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 ≤ 100 ≤ y ≤ 5
Constraints:0 ≤ 2 * x + 5 * y ≤ 100 ≤ 10 * x + 3 * y ≤ 20
Objective:
Maximize x + y
constengine=LinearOptimizationService.createEngine();// Add variables, constraints and define the objective with addVariable(),// addConstraint(), etc Add two variables, 0 <= x <= 10 and 0 <= y <= 5engine.addVariable('x',0,10);engine.addVariable('y',0,5);// Create the constraint: 0 <= 2 * x + 5 * y <= 10letconstraint=engine.addConstraint(0,10);constraint.setCoefficient('x',2);constraint.setCoefficient('y',5);// Create the constraint: 0 <= 10 * x + 3 * y <= 20constraint=engine.addConstraint(0,20);constraint.setCoefficient('x',10);constraint.setCoefficient('y',3);// Set the objective to be x + yengine.setObjectiveCoefficient('x',1);engine.setObjectiveCoefficient('y',1);// Engine should maximize the objectiveengine.setMaximization();// Solve the linear programconstsolution=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.
constengine=LinearOptimizationService.createEngine();// Create a linear constraint with the bounds 0 and 10constconstraint=engine.addConstraint(0,10);// Create a variable so we can add it to the constraintengine.addVariable('x',0,5);// Set the coefficient of the variable in the constraint. The constraint is now:// 0 <= 2 * x <= 5constraint.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.
constengine=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 <= 5engine.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.
constengine=LinearOptimizationService.createEngine();constconstraint=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.
constengine=LinearOptimizationService.createEngine();constconstraint=engine.addConstraint(0,10);// Add a boolean variable (integer >= 0 and <= 1)engine.addVariable('x',0,1,LinearOptimizationService.VariableType.INTEGER);// Add a real (continuous) variableengine.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.
constengine=LinearOptimizationService.createEngine();constconstraint=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) variableengine.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.
constengine=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.
constengine=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 * yengine.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.
constengine=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 * yengine.setObjectiveCoefficient('y',5);// We want to minimizeengine.setMinimization();
Return
Linear — a linear optimization engine
setObjectiveCoefficient(variableName, coefficient)
Sets the coefficient of a variable in the linear objective function.
constengine=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 * yengine.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.
constengine=LinearOptimizationService.createEngine();// Add variables, constraints and define the objective with addVariable(),// addConstraint(), etcengine.addVariable('x',0,10);// ...// Solve the linear programconstsolution=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.
constengine=LinearOptimizationService.createEngine();// Add variables, constraints and define the objective with addVariable(),// addConstraint(), etcengine.addVariable('x',0,10);// ...// Solve the linear programconstsolution=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
