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In diesem Beispiel wird gezeigt, wie Sie die Ergebnisse eines einfachen linearen Programms (LP) mit MathOpt erstellen, lösen und untersuchen. Informationen zur Installation von OR-Tools finden Sie in der Installationsanleitung. Zusätzliche Hinweise zum Erstellen und Ausführen aus der Quelle werden bis zum Ende verschoben.
MathOpt-Modell erstellen
In der Quelle müssen Sie in der Regel nur eine einzelne MathOpt-Abhängigkeit hinzufügen:
Das folgende lineare Programmierproblem wird in diesem Leitfaden verwendet und mit GLOP gelöst.
$$\begin{aligned}
&\max &x + 2 \cdot y\\
&\text{subject to} &x + y &\leq 1.5 \\
&&-1 \leq x &\leq 1.5 \\
&&0 \leq y &\leq 1
\end{aligned}$$
Erstellen Sie zuerst das Modell:
Python
# Build the model.
model = mathopt.Model(name="getting_started_lp")
x = model.add_variable(lb=-1.0, ub=1.5, name="x")
y = model.add_variable(lb=0.0, ub=1.0, name="y")
model.add_linear_constraint(x + y <= 1.5)
model.maximize(x + 2 * y)
C++
// Build the model.
namespace math_opt = ::operations_research::math_opt;
math_opt::Model lp_model("getting_started_lp");
const math_opt::Variable x = lp_model.AddContinuousVariable(-1.0, 1.5, "x");
const math_opt::Variable y = lp_model.AddContinuousVariable(0.0, 1.0, "y");
lp_model.AddLinearConstraint(x + y <= 1.5, "c");
lp_model.Maximize(x + 2 * y);
Lösung lösen und untersuchen
Als Nächstes legen Sie die Parameter für die Lösung fest. Die Lösung von Optimierungsmodellen
mit MathOpt lässt sich hochgradig konfigurieren. Es gibt lösungsunabhängige Parameter (z.B. Ausgabe aktivieren), löserspezifische Parameter (z.B. GlopParameters.Optimization_rule), Parameter, die von Eigenschaften des Modells (z.B. Verzweigungspriorität) abhängen, einen Callback für die Solver-Logs und einen Callback zum Überwachen und Steuern der Optimierung. Mit dem folgenden Code werden die Solver-Logs aktiviert.
Python
# Set parameters, e.g. turn on logging.
params = mathopt.SolveParameters(enable_output=True)
C++
// Set parameters, e.g. turn on logging.
math_opt::SolveArguments args;
args.parameters.enable_output = true;
Verwenden Sie die Funktion Solve(), um das Problem mit GLOP, dem unidirektionalen LP-Resolver von Google, zu lösen.
Python
# Solve and ensure an optimal solution was found with no errors.
# (mathopt.solve may raise a RuntimeError on invalid input or internal solver
# errors.)
result = mathopt.solve(model, mathopt.SolverType.GLOP, params=params)
if result.termination.reason != mathopt.TerminationReason.OPTIMAL:
raise RuntimeError(f"model failed to solve: {result.termination}")
C++
// Solve and ensure an optimal solution was found with no errors.
const absl::StatusOr<math_opt::SolveResult> result =
math_opt::Solve(lp_model, math_opt::SolverType::kGlop, args);
CHECK_OK(result.status());
CHECK_OK(result->termination.EnsureIsOptimal());
Untersuchen Sie zuletzt den Zielwert der optimalen Lösung und die optimalen Variablenwerte. Da der Beendigungsgrund optimal war, kann davon ausgegangen werden, dass diese Werte vorhanden sind. Aus anderen Beendigungsgründen (z. B. unmöglich oder unbegrenzt) kann das Aufrufen dieser Methoden jedoch CHECK fail (in C++) oder raise an exception (in Python) sein.
