此页面由 Cloud Translation API 翻译。

Class LinearOptimizationEngine

用于对线性规划进行建模和求解的引擎。以下示例会解析以下线性规划：

两个变量 x 和 y：
0 ≤ x ≤ 10
0 ≤ y ≤ 5

限制：
0 ≤ 2 * x + 5 * y ≤ 10
0 ≤ 10 * x + 3 * y ≤ 20

目标：
尽可能提高 x + y

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc Add two variables, 0 <= x <= 10 and 0 <= y <= 5
engine.addVariable('x', 0, 10);
engine.addVariable('y', 0, 5);

// Create the constraint: 0 <= 2 * x + 5 * y <= 10
let constraint = engine.addConstraint(0, 10);
constraint.setCoefficient('x', 2);
constraint.setCoefficient('y', 5);

// Create the constraint: 0 <= 10 * x + 3 * y <= 20
constraint = engine.addConstraint(0, 20);
constraint.setCoefficient('x', 10);
constraint.setCoefficient('y', 3);

// Set the objective to be x + y
engine.setObjectiveCoefficient('x', 1);
engine.setObjectiveCoefficient('y', 1);

// Engine should maximize the objective
engine.setMaximization();

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  Logger.log(`No solution ${solution.getStatus()}`);
} else {
  Logger.log(`Value of x: ${solution.getVariableValue('x')}`);
  Logger.log(`Value of y: ${solution.getVariableValue('y')}`);
}

方法

方法	返回类型	简介
`addConstraint(lowerBound, upperBound)`	`LinearOptimizationConstraint`	在模型中添加新的线性约束条件。
`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`	`LinearOptimizationEngine`	向模型批量添加约束条件。
`addVariable(name, lowerBound, upperBound)`	`LinearOptimizationEngine`	向模型添加新的连续变量。
`addVariable(name, lowerBound, upperBound, type)`	`LinearOptimizationEngine`	向模型添加新变量。
`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`	`LinearOptimizationEngine`	向模型添加新变量。
`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`	`LinearOptimizationEngine`	将变量批量添加到模型。
`setMaximization()`	`LinearOptimizationEngine`	将优化方向设置为最大限度地提高线性目标函数的值。
`setMinimization()`	`LinearOptimizationEngine`	将优化方向设置为使线性目标函数最小化。
`setObjectiveCoefficient(variableName, coefficient)`	`LinearOptimizationEngine`	设置线性目标函数中变量的系数。
`solve()`	`LinearOptimizationSolution`	使用默认截止期限 30 秒求解当前线性规划问题。
`solve(seconds)`	`LinearOptimizationSolution`	求解当前线性规划。

详细文档

`addConstraint(lowerBound, upperBound)`

在模型中添加新的线性约束条件。约束条件的上限和下限是在创建时定义的。变量的系数是通过调用 LinearOptimizationConstraint.setCoefficient(variableName, coefficient) 定义的。

const engine = LinearOptimizationService.createEngine();

// Create a linear constraint with the bounds 0 and 10
const constraint = engine.addConstraint(0, 10);

// Create a variable so we can add it to the constraint
engine.addVariable('x', 0, 5);

// Set the coefficient of the variable in the constraint. The constraint is now:
// 0 <= 2 * x <= 5
constraint.setCoefficient('x', 2);

参数

名称	类型	说明
`lowerBound`	`Number`	约束条件的下限
`upperBound`	`Number`	约束条件的上限

LinearOptimizationConstraint - 创建的约束条件

`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`

向模型批量添加约束条件。

const engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >=
// 0 and <= 100) variable 'y'.
engine.addVariables(
    ['x', 'y'],
    [0, 0],
    [1, 100],
    [
      LinearOptimizationService.VariableType.INTEGER,
      LinearOptimizationService.VariableType.CONTINUOUS,
    ],
);

// Adds two constraints:
//   0 <= x + y <= 3
//   1 <= 10 * x - y <= 5
engine.addConstraints(
    [0.0, 1.0],
    [3.0, 5.0],
    [
      ['x', 'y'],
      ['x', 'y'],
    ],
    [
      [1, 1],
      [10, -1],
    ],
);

