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
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 Linear
.
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 |
---|---|---|
lower | Number | lower bound of the constraint |
upper | Number | upper bound of the constraint |
Return
Linear
— 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 |
---|---|---|
lower | Number[] | lower bounds of the constraints |
upper | Number[] | upper bounds of the constraints |
variable | String[][] | the names of variables for which the coefficients are being set |
coefficients | Number[][] | coefficients being set |
Return
Linear
— 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 Variable
.
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 |
lower | Number | lower bound of the variable |
upper | Number | upper bound of the variable |
Return
Linear
— 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 |
lower | Number | lower bound of the variable |
upper | Number | upper bound of the variable |
type | Variable | type of the variable, can be one of Variable |
Return
Linear
— 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 |
lower | Number | lower bound of the variable |
upper | Number | upper bound of the variable |
type | Variable | type of the variable, can be one of Variable |
objective | Number | objective coefficient of the variable |
Return
Linear
— 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 |
lower | Number[] | lower bounds of the variables |
upper | Number[] | upper bounds of the variables |
types | Variable | types of the variables, can be one of Variable |
objective | Number[] | objective coefficients of the variables |
Return
Linear
— 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
Linear
— 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
Linear
— 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 |
---|---|---|
variable | String | name of variable for which the coefficient is being set |
coefficient | Number | coefficient of the variable in the objective function |
Return
Linear
— 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
Linear
— 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
Linear
— solution of the optimization