用來建立模型及解決線性程式模型的引擎。以下範例會解決以下線性程式:
兩個變數,x
和 y
:
0 ≤ x ≤ 10
0 ≤ y ≤ 5
限制:
0 ≤ 2 * x + 5 * y ≤ 10
0 ≤ 10 * x + 3 * y ≤ 20
目標:
盡量提高 x + y
var 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 var constraint = engine.addConstraint(0, 10); constraint.setCoefficient('x', 2); constraint.setCoefficient('y', 5); // Create the constraint: 0 <= 10 * x + 3 * y <= 20 var 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 var 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
內容詳盡的說明文件
addConstraint(lowerBound, upperBound)
在模型中新增線性限制。限制條件的上下限是在建立時定義。變數的係數是透過呼叫 LinearOptimizationConstraint.setCoefficient(variableName, coefficient)
加以定義。
var engine = LinearOptimizationService.createEngine(); // Create a linear constraint with the bounds 0 and 10 var 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);
參數
名稱 | 類型 | 說明 |
---|---|---|
lowerBound | Number | 限制條件下限 |
upperBound | Number | 限制的上限 |
回攻員
LinearOptimizationConstraint
:已建立限制條件
addConstraints(lowerBounds, upperBounds, variableNames, coefficients)
對模型新增批次限制。
var 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]]);
參數
名稱 | 類型 | 說明 |
---|---|---|
lowerBounds | Number[] | 限制的下限 |
upperBounds | Number[] | 限制的上限 |
variableNames | String[][] | 要設定係數的變數名稱 |
coefficients | Number[][] | 設定係數 |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
addVariable(name, lowerBound, upperBound)
將新的連續變數新增至模型。透過名稱參照變數。類型設為 VariableType.CONTINUOUS
。
var engine = LinearOptimizationService.createEngine(); var 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);
參數
名稱 | 類型 | 說明 |
---|---|---|
name | String | 變數的專屬名稱 |
lowerBound | Number | 變數下限 |
upperBound | Number | 變數上限 |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
addVariable(name, lowerBound, upperBound, type)
將新變數新增至模型。透過名稱參照變數。
var engine = LinearOptimizationService.createEngine(); var 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);
參數
名稱 | 類型 | 說明 |
---|---|---|
name | String | 變數的專屬名稱 |
lowerBound | Number | 變數下限 |
upperBound | Number | 變數上限 |
type | VariableType | 變數的類型,可以是 VariableType |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)
將新變數新增至模型。透過名稱參照變數。
var engine = LinearOptimizationService.createEngine(); var 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.
參數
名稱 | 類型 | 說明 |
---|---|---|
name | String | 變數的專屬名稱 |
lowerBound | Number | 變數下限 |
upperBound | Number | 變數上限 |
type | VariableType | 變數的類型,可以是 VariableType |
objectiveCoefficient | Number | 變數的目標係數 |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)
將批次中的變數新增至模型。變數會透過名稱參照。
var 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]);
參數
名稱 | 類型 | 說明 |
---|---|---|
names | String[] | 變數的不重複名稱 |
lowerBounds | Number[] | 變數的下限 |
upperBounds | Number[] | 變數上限 |
types | VariableType[] | 變數的類型,可以是 VariableType |
objectiveCoefficients | Number[] | 變數的目標係數 |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
setMaximization()
設定最佳化方向,盡量提高線性目標函式。
var 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();
回攻員
LinearOptimizationEngine
:線性最佳化引擎
setMinimization()
設定最佳化方向,盡可能減少線性目標函式。
var 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();
回攻員
LinearOptimizationEngine
:線性最佳化引擎
setObjectiveCoefficient(variableName, coefficient)
在線性目標函式中設定變數的係數。
var 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);
參數
名稱 | 類型 | 說明 |
---|---|---|
variableName | String | 要設定係數的變數名稱 |
coefficient | Number | 目標函式中變數的係數 |
回攻員
LinearOptimizationEngine
:線性最佳化引擎
solve()
解決目前的線性程式預設期限 30 秒。傳回找到的解決方案。
var engine = LinearOptimizationService.createEngine(); // Add variables, constraints and define the objective with addVariable(), addConstraint(), etc engine.addVariable('x', 0, 10); // ... // Solve the linear program var solution = engine.solve(); if (!solution.isValid()) { throw 'No solution ' + solution.getStatus(); } Logger.log('Value of x: ' + solution.getVariableValue('x'));
回攻員
LinearOptimizationSolution
:最佳化解決方案
solve(seconds)
解決目前的線性程式問題。傳回找到的解決方案,以及是否為最佳解決方案。
var engine = LinearOptimizationService.createEngine(); // Add variables, constraints and define the objective with addVariable(), addConstraint(), etc engine.addVariable('x', 0, 10); // ... // Solve the linear program var solution = engine.solve(300); if (!solution.isValid()) { throw 'No solution ' + solution.getStatus(); } Logger.log('Value of x: ' + solution.getVariableValue('x'));
參數
名稱 | 類型 | 說明 |
---|---|---|
seconds | Number | 解決問題的期限 (以秒為單位),最長為 300 秒 |
回攻員
LinearOptimizationSolution
:最佳化解決方案