80 lines
2.8 KiB
Markdown
80 lines
2.8 KiB
Markdown
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# Linear Programming (LP) and Integer Programming (IP) Solver
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Linear optimization problems are common throughout Google, and the Operations
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Research team has a few ways to help with them.
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These models have the form:
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$$\begin{array}{lll}
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(P) & \max & cx\\
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& s.t. & L\leq Ax\leq U\\
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& & l\leq x\leq u\\
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& &x_i\in\mathbb{Z}\quad\forall i\in I
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\end{array}$$
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Where $$A\in\mathbb{R}^{m\times n}$$, $$l,u,c\in\mathbb{R}^n$$,
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$$L,U\in\mathbb{R}^m$$, $$n,m\in\mathbb{N}^+$$ and $$I\subseteq\{1,\ldots,n\}$$.
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This module provides:
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* The `MPModelRequest` Proto API (in `linear_solver.proto`) for modeling an
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optimization problem.
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* The function `SolveMPModel()` (in `solve_mp_model.h`) for solving an
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optimization problem with a solver (Glop, Bop, Sat, SCIP, Gurobi etc.)
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* `ModelBuilder` (in `model_builder.h`) and similar classes in Python and Java
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to help construct an `MPModelRequest` (e.g. to provide linear expressions).
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* `MPSolver` which is no longer in development. `MPSolver` is largely
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interoperable with the `MPModelRequest` API, although the features supported
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are not identical.
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To begin, skim
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* [linear_solver.proto](../linear_solver/linear_solver.proto):
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Specifically, look at `MPModelProto`. This gives a succinct description of
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what problems can be solved.
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* [solve_mp_model.h](../linear_solver/solve_mp_model.h):
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This file contains the key functions to run various solvers.
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## Available solvers
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Each *\*_interface.cc* file corresponds to one of the solver accessible
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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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* Google's PLDP solver: [pdlp_interface.cc](../linear_solver/pdlp_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)
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* CPLEX (MIP) solver: [cplex_interface.cc](../linear_solver/cplex_interface.cc)
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* GLPK (MIP) solver: [glpk_interface.cc](../linear_solver/glpk_interface.cc)
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* Xpress (MIP) solver: [xpress_interface.cc](../linear_solver/xpress_interface.cc)
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## Wrappers
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* [python](python): the SWIG code that makes the wrapper available in Python,
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and its unit tests.
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* [java](java): the SWIG code that makes the wrapper available in Java,
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and its unit tests.
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* [csharp](csharp): the SWIG code that makes the wrapper available in C#,
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and its unit tests.
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## Samples
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You can find some canonical examples in [samples](../linear_solver/samples/)
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