Python
# Print some information from the result.
print("MathOpt solve succeeded")
print("Objective value:", result.objective_value())
print("x:", result.variable_values()[x])
print("y:", result.variable_values()[y])
C++
// Print some information from the result.
std::cout << "MathOpt solve succeeded" << std::endl;
std::cout << "Objective value: " << result->objective_value() << std::endl;
std::cout << "x: " << result->variable_values().at(x) << std::endl;
std::cout << "y: " << result->variable_values().at(y) << std::endl;
Hinweise zum Erstellen und Ausführen von Code mit Bazel
Wenn Sie MathOpt aus der Quelle mit bazel erstellen, benötigt dieses Beispiel die folgenden Abhängigkeiten im Build-Ziel:
[null,null,["Zuletzt aktualisiert: 2024-08-08 (UTC)."],[[["\u003cp\u003eThis guide demonstrates how to build, solve, and analyze a simple linear program (LP) using MathOpt, Google's optimization modeling library.\u003c/p\u003e\n"],["\u003cp\u003eThe example uses GLOP, Google's simplex-based LP solver, to find the optimal solution for a given problem with constraints.\u003c/p\u003e\n"],["\u003cp\u003eThe guide provides code snippets in both Python and C++ for model building, parameter setting, solving the LP, and inspecting the results.\u003c/p\u003e\n"],["\u003cp\u003eBuilding MathOpt from source using Bazel requires specific dependencies to be included in the build target for both Python and C++ projects.\u003c/p\u003e\n"],["\u003cp\u003eWhen building with Bazel, ensure the GLOP solver is enabled using build flags, and consider disabling unused solvers for smaller binaries.\u003c/p\u003e\n"]]],["The core process involves building a linear programming (LP) model, solving it, and inspecting the results using MathOpt. First, a model is built by defining variables (x, y) with bounds and adding a linear constraint. Next, solver parameters are set, and the model is solved using GLOP. Finally, the solution's objective value and variable values are retrieved and printed. When using Bazel to build the source code, MathOpt and Glop dependencies must be added to the build target.\n"],null,["# Getting Started\n\nThis example shows how to build, solve, and explore the results of a simple\nlinear program (LP) using MathOpt. Information about installing OR-Tools is\navailable in the [install guide](/optimization/install). Additional notes on how to build and run\nfrom [source](https://github.com/google/or-tools/tree/stable/ortools/math_opt) are deferred to the end.\n\nBuild a MathOpt model\n---------------------\n\nIn your source, you typically *only* need to add a single MathOpt dependency: \n\n### Python\n\n```python\nfrom ortools.math_opt.python import mathopt\n```\n\n### C++\n\n```c++\n#include \u003ciostream\u003e\n#include \u003costream\u003e\n\n#include \"absl/log/check.h\"\n#include \"absl/status/statusor.h\"\n#include \"ortools/base/init_google.h\"\n#include \"ortools/math_opt/cpp/math_opt.h\"\n```\n\nThe following linear programming problem is used throughout this guide, and it\nis solved with GLOP. \n$$\\\\begin{aligned} \\&\\\\max \\&x + 2 \\\\cdot y\\\\\\\\ \\&\\\\text{subject to} \\&x + y \\&\\\\leq 1.5 \\\\\\\\ \\&\\&-1 \\\\leq x \\&\\\\leq 1.5 \\\\\\\\ \\&\\&0 \\\\leq y \\&\\\\leq 1 \\\\end{aligned}$$\n\nFirst, build the model: \n\n### Python\n\n```python\n# Build the model.\nmodel = mathopt.Model(name=\"getting_started_lp\")\nx = model.add_variable(lb=-1.0, ub=1.5, name=\"x\")\ny = model.add_variable(lb=0.0, ub=1.0, name=\"y\")\nmodel.add_linear_constraint(x + y \u003c= 1.5)\nmodel.maximize(x + 2 * y)\n```\n\n### C++\n\n```c++\n// Build the model.