Class 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 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'));
}

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).

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);

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.

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]]);

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.

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);

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.

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);

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.

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.

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.

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

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.

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();

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.
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.

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);

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.

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'));

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();

// 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'));

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