Class: IntVar

Integer decision variable with a domain.

Remarks

Integer variable represents an unknown (integer) value that solver has to find.

The value of the integer variable can be constrained using mathematical expressions, such as Model.plus, Model.times, Model.le, Model.sum.

OptalCP solver focuses on scheduling problems and concentrates on IntervalVar variables. Therefore, interval variables should be the primary choice for modeling in OptalCP. However, integer variables can be used for other purposes, such as counting or indexing. In particular, integer variables can be helpful for cumulative expressions with variable heights; see Model.pulse, Model.stepAtStart, Model.stepAtEnd, and Model.stepAt.

The integer variable can be optional. In this case, the solver can make the variable absent, which is usually interpreted as the fact that the solver does not use the variable at all. Functions Model.presence and IntExpr.presence can constrain the presence of the variable.

Integer variables can be created using the function Model.intVar.

Example

In the following example we create three integer variables x, y and z. Variables x and y are present, but variable z is optional. Each variable has a different range of possible values.

let model = new CP.Model();
let x = model.intVar({ name: "x", range: [1, 3] });
let y = model.intVar({ name: "y", range: [0, 100] });
let z = model.intVar({ name: "z", range: [10, 20], optional: true });

Extends

• IntExpr

Accessors

max

Get Signature

get max(): number

The maximum value of the integer variable's domain.

Remarks

Gets or sets the maximum value of the integer variable's domain.

The initial value is set during construction by Model.intVar.

Note: This property reflects the variable's domain in the model (before the solve), not in the solution.

The value must be in the range IntVarMin to IntVarMax.

See

IntVar.min, IntVar.optional.

Example

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 5, max: 10, name: "x" });

console.log(x.max);  // 10

x.max = 8;
console.log(x.max);  // 8

Returns

number

Set Signature

set max(value: number): void

Parameters

Parameter	Type
value	number

Returns

void

---

min

Get Signature

get min(): number

The minimum value of the integer variable's domain.

Remarks

Gets or sets the minimum value of the integer variable's domain.

The initial value is set during construction by Model.intVar.

Note: This property reflects the variable's domain in the model (before the solve), not in the solution.

The value must be in the range IntVarMin to IntVarMax.

See

IntVar.max, IntVar.optional.

Example

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 5, max: 10, name: "x" });

console.log(x.min);  // 5

x.min = 7;
console.log(x.min);  // 7

Returns

number

Set Signature

set min(value: number): void

Parameters

Parameter	Type
value	number

Returns

void

---

name

Get Signature

get name(): string | undefined

The name assigned to this model element.

Remarks

The name is optional and primarily useful for debugging purposes. When set, it helps identify the element in solver logs, error messages, and when inspecting solutions.

Names can be assigned to any model element including variables, expressions, and constraints.

Example

import * as CP from "optalcp";

const model = new CP.Model();

// Name a variable at creation
const task = model.intervalVar({ length: 10, name: "assembly" });

// Or set name later
const x = model.intVar({ min: 0, max: 100 });
x.name = "quantity";

console.log(task.name);  // "assembly"
console.log(x.name);     // "quantity"

Returns

string | undefined

Set Signature

set name(value: string): void

Parameters

Parameter	Type
value	string

Returns

void

Inherited from

IntExpr.name

---

optional

Get Signature

get optional(): boolean

Whether the integer variable is optional.

Remarks

Gets or sets whether the integer variable is optional:

• True / true: The variable is optional - the solver decides whether it is present or absent in the solution.
• False / false: The variable is present - it must have a value in the solution.

To force a variable to be absent, make it optional and constrain its presence to be false: model.enforce(~model.presence(x)) (Python), model.enforce(model.presence(x).not()) (TypeScript), or model.Enforce(!model.Presence(x)) (C#).

Note: This property reflects the presence status in the model (before the solve), not in the solution.

See

IntVar.min, IntVar.max.

