# 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
`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

// 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
`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]);

//   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
`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();

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

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

#### Parameters

NameTypeDescription
`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();

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

// Add a real (continuous) variable

#### Parameters

NameTypeDescription
`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();

// 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
`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

NameTypeDescription
`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.

// 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
`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();

// ...

// 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
`seconds``Number`deadline for solving the problem, in seconds; the maximum deadline is 300 seconds

#### Return

`LinearOptimizationSolution` — solution of the optimization