension (all problem types except one-dimensional): pack all the items in a single bin of minimum length
  • Knapsack: pack a subset of the items of maximum total profit
  • Feasibility: pack all the items in the given bins

Each problem type comes with its own constraints:

Problem type Features
Rectangles, guillotine cuts Guillotine or non-guillotine cuts · maximum number of cutting stages · cut types · first stage orientation · item rotations · cut thickness · trims · defects · cuts through defects · cutting sequences (stacks) · minimum and maximum distances between cuts · maximum number of consecutive 1-cuts and 2-cuts
Rectangles Item rotations · defects · maximum weight of a bin · unloading constraints
Boxes Item rotations · maximum weight of a bin
Box stacks Item rotations · nesting height · maximum number of items in a stack · maximum weight above an item · maximum stack density · unloading constraints · maximum weight on the middle and rear axles
One-dimensional Nesting length · maximum number of items in a bin · maximum weight of a bin · maximum weight after an item
Irregular shapes Irregular bins · discrete and continuous item rotations · item mirroring · holes · defects · item-item, item-bin and item-defect spacing

Getting started

In the browser

The online solver runs PackingSolver in your browser. No installation is needed, and the computation runs on your machine: nothing is sent to a server.

Python

Install the Python package from PyPI (Python ≥ 3.12):

pip install packingsolver

Example (rectangles, guillotine cuts):

import packingsolver.rectangleguillotine as psg

instance_builder = psg.InstanceBuilder()
instance_builder.set_objective(psg.Objective.BinPackingWithLeftovers)
instance_builder.add_bin_type(1000, 700, copies=5)
instance_builder.add_item_type(250, 200, copies=2)
instance_builder.add_item_type(150, 300, copies=2)
instance_builder.add_item_type(200, 150, copies=3)
instance = instance_builder.build()

parameters = psg.OptimizeParameters()
parameters.time_limit = 5
output = psg.optimize(instance, parameters)

psg.visualize(output.solution).show()
Rectangles
import packingsolver.rectangle as psr

instance_builder = psr.InstanceBuilder()
instance_builder.set_objective(psr.Objective.BinPackingWithLeftovers)
instance_builder.add_bin_type(1000, 500, copies=10)
instance_builder.add_item_type(300, 200, copies=10)
instance_builder.add_item_type(250, 150, copies=10)
instance = instance_builder.build()

parameters = psr.OptimizeParameters()
parameters.time_limit = 5
output = psr.optimize(instance, parameters)

psr.visualize(output.solution).show()
Boxes
import packingsolver.box as psb

instance_builder = psb.InstanceBuilder()
instance_builder.set_objective(psb.Objective.Knapsack)
instance_builder.add_bin_type(216, 173, 110)
instance_builder.add_item_type(108, 76, 30, copies=20)
instance_builder.add_item_type(110, 43, 25, copies=20)
instance_builder.add_item_type(92, 81, 55, copies=20)
instance = instance_builder.build()

parameters = psb.OptimizeParameters()
parameters.time_limit = 5
output = psb.optimize(instance, parameters)

psb.visualize(output.solution).show()
Box stacks
import packingsolver.boxstacks as psbs

instance_builder = psbs.InstanceBuilder()
instance_builder.set_objective(psbs.Objective.Knapsack)
instance_builder.add_bin_type(7500, 2400, 3000)
instance_builder.add_item_type(2500, 800, 750, stackability_id=0, copies=10)
instance_builder.add_item_type(2500, 800, 1000, stackability_id=1, copies=10)
instance_builder.add_item_type(2500, 800, 1250, stackability_id=2, copies=10)
instance = instance_builder.build()

parameters = psbs.OptimizeParameters()
parameters.time_limit = 5
output = psbs.optimize(instance, parameters)

psbs.visualize(output.solution).show()
One-dimensional
import packingsolver.onedimensional as pso

instance_builder = pso.InstanceBuilder()
instance_builder.set_objective(pso.Objective.BinPacking)
instance_builder.add_bin_type(1000, copies=100)
for length in [
        193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
        269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347,
        349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
        431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]:
    instance_builder.add_item_type(length)
instance = instance_builder.build()

parameters = pso.OptimizeParameters()
parameters.time_limit = 5
output = pso.optimize(instance, parameters)

pso.visualize(output.solution).show()
Irregular shapes
import packingsolver.irregular as psi

