Class LinearOptimizationEngine

AI-generated Key Takeaways

• LinearOptimizationEngine is used to model and solve linear programs by defining variables, constraints, and objectives.

• You can add variables with specified bounds and types using methods like addVariable and addVariables.

• Constraints with defined bounds can be added using addConstraint or addConstraints, and variable coefficients within these constraints are set separately.

• The objective function is defined by setting the coefficient for each variable using setObjectiveCoefficient.

• The optimization direction can be set to maximization or minimization using setMaximization or setMinimization.

• The solve() method is used to find the solution to the defined linear program.

LinearOptimizationEngine

The engine used to model and solve a linear program. The example below solves the following linear program:

Two variables, x and y:
0 ≤ x ≤ 10
0 ≤ y ≤ 5

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

Objective:
Maximize 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')}`);
}

Methods

Method	Return type	Brief description
addConstraint(lowerBound, upperBound)	LinearOptimizationConstraint	Adds a new linear constraint in the model.
addConstraints(lowerBounds, upperBounds, variableNames, coefficients)	LinearOptimizationEngine	Adds constraints in batch to the model.
addVariable(name, lowerBound, upperBound)	LinearOptimizationEngine	Adds a new continuous variable to the model.
addVariable(name, lowerBound, upperBound, type)	LinearOptimizationEngine	Adds a new variable to the model.
addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)	LinearOptimizationEngine	Adds a new variable to the model.
addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)	LinearOptimizationEngine	Adds variables in batch to the model.
setMaximization()	LinearOptimizationEngine	Sets the optimization direction to maximizing the linear objective function.
setMinimization()	LinearOptimizationEngine	Sets the optimization direction to minimizing the linear objective function.
setObjectiveCoefficient(variableName, coefficient)	LinearOptimizationEngine	Sets the coefficient of a variable in the linear objective function.
solve()	LinearOptimizationSolution	Solves the current linear program with the default deadline of 30 seconds.
solve(seconds)	LinearOptimizationSolution	Solves the current linear program.

Detailed documentation

addConstraint(lowerBound, upperBound)

Adds a new linear constraint in the model. The upper and lower bound of the constraint are defined at creation time. Coefficients for the variables are defined via calls to LinearOptimizationConstraint.setCoefficient(variableName, coefficient).

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);

Parameters

Name	Type	Description
lowerBound	Number	lower bound of the constraint
upperBound	Number	upper bound of the constraint

Return

LinearOptimizationConstraint — the constraint created

---

addConstraints(lowerBounds, upperBounds, variableNames, coefficients)

Adds constraints in batch to the model.

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],
    ],
);

Parameters

Name	Type	Description
lowerBounds	Number[]	lower bounds of the constraints
upperBounds	Number[]	upper bounds of the constraints
variableNames	String[][]	the names of variables for which the coefficients are being set
coefficients	Number[][]	coefficients being set

Return

LinearOptimizationEngine — a linear optimization engine

---

addVariable(name, lowerBound, upperBound)

Adds a new continuous variable to the model. The variable is referenced by its name. The type is set to 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);

Parameters

Name	Type	Description
name	String	unique name of the variable
lowerBound	Number	lower bound of the variable
upperBound	Number	upper bound of the variable

Return

LinearOptimizationEngine — a linear optimization engine

---

addVariable(name, lowerBound, upperBound, type)

Adds a new variable to the model. The variable is referenced by its name.

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,
);

Parameters

Name	Type	Description
name	String	unique name of the variable
lowerBound	Number	lower bound of the variable
upperBound	Number	upper bound of the variable
type	VariableType	type of the variable, can be one of VariableType

Return

LinearOptimizationEngine — a linear optimization engine

---

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

Adds a new variable to the model. The variable is referenced by its name.

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.

Parameters

Name	Type	Description
name	String	unique name of the variable
lowerBound	Number	lower bound of the variable
upperBound	Number	upper bound of the variable
type	VariableType	type of the variable, can be one of VariableType
objectiveCoefficient	Number	objective coefficient of the variable

Return

LinearOptimizationEngine — a linear optimization engine

---

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

Adds variables in batch to the model. The variables are referenced by their names.

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,
    ],
);

Parameters

Name	Type	Description
names	String[]	unique names of the variables
lowerBounds	Number[]	lower bounds of the variables
upperBounds	Number[]	upper bounds of the variables
types	VariableType[]	types of the variables, can be one of VariableType
objectiveCoefficients	Number[]	objective coefficients of the variables

Return

LinearOptimizationEngine — a linear optimization engine

---

setMaximization()

Sets the optimization direction to maximizing the linear objective function.

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();

Return

LinearOptimizationEngine — a linear optimization engine

---

setMinimization()

Sets the optimization direction to minimizing the linear objective function.

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();

Return

LinearOptimizationEngine — a linear optimization engine

---

setObjectiveCoefficient(variableName, coefficient)

Sets the coefficient of a variable in the linear objective function.

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);

Parameters

Name	Type	Description
variableName	String	name of variable for which the coefficient is being set
coefficient	Number	coefficient of the variable in the objective function

Return

LinearOptimizationEngine — a linear optimization engine

---

solve()

Solves the current linear program with the default deadline of 30 seconds. Returns the solution found.

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')}`);

Return

LinearOptimizationSolution — solution of the optimization

---

solve(seconds)

Solves the current linear program. Returns the solution found. and if it is an optimal solution.

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')}`);

Parameters

Name	Type	Description
seconds	Number	deadline for solving the problem, in seconds; the maximum deadline is 300 seconds

Return

LinearOptimizationSolution — solution of the optimization