Arc-flow Vector Packing Solver (VPSolver)

Copyright (C) 2013-2022, Filipe Brandão fdabrandao@gmail.com

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VPSolver is a multiple-choice vector packing solver based on an arc-flow formulation with graph compression (see, e.g., [1]). VPSolver generates very strong models (equivalent to Gilmore and Gomory's) that can be solved using general-purpose mixed-integer programming solvers such as Gurobi and GLPK (see, e.g., [2] and [3]). VPSolver does not explicitly require any MIP solver in particular, though a good MIP solver may be necessary for solving large models.

For modelling other problems easily, VPSolver includes a Python API, a modelling toolbox (PyMPL), and a Web App. VPSolver has been successfully compiled and run on Linux, macOS, and Windows. VPSolver can also be used in Docker containers.

For more details, please refer to the project wiki or to the manual.

Repositories

• Project Homepage: http://vpsolver.fdabrandao.pt
• GiHub repository: https://github.com/fdabrandao/vpsolver
• BitBucket repository: https://bitbucket.org/fdabrandao/vpsolver
• Docker repository: https://hub.docker.com/r/fdabrandao/vpsolver
• PyPI repository: https://pypi.python.org/pypi/pyvpsolver

Requirements

Mandatory

• To use vpsolver scripts for various solvers:

  • MIP solver: Gurobi, CPLEX, GLPK, COIN-OR, SCIP, lp_solve, ...
  • UNIX-like operating system or a UNIX-like environment such as Cygwin on Windows
  • g++, clang, or Visual Studio; cmake >= 3.3; bash >= 3.0

• To build the vpsolver executable linked to Gurobi:

  • gurobi
  • cmake >= 3.3

Optional

For the Python API and Web App:

• python-2.7 or python-3.x
• python-pip
• python-dev
• glpk-utils

Platforms

It has been successfully compiled and run on the following platforms:

• Linux
• macOS
• Windows (note that vpsolver scripts require bash)

Setup

Without the python interface:

$ mkdir build
$ cd build/
$ cmake ..
$ cmake --build . --config Release

Note: In order to compile the components that require Gurobi, you need to have set the environment variable GUROBI_HOME or specify the location of the Gurobi installation in the third step:

• Linux: cmake .. -DGUROBI_DIR=/opt/gurobi952/linux64/
• macOS: cmake .. -DGUROBI_DIR=/Library/gurobi952/macos_universal2/
• Windows: cmake .. -DGUROBI_DIR=C:\\gurobi952\\win64

With the python interface:

$ pip install -r requirements.txt
$ pip install . --upgrade
$ cd examples; py.test -v --cov pyvpsolver

Or simply install from the repository:

$ pip install pyvpsolver

Python interface

The python interface is fully compatible with both python 2 and 3.

Jupyter Notebooks for a quick introduction:

• Simple VBP example
• Simple MVP example

Docker

Docker Setup

Docker is an open platform for building, shipping and running applications. Docker allows VPSolver to run on a large variety of platforms with very little effort.

Install Docker [Docker installation instructions].

Option 1: simply pull VPSolver from Docker repository (without building):

$ docker pull fdabrandao/vpsolver

Option 2: clone VPSolver and build locally:

$ git clone https://github.com/fdabrandao/vpsolver.git vpsolver
$ docker build -t fdabrandao/vpsolver vpsolver

Usage

Directly using the command line interface:

$ docker run --rm -it fdabrandao/vpsolver bash
root@55d14f6b6f32:~# source venv2.7/bin/activate # load a virtualenv
(venv2.7)root@55d14f6b6f32:~# python examples/vpsolver/example_vbp.py
...

or through the VPSolver Web App (example URL: http://172.17.0.60:5555/):

$ docker run --rm -it -p 5555 fdabrandao/vpsolver 
eth0      Link encap:Ethernet  HWaddr 02:42:ac:11:00:3c  
          inet addr:172.17.0.60  Bcast:0.0.0.0  Mask:255.255.0.0
          inet6 addr: fe80::42:acff:fe11:3c/64 Scope:Link
          UP BROADCAST  MTU:1500  Metric:1
          RX packets:2 errors:0 dropped:0 overruns:0 frame:0
          TX packets:2 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:168 (168.0 B)  TX bytes:180 (180.0 B)

URL: http://172.17.0.60:5555/
 * Running on http://0.0.0.0:5555/
...