\nnamespace math_opt = ::operations_research::math_opt;\nmath_opt::Model lp_model(\"getting_started_lp\");\nconst math_opt::Variable x = lp_model.AddContinuousVariable(-1.0, 1.5, \"x\");\nconst math_opt::Variable y = lp_model.AddContinuousVariable(0.0, 1.0, \"y\");\nlp_model.AddLinearConstraint(x + y \u003c= 1.5, \"c\");\nlp_model.Maximize(x + 2 * y);\n```\n\nSolve and inspect the solution\n------------------------------\n\nNext, set the parameters for the solve. Solving optimization models with MathOpt\nis highly configurable. There are solver-independent parameters (e.g. enable\noutput), solver-specific parameters (e.g. GlopParameters.optimization_rule),\nparameters that depend on properties of the model (e.g. branching priority), a\ncallback for the solver logs, and a callback to monitor and control the\noptimization. The following code turns the solver logs on. \n\n### Python\n\n```python\n# Set parameters, e.g. turn on logging.\nparams = mathopt.SolveParameters(enable_output=True)\n```\n\n### C++\n\n```c++\n// Set parameters, e.g. turn on logging.\nmath_opt::SolveArguments args;\nargs.parameters.enable_output = true;\n```\n\nTo solve the problem using GLOP, Google's simplex-based LP solver, use the\n`Solve()` function. \n\n### Python\n\n```python\n# Solve and ensure an optimal solution was found with no errors.\n# (mathopt.solve may raise a RuntimeError on invalid input or internal solver\n# errors.)\nresult = mathopt.solve(model, mathopt.SolverType.GLOP, params=params)\nif result.termination.reason != mathopt.TerminationReason.OPTIMAL:\n raise RuntimeError(f\"model failed to solve: {result.termination}\")\n```\n\n### C++\n\n```c++\n// Solve and ensure an optimal solution was found with no errors.\nconst absl::StatusOr\u003cmath_opt::SolveResult\u003e result =\n math_opt::Solve(lp_model, math_opt::SolverType::kGlop, args);\nCHECK_OK(result.status());\nCHECK_OK(result-\u003etermination.EnsureIsOptimal());\n```\n\nLast, inspect the objective value of the optimal solution and the optimal\nvariable values. Note that because the termination reason was optimal, it is\nsafe to assume these values exist, but for other termination reasons (for\nexample, infeasible or unbounded) calling these methods can `CHECK fail` (in\nC++) or `raise an exception` (in Python). \n\n### Python\n\n```python\n# Print some information from the result.\nprint(\"MathOpt solve succeeded\")\nprint(\"Objective value:\", result.objective_value())\nprint(\"x:\", result.variable_values()[x])\nprint(\"y:\", result.variable_values()[y])\n```\n\n### C++\n\n```c++\n// Print some information from the result.\nstd::cout \u003c\u003c \"MathOpt solve succeeded\" \u003c\u003c std::endl;\nstd::cout \u003c\u003c \"Objective value: \" \u003c\u003c result-\u003eobjective_value() \u003c\u003c std::endl;\nstd::cout \u003c\u003c \"x: \" \u003c\u003c result-\u003evariable_values().at(x) \u003c\u003c std::endl;\nstd::cout \u003c\u003c \"y: \" \u003c\u003c result-\u003evariable_values().at(y) \u003c\u003c std::endl;\n```\n\nNotes on building and running your code with **Bazel**\n------------------------------------------------------\n\nIf you are building MathOpt from source using\n[bazel](https://bazel.build/), this example needs the following\ndependencies in the build target: \n\n### Python\n\n```python\n\"//util/operations_research/math_opt/python:mathopt\"\n```\n\n### C++\n\n```c++\n\"//util/operations_research/math_opt/cpp:math_opt\"\n\"//util/operations_research/math_opt/solvers:glop_solver\"\n```\n| **Note:** If you are using Python, you need to pass the flag `--with_glop=true` when building your target so that the solver is compiled. By default, many of the solvers in OR-Tools are enabled. We recommend disabling the solvers you are not using to get smaller binaries and avoid unnecessary dependencies. For example, you can also pass the flags `--with_scip=false --with_cp_sat=false\n| --with_glpk=false --with_glop=true`.\n\nTo run your code, the following bazel command builds and runs your target. \n\n### Python\n\n```python\nbazel run path/to/you:target --with_scip=false --with_cp_sat=false\n--with_glpk=false --with_glop=true -- --your_flags\n```\n\n### C++\n\n```c++\nbazel run path/to/you:target -- --your_flags\n```"]]
