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Python since 3.8 no longer links to the interpreter library, so symbols like `PyExc_AttributeError` will be undefined at link time. This causes build failures when shared libraries are linked with `-Wl,--no-undefined`. Use `TYPE MODULE` for python extension modules, which allows to specify distinct flags via CMAKE_MODULE_LINKER_FLAGS vs CMAKE_SHARED_LINKER_FLAGS. (The same is already used by `pybind11_add_module(... MODULE ...)`). Fixes #3258.
Linear Programming (LP) and Integer Programming (IP) Solver
Linear optimization problems are common throughout Google, and the Operations Research team has a few ways to help with them.
These models have the form: $$\begin{array}{lll} (P) & \max & cx\ & s.t. & L\leq Ax\leq U\ & & l\leq x\leq u\ & &x_i\in\mathbb{Z}\quad\forall i\in I \end{array}$$
Where A\in\mathbb{R}^{m\times n}, l,u,c\in\mathbb{R}^n,
L,U\in\mathbb{R}^m, n,m\in\mathbb{N}^+ and I\subseteq\{1,\ldots,n\}.
This module provides an unified wrapper (MPSolver) around different linear and integer solvers (Glop, Bop, Sat, SCIP, Gurobi etc.).
To begin, skim
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linear_solver.h: the point of entry for the MPSolver wrapper that provides a simple and unified interface to several linear programming and mixed integer programming solvers.
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linear_solver.cc: the C++ code of the MPSolver wrapper that is common to all solvers accessible through the wrapper.
Parameters and Solution
MPSolver uses a proto interface MPModelProto.
You can find the protocol buffer definition here:
- linear_solver.proto: MPSolver parameters, model and solution messages.
Available solvers
Each *_interface.cc file corresponds to one of the solver accessible through the wrapper.
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Google's BOP (boolean) solver: [bop_interface.cc] (../linear_solver/bop_interface.cc)
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Google's GLOP (lp) solver: [glop_interface.cc] (../linear_solver/glop_interface.cc)
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Gurobi (MIP) solver: [gurobi_interface.cc] (../linear_solver/gurobi_interface.cc)
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SCIP (MIP) solver: [scip_interface.cc] (../linear_solver/scip_interface.cc)
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Google's CP-SAT Solver: [sat_interface.cc] (../linear_solver/sat_interface.cc)
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Coin-OR Cbc (MIP) solver: [cbc_interface.cc] (../linear_solver/cbc_interface.cc)
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Coin-OR Clp (LP) solver: [clp_interface.cc] (../linear_solver/clp_interface.cc)
Wrappers
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python: the SWIG code that makes the wrapper available in Python, and its unit tests.
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java: the SWIG code that makes the wrapper available in Java, and its unit tests.
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csharp: the SWIG code that makes the wrapper available in C#, and its unit tests.
Samples
You can find some canonical examples in samples