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.
`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.
`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

`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

`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

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Last updated February 26, 2015.