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# Class LinearOptimizationEngine

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

var engine = LinearOptimizationService.createEngine();

// Add two variables, 0 <= x <= 10 and 0 <= y <= 5

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

// Create the constraint: 0 <= 10 * x + 3 * y <= 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'));
}

### Methods

MethodReturn typeBrief description
setMaximization()LinearOptimizationEngineSets the optimization direction to maximizing the linear objective function.
setMinimization()LinearOptimizationEngineSets the optimization direction to minimizing the linear objective function.
setObjectiveCoefficient(variableName, coefficient)LinearOptimizationEngineSets the coefficient of a variable in the linear objective function.
solve()LinearOptimizationSolutionSolves the current linear program with the default deadline of 30 seconds.
solve(seconds)LinearOptimizationSolutionSolves the current linear program.

## Detailed documentation

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).

var engine = LinearOptimizationService.createEngine();

// Create a linear constraint with the bounds 0 and 10

// Create a variable so we can add it to the constraint

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

#### Parameters

NameTypeDescription
lowerBoundNumberlower bound of the constraint
upperBoundNumberupper bound of the constraint

#### Return

LinearOptimizationConstraint — the constraint created

Adds constraints in batch to the model.

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]);

//   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

NameTypeDescription
lowerBoundsNumber[]lower bounds of the constraints
upperBoundsNumber[]upper bounds of the constraints
variableNamesString[][]the names of variables for which the coefficients are being set
coefficientsNumber[][]coefficients being set

#### Return

LinearOptimizationEngine — a linear optimization engine

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

var engine = LinearOptimizationService.createEngine();

// Add a boolean variable (integer >= 0 and <= 1)

// Add a real (continuous) variable. Notice the lack of type specification.

#### Parameters

NameTypeDescription
nameStringunique name of the variable
lowerBoundNumberlower bound of the variable
upperBoundNumberupper bound of the variable

#### Return

LinearOptimizationEngine — a linear optimization engine

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

var engine = LinearOptimizationService.createEngine();

// Add a boolean variable (integer >= 0 and <= 1)

// Add a real (continuous) variable

#### Parameters

NameTypeDescription
nameStringunique name of the variable
lowerBoundNumberlower bound of the variable
upperBoundNumberupper bound of the variable
typeVariableTypetype 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.

var engine = LinearOptimizationService.createEngine();

// Add a boolean variable (integer >= 0 and <= 1)
// The objective is now 2 * x.

// Add a real (continuous) variable
// The objective is now 2 * x - 5 * y.

#### Parameters

NameTypeDescription
nameStringunique name of the variable
lowerBoundNumberlower bound of the variable
upperBoundNumberupper bound of the variable
typeVariableTypetype of the variable, can be one of VariableType
objectiveCoefficientNumberobjective 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.

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]);

#### Parameters

NameTypeDescription
namesString[]unique names of the variables
lowerBoundsNumber[]lower bounds of the variables
upperBoundsNumber[]upper bounds of the variables
typesVariableType[]types of the variables, can be one of VariableType
objectiveCoefficientsNumber[]objective coefficients of the variables

#### Return

LinearOptimizationEngine — a linear optimization engine

### setMaximization()

Sets the optimization direction to maximizing the linear objective function.

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.

// 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.

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.

// 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.

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.

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

#### Parameters

NameTypeDescription
variableNameStringname of variable for which the coefficient is being set
coefficientNumbercoefficient 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.

var engine = LinearOptimizationService.createEngine();

// ...

// Solve the linear program
var 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.

var engine = LinearOptimizationService.createEngine();

// ...

// 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'));

#### Parameters

NameTypeDescription
secondsNumberdeadline for solving the problem, in seconds; the maximum deadline is 300 seconds

#### Return

LinearOptimizationSolution — solution of the optimization