参数

名称	类型	说明
`lowerBounds`	`Number[]`	约束条件的下限
`upperBounds`	`Number[]`	约束条件的上限
`variableNames`	`String[][]`	要设置系数的变量的名称
`coefficients`	`Number[][]`	要设置的系数

LinearOptimizationEngine - 线性优化引擎

`addVariable(name, lowerBound, upperBound)`

向模型添加新的连续变量。系统会通过变量名称引用该变量。类型设置为 VariableType.CONTINUOUS。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

参数

名称	类型	说明
`name`	`String`	变量的唯一名称
`lowerBound`	`Number`	变量的下限
`upperBound`	`Number`	变量的上限

LinearOptimizationEngine - 线性优化引擎

`addVariable(name, lowerBound, upperBound, type)`

向模型添加新变量。系统会通过变量名称引用该变量。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable
engine.addVariable(
    'y',
    0,
    100,
    LinearOptimizationService.VariableType.CONTINUOUS,
);

参数

名称	类型	说明
`name`	`String`	变量的唯一名称
`lowerBound`	`Number`	变量的下限
`upperBound`	`Number`	变量的上限
`type`	`VariableType`	变量类型，可以是 `VariableType` 之一

LinearOptimizationEngine - 线性优化引擎

`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`

向模型添加新变量。系统会通过变量名称引用该变量。

const engine = LinearOptimizationService.createEngine();
const constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable(
    'x',
    0,
    1,
    LinearOptimizationService.VariableType.INTEGER,
    2,
);
// The objective is now 2 * x.

// Add a real (continuous) variable
engine.addVariable(
    'y',
    0,
    100,
    LinearOptimizationService.VariableType.CONTINUOUS,
    -5,
);
// The objective is now 2 * x - 5 * y.

参数

名称	类型	说明
`name`	`String`	变量的唯一名称
`lowerBound`	`Number`	变量的下限
`upperBound`	`Number`	变量的上限
`type`	`VariableType`	变量类型，可以是 `VariableType` 之一
`objectiveCoefficient`	`Number`	变量的目标系数

LinearOptimizationEngine - 线性优化引擎

`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`

将变量批量添加到模型。系统会按名称引用变量。

const engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >=0
// and <= 100) variable 'y'.
engine.addVariables(
    ['x', 'y'],
    [0, 0],
    [1, 100],
    [
      LinearOptimizationService.VariableType.INTEGER,
      LinearOptimizationService.VariableType.CONTINUOUS,
    ],
);

参数

名称	类型	说明
`names`	`String[]`	变量的唯一名称
`lowerBounds`	`Number[]`	变量的下限
`upperBounds`	`Number[]`	变量的上限
`types`	`VariableType[]`	变量的类型，可以是 `VariableType` 之一
`objectiveCoefficients`	`Number[]`	变量的目标系数

LinearOptimizationEngine - 线性优化引擎

`setMaximization()`

将优化方向设置为最大限度地提高线性目标函数的值。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to maximize.
engine.setMaximization();

LinearOptimizationEngine - 线性优化引擎

`setMinimization()`

将优化方向设置为使线性目标函数最小化。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to minimize
engine.setMinimization();

LinearOptimizationEngine - 线性优化引擎

`setObjectiveCoefficient(variableName, coefficient)`

设置线性目标函数中变量的系数。

const engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

参数

名称	类型	说明
`variableName`	`String`	要设置系数的变量的名称
`coefficient`	`Number`	目标函数中变量的系数

LinearOptimizationEngine - 线性优化引擎

`solve()`

求解当前线性规划问题，默认截止期限为 30 秒。返回找到的解决方案。

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve();
if (!solution.isValid()) {
  throw `No solution ${solution.getStatus()}`;
}
Logger.log(`Value of x: ${solution.getVariableValue('x')}`);

LinearOptimizationSolution - 优化解

`solve(seconds)`

求解当前线性规划。返回找到的解决方案，以及它是否为最佳解决方案。

const engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(),
// addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
const solution = engine.solve(300);
if (!solution.isValid()) {
  throw `No solution ${solution.getStatus()}`;
}
Logger.log(`Value of x: ${solution.getVariableValue('x')}`);

参数

名称	类型	说明
`seconds`	`Number`	解决问题的截止时间（以秒为单位）；截止时间上限为 300 秒

LinearOptimizationSolution - 优化解