Example

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, optional: true, name: "y" });

console.log(x.optional);  // false (present by default)
console.log(y.optional);  // true (optional)

// Make x optional
x.optional = true;
console.log(x.optional);  // true

Returns

boolean

Set Signature

set optional(value: boolean): void

Parameters

Parameter	Type
value	boolean

Returns

void

Constructors

Constructor

new IntVar(): IntVar

Returns

IntVar

Inherited from

IntExpr.constructor

Methods

abs()

abs(): IntExpr

Creates an integer expression which is absolute value of the expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression has value absent, the resulting expression also has value absent.

Same as Model.abs.

Inherited from

IntExpr.abs

---

div()

div(rhs: number | IntExpr): IntExpr

Returns integer division of the expression arg. The division rounds towards zero.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The second integer expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.div.

Inherited from

IntExpr.div

---

eq()

eq(rhs: number | IntExpr): BoolExpr

Create an equality constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self equals rhs.

Remarks

Returns a BoolExpr representing self == other.

If either operand has value absent, the result is also absent.

See

• IntExpr.ne for inequality comparison.
• Model.eq for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.eq(IntExpr)
model.enforce(x.eq(y));

// IntExpr.eq(constant)
model.enforce(x.eq(5));

Inherited from

IntExpr.eq

---

ge()

ge(rhs: number | IntExpr): BoolExpr

Create a greater-than-or-equal constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self is greater than or equal to rhs.

Remarks

Returns a BoolExpr representing self >= other.

If either operand has value absent, the result is also absent.

See

• IntExpr.gt for strict greater-than comparison.
• IntExpr.le for less-than-or-equal comparison.
• Model.ge for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.ge(IntExpr)
model.enforce(x.ge(y));

// IntExpr.ge(constant)
model.enforce(x.ge(5));

Inherited from

IntExpr.ge

---

gt()

gt(rhs: number | IntExpr): BoolExpr

Create a greater-than constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self is greater than rhs.

Remarks

Returns a BoolExpr representing self > other.

If either operand has value absent, the result is also absent.

See

• IntExpr.ge for greater-than-or-equal comparison.
• IntExpr.lt for less-than comparison.
• Model.gt for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.gt(IntExpr)
model.enforce(x.gt(y));

// IntExpr.gt(constant)
model.enforce(x.gt(5));

Inherited from

IntExpr.gt

---

guard()

guard(absentValue?: number): IntExpr

Creates an expression that replaces value absent by a constant.

Parameters

Parameter	Type	Default value	Description
absentValue	number	0	The value to use when the expression is absent.

Returns

IntExpr

The resulting integer expression

Remarks

The resulting expression is:

• equal to the expression if the expression is present
• and equal to absentValue otherwise (i.e. when the expression is absent).

The default value of absentValue is 0.

The resulting expression is never absent.

Same as Model.guard.

Inherited from

IntExpr.guard

---

identity()

identity(rhs: number | IntExpr): Constraint

Constrains two expressions to be identical, including their presence status.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The right-hand side operand (IntExpr or int).

Returns

Constraint

The constraint object

Remarks

Identity is different than equality. For example, if x is absent, then x == 0 is absent, but x.identity(0) is false.

Same as Model.identity.

Inherited from

IntExpr.identity

---

inRange()

inRange(lb: number, ub: number): BoolExpr

Creates Boolean expression lb ≤ this ≤ ub.

Parameters

Parameter	Type	Description
lb	number	The lower bound of the range.
ub	number	The upper bound of the range.

Returns

BoolExpr

The resulting Boolean expression

Remarks

If the expression has value absent, then the resulting expression has also value absent.

Use Model.enforce to add this expression as a constraint to the model.

Same as Model.inRange.

Inherited from

IntExpr.inRange

---

le()

le(rhs: number | IntExpr): BoolExpr

Create a less-than-or-equal constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self is less than or equal to rhs.

Remarks

Returns a BoolExpr representing self <= other.

If either operand has value absent, the result is also absent.

See

• IntExpr.lt for strict less-than comparison.
• IntExpr.ge for greater-than-or-equal comparison.
• Model.le for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.le(IntExpr)
model.enforce(x.le(y));

// IntExpr.le(constant)
model.enforce(x.le(5));

Inherited from

IntExpr.le

---

lt()

lt(rhs: number | IntExpr): BoolExpr

Create a less-than constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self is less than rhs.

Remarks

Returns a BoolExpr representing self < other.

