BendersDecompositionSolver

Definition and implementation of the BendersDecompositionSolver class, which implements the CDASolver interface within the SMS++ framework to automate the Benders decomposition of a block-structured problem.

Attached to a suitably structured Block (B), BendersDecompositionSolver keeps the "complicating" (first-stage) Variable of (B) in a master problem and projects out the Variable of each sub-Block, representing the resulting value function as a BendersBFunction. The Benders optimality and feasibility cuts are produced by the BendersBFunction through the standard C05Function interface, so the solver concentrates on the automation layer: detecting the complicating Variable, building one BendersBFunction per sub-Block, assembling the master problem and driving the cut loop.

The Block (B) is assumed to have the following structure:

• the root (B) plays the role of the master: its ColVariable are the complicating Variable, and its Objective and Constraint are the first-stage objective and feasible region;

• each sub-Block is a subproblem, with its own Variable, Objective and Constraint, coupled to the master only through the appearance of (some of) the complicating Variable in (some of) its Constraint.

Two regimes are supported for solving the master problem, selected by a parameter:

• a convex regime, in which the value functions enter the master objective as C05Function and the master is solved by a bundle-type CDASolver, which performs the (stabilized) cutting-plane loop internally;

• a MILP regime, in which the master is a MILP with epigraph Variable and the Benders cuts are added as dynamic Constraint, the solver driving the outer cut loop until no violated cut remains.

The master and the subproblem Solver are instantiated through the Solver factory and configured via Configuration, so that how the master and the subproblems are solved is not hard-wired. See the class documentation for the full description of the assumptions, parameters and solution recovery.

The method is described in

W. van Ackooij, A. Frangioni, W. de Oliveira "Inexact Stabilized Benders' Decomposition Approaches, with Application to Chance-Constrained Problems with Finite Support" Computational Optimization and Applications 65(3), 637-669, 2016

and in

D. Baena, J. Castro, A. Frangioni "Stabilized Benders Methods for Large-scale Combinatorial Optimization, with Application to Data Privacy" Management Science 66(7), 3051-3068, 2020

Getting started

These instructions will let you build BendersDecompositionSolver.

Requirements

• SMS++ core library

It's not a build requirement, but you will need a SMS++ Solver capable of solving the master problem, such as BundleSolver for the convex regime or MILPSolver for the MILP regime.

Build and install with CMake

Configure and build the library with:

mkdir build
cd build
cmake ..
cmake --build .

The library has the same configuration options of SMS++.

Optionally, install the library in the system with:

cmake --install .

Usage with CMake

After the library is built, you can use it in your CMake project with:

find_package(BendersDecompositionSolver)
target_link_libraries(<my_target> SMS++::BendersDecompositionSolver)

Build and install with makefiles

Carefully hand-crafted makefiles have also been developed for those unwilling to use CMake. Makefiles build the executable in-source (in the same directory tree where the code is) as opposed to out-of-source (in the copy of the directory tree constructed in the build/ folder) and therefore it is more convenient when having to recompile often, such as when developing/debugging a new module, as opposed to the compile-and-forget usage envisioned by CMake.

Each executable using BendersDecompositionSolver has to include a "main makefile" of the module, which typically is either makefile-c including all necessary libraries comprised the "core SMS++" one, or makefile-s including all necessary libraries but not the "core SMS++" one (for the common case in which this is used together with other modules that already include them). The makefiles in turn recursively include all the required other makefiles, hence one should only need to edit the "main makefile" for compilation type (C++ compiler and its options) and it all should be good to go. In case some of the external libraries are not at their default location, it should only be necessary to create the ../extlib/makefile-paths out of the extlib/makefile-default-paths-* for your OS * and edit the relevant bits (commenting out all the rest).

Check the SMS++ installation wiki for further details.

Getting help

If you need support, you want to submit bugs or propose a new feature, you can open a new issue.

Contributing

Please read CONTRIBUTING.md for details on our code of conduct, and the process for submitting merge requests to us.

Authors

Current Lead Authors

• Antonio Frangioni
  Dipartimento di Informatica
  Università di Pisa

• Donato Meoli
  Dipartimento di Informatica
  Università di Pisa

Contributors

License

This code is provided free of charge under the GNU Lesser General Public License version 3.0 - see the LICENSE file for details.

Disclaimer

The code is currently provided free of charge under an open-source license. As such, it is provided "as is", without any explicit or implicit warranty that it will properly behave or it will suit your needs. The Authors of the code cannot be considered liable, either directly or indirectly, for any damage or loss that anybody could suffer for having used it. More details about the non-warranty attached to this code are available in the license description file.