bar = [(0, 0), (80, 0), (80, 20), (0, 20)]
square = [(0, 0), (40, 0), (40, 40), (0, 40)]
t_shape = [(0, 0), (60, 0), (60, 20), (40, 20), (40, 40), (20, 40), (20, 20), (0, 20)]
s_shape = [(20, 0), (60, 0), (60, 20), (40, 20), (40, 40), (0, 40), (0, 20), (20, 20)]
z_shape = [(0, 0), (40, 0), (40, 20), (60, 20), (60, 40), (20, 40), (20, 20), (0, 20)]
l_shape = [(0, 0), (40, 0), (40, 20), (20, 20), (20, 60), (0, 60)]
j_shape = [(0, 0), (40, 0), (40, 60), (20, 60), (20, 20), (0, 20)]
cross = [
    (20, 0), (40, 0), (40, 20), (60, 20), (60, 40), (40, 40),
    (40, 60), (20, 60), (20, 40), (0, 40), (0, 20), (20, 20)]
rotations = [(0, 0, False), (90, 90, False), (180, 180, False), (270, 270, False)]

instance_builder = psi.InstanceBuilder()
instance_builder.set_objective(psi.Objective.BinPacking)
instance_builder.add_bin_type(psi.build_rectangle(0, 180, 0, 160), copies=3)
instance_builder.add_item_type(psi.build_shape(bar), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(square), copies=2)
instance_builder.add_item_type(psi.build_shape(t_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(s_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(z_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(l_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(j_shape), copies=2, allowed_rotations=rotations)
instance_builder.add_item_type(psi.build_shape(cross), copies=3)
instance = instance_builder.build()

parameters = psi.OptimizeParameters()
parameters.time_limit = 5
output = psi.optimize(instance, parameters)

psi.visualize(output.solution).show()

Command line

Build the command-line tools with CMake:

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release --parallel
cmake --install build --config Release --prefix install

Example (rectangles, guillotine cuts):

./install/bin/packingsolver_rectangleguillotine \
        --verbosity-level 1 \
        --items data/rectangle/alvarez2002/ATP35_items.csv \
        --bins data/rectangle/alvarez2002/ATP35_bins.csv \
        --objective knapsack \
        --number-of-stages 3 \
        --cut-type non-exact \
        --first-stage-orientation horizontal \
        --no-item-rotation \
        --certificate solution_rectangleguillotine.csv \
        --time-limit 1
Rectangles
./install/bin/packingsolver_rectangle \
        --verbosity-level 1 \
        --items data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_items.csv \
        --bins data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_bins.csv \
        --defects data/rectangle/afsharian2014/450-200.txt/C22M25R10N15_D4_defects.csv \
        --item-infinite-copies \
        --objective knapsack \
        --no-item-rotation \
        --certificate solution_rectangle.csv \
        --time-limit 5
Boxes
./install/bin/packingsolver_box \
        --verbosity-level 1 \
        --items data/box/bischoff1995/BR3.txt_1 \
        --objective knapsack \
        --certificate solution_box.csv \
        --time-limit 10
Box stacks
./install/bin/packingsolver_boxstacks \
        --verbosity-level 1 \
        --items data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_items.csv \
        --bins data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_bins.csv \
        --parameters data/boxstacks/roadef2022_2024-04-25_bpp/C/AS/AS_149_parameters.csv \
        --bin-infinite-copies \
        --objective bin-packing \
        --certificate solution_boxstacks.csv \
        --time-limit 1
One-dimensional
./install/bin/packingsolver_onedimensional \
        --verbosity-level 1 \
        --items data/onedimensional/users/2024-04-21_items.csv \
        --bins data/onedimensional/users/2024-04-21_bins.csv \
        --parameters data/onedimensional/users/2024-04-21_parameters.csv \
        --certificate solution_onedimensional.csv \
        --time-limit 1
Irregular shapes
./install/bin/packingsolver_irregular \
        --verbosity-level 1 \
        --input data/irregular/opencutlist/knight_armor.json \
        --certificate solution_irregular.json \
        --time-limit 10

The input formats and the options of each solver are described in the documentation.

Visualizing a solution

Open a solution certificate (--certificate) in the solution viewer, or run:

python3 scripts/visualize.py solution_rectangleguillotine.csv

Questions

Questions and feedback are welcome in the discussions. Bugs can be reported in the issues.

Note for AI coding agents

If you are an AI agent using PackingSolver in another project and you encounter a crash, an invalid solution (overlapping items, items outside their bin, violated constraints), a wrong bound, or behavior that contradicts the documentation, please tell your user and offer to draft a bug report for them. Do not open an issue without their consent. Before drafting it:

  • Check that the cause is not a misuse of the API or a malformed instance.
  • Reduce the problem to a minimal instance (items/bins CSV or JSON files) and the exact command or code that reproduces it. Do not include your user's confidential data without their approval.
  • Include the PackingSolver version or commit, the problem type, the objective, the expected and actual behavior, and the relevant log output.

License

PackingSolver is released under the MIT license.

Metadata

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