If either operand has value absent, the result is also absent.

See

• IntExpr.le for less-than-or-equal comparison.
• IntExpr.gt for greater-than comparison.
• Model.lt for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.lt(IntExpr)
model.enforce(x.lt(y));

// IntExpr.lt(constant)
model.enforce(x.lt(5));

Inherited from

IntExpr.lt

---

max2()

max2(rhs: number | IntExpr): IntExpr

Creates an integer expression which is the maximum of the expression and arg.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The right-hand side operand (IntExpr or int).

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.max2. See Model.max for n-ary maximum.

Inherited from

IntExpr.max2

---

maximize()

maximize(): Objective

Creates a maximization objective for this expression.

Returns

Objective

An Objective that maximizes this expression.

Remarks

Creates an objective to maximize the value of this integer expression. A model can have at most one objective. New objective replaces the old one.

This is a fluent-style alternative to Model.maximize that allows creating objectives directly from expressions.

Example

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intervalVar({start: [0, 100], length: 10, name: "x"});

// Fluent style - maximize the start of x
x.start().maximize();

// Equivalent Model.maximize() style:
model.maximize(x.start());

See

• Model.maximize for Model-centric maximization.
• IntExpr.minimize for minimization.

Inherited from

IntExpr.maximize

---

min2()

min2(rhs: number | IntExpr): IntExpr

Creates an integer expression which is the minimum of the expression and arg.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The right-hand side operand (IntExpr or int).

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.min2. See Model.min for the n-ary minimum.

Inherited from

IntExpr.min2

---

minimize()

minimize(): Objective

Creates a minimization objective for this expression.

Returns

Objective

An Objective that minimizes this expression.

Remarks

Creates an objective to minimize the value of this integer expression. A model can have at most one objective. New objective replaces the old one.

This is a fluent-style alternative to Model.minimize that allows creating objectives directly from expressions.

Example

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intervalVar({length: 10, name: "x"});
const y = model.intervalVar({length: 20, name: "y"});

// Fluent style - minimize the end of y
y.end().minimize();

// Equivalent Model.minimize() style:
model.minimize(y.end());

See

• Model.minimize for Model-centric minimization.
• IntExpr.maximize for maximization.

Inherited from

IntExpr.minimize

---

minus()

minus(rhs: number | IntExpr): IntExpr

Returns subtraction of the expression and arg.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The second integer expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.minus.

Inherited from

IntExpr.minus

---

ne()

ne(rhs: number | IntExpr): BoolExpr

Create an inequality constraint.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The expression or constant to compare against.

Returns

BoolExpr

A boolean expression that is true when self does not equal rhs.

Remarks

Returns a BoolExpr representing self != other.

If either operand has value absent, the result is also absent.

See

• IntExpr.eq for equality comparison.
• Model.ne for the Model-centric style.

import * as CP from "optalcp";

const model = new CP.Model();
const x = model.intVar({ min: 0, max: 10, name: "x" });
const y = model.intVar({ min: 0, max: 10, name: "y" });

// IntExpr.ne(IntExpr)
model.enforce(x.ne(y));

// IntExpr.ne(constant)
model.enforce(x.ne(5));

Inherited from

IntExpr.ne

---

neg()

neg(): IntExpr

Returns negation of the expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression has value absent then the resulting expression has also value absent.

Same as Model.neg.

Inherited from

IntExpr.neg

---

plus()

plus(rhs: number | IntExpr): IntExpr

Returns addition of the expression and the argument.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The second integer expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.plus.

Inherited from

IntExpr.plus

---

presence()

presence(): BoolExpr

Returns an expression which is true if the expression is present and false when it is absent.

Returns

BoolExpr

The resulting Boolean expression

Remarks

The resulting expression is never absent.

Same as Model.presence.

Inherited from

IntExpr.presence

---

times()

times(rhs: number | IntExpr): IntExpr

Returns multiplication of the expression and arg.

Parameters

Parameter	Type	Description
rhs	number | IntExpr	The second integer expression.

Returns

IntExpr

The resulting integer expression

Remarks

If the expression or arg has value absent, then the resulting expression has also value absent.

Same as Model.times.

Inherited from

IntExpr.times