For more details, please refer to the project wiki.

VPSolver binaries

• $ bin/vpsolver intance.vbp/.mvp: solves a multiple-choice vector packing instance using the method described in [1]. Note: requires Gurobi 5.0.0 or superior;
• $ bin/vbp2afg instance.vbp/.mvp graph.afg: builds an arc-flow graph graph.afg for instance.vbp/.mvp;
• $ bin/afg2mps graph.afg model.mps: creates a MPS model model.mps for graph.afg;
• $ bin/afg2lp graph.afg model.lp: creates a LP model model.lp for graph.afg;
• $ bin/vbpsol graph.afg vars.sol: extracts a vector packing solution from an arc-flow solution vars.sol associated with the graph graph.afg.

Usage:

# 1. Build the arc-flow graph graph.afg for example.vbp:  
$ bin/vbp2afg example.vbp graph.afg  
# 2. Convert the arc-flow graph into a .mps file model.mps:  
$ bin/afg2mps graph.afg model.mps  
# 3. Solve the MIP model and store the solution in vars.sol:
$ scritps/vpsolver_gurobi.sh --mps model.mps --wsol vars.sol
# 4. Extract the vector packing solution:  
$ bin/vbpsol graph.afg vars.sol  

For more details, please refer to the manual.

VPSolver Scripts

VPSolver includes several scripts for solving arc-flow models using different solvers:

• scripts/vpsolver_gurobi.sh: Gurobi
• scripts/vpsolver_cplex.sh: IBM CPLEX
• scripts/vpsolver_coinor.sh: COIN-OR CBC
• scripts/vpsolver_glpk.sh: GLPK
• scripts/vpsolver_scip.sh: SCIP
• scripts/vpsolver_lpsolve.sh: lp_solve

Usage:

$ vpsolver_X.sh --vbp/--mvp instance.vbp/.mvp
$ vpsolver_X.sh --afg graph.afg
$ vpsolver_X.sh --mps/--lp model.mps/.lp
$ vpsolver_X.sh --mps/--lp model.mps/.lp --afg graph.afg

For more details, please refer to the manual.

Folders

• docs: documentation
• scripts: vpsolver scripts
• src: vpsolver source code in C++
• pyvpsolver: pyvpsolver source code in Python
• examples: vpsolver and pyvpsolver examples
• examples/notebooks: jupyter notebooks
• docs/reports: technical reports on the underlying algorithms and models

References

The current solution method is described in:

• [1] Brandão, F. (2016). VPSolver 3: Multiple-choice Vector Packing Solver. arXiv:1602.04876.

VPSolver was proposed in:

• [2] Brandão, F. and Pedroso, J. P. (2016). Bin packing and related problems: General arc-flow formulation with graph compression. Computers & Operations Research, 69:56 – 67.
  doi: http://dx.doi.org/10.1016/j.cor.2015.11.009.

• [3] Brandão, F. and Pedroso, J. P. (2013). Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression. Technical Report DCC-2013-08, Faculdade de Ciências da Universidade do Porto, Universidade do Porto, Portugal. arXiv:1310.6887.

See also:

• [4] Brandão, F. and Pedroso, J. P. (2013). Multiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression. Technical Report DCC-2013-13, Faculdade de Ciências da Universidade do Porto, Universidade do Porto, Portugal. arXiv:1312.3836

• [5] Brandão, F. and Pedroso, J. P. (2013). Cutting Stock with Binary Patterns: Arc-flow Formulation with Graph Compression. Technical Report DCC-2013-09, Faculdade de Ciências da Universidade do Porto, Universidade do Porto, Portugal. arXiv:1502.02899.

• [6] Brandão, F. (2012). Bin Packing and Related Problems: Pattern-Based Approaches. Master’s thesis, Faculdade de Ciências da Universidade do Porto, Portugal.

• [7] Computational results on several benchmark test data sets:
  https://research.fdabrandao.pt/research/vpsolver/results/

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Copyright © 2013-2022 Filipe Brandão < fdabrandao@gmail.com >. All rights reserved.