Linear
Optimization
Engine
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
| Method | Return type | Brief description |
|---|---|---|
Linear
|
Adds a new linear constraint in the model. | |
Linear
|
Adds constraints in batch to the model. | |
Linear
|
Adds a new continuous variable to the model. | |
Linear
|
Adds a new variable to the model. | |
Linear
|
Adds a new variable to the model. | |
Linear
|
Adds variables in batch to the model. | |
Linear
|
Sets the optimization direction to maximizing the linear objective function. | |
Linear
|
Sets the optimization direction to minimizing the linear objective function. | |
Linear
|
Sets the coefficient of a variable in the linear objective function. | |
Linear
|
Solves the current linear program with the default deadline of 30 seconds. | |
Linear
|
Solves the current linear program. |
Detailed documentation
add
Constraint(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 |
|---|---|
lower
|
Number
|
Description : lower bound of the constraint | |
upper
|
Number
|
Description : upper bound of the constraint | |
Return
Linear
— the constraint created
add
Constraints(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
add
Variable(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 |
|---|---|
name
|
String
|
Description : unique name of the variable | |
lower
|
Number
|
Description : lower bound of the variable | |
upper
|
Number
|
Description : upper bound of the variable | |
Return
Linear
— a linear optimization engine
add
Variable(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
add
Variable(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
add
Variables(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
set
Maximization()
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
set
Minimization()
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
set
Objective
Coefficient(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
