intervalVar

Syntax

The function intervalVar uses named parameters syntax. All parameters are optional and can be specified in any order. Presence status of the interval is set using keywords present, absent or optional (without specifying the value because it is already encoded in the parameter name), the remaining arguments are specified using parameter = value syntax.

If the allowed value for the parameter is an integer range then it can be specified as min..max where min and max are integer constants or simply as v if the range contains only one value v.

To simplify code generation, a trailing comma is allowed after the last parameter.

Parameters

Parameters present, absent and optional set initial presence status of the interval variable, only one of them can be used. If the presence status is not specified then present is used by default.

The remaining parameters all take a value:

It is not allowed to specify any parameter twice (even with the same value).

Description

The function intervalVar creates a new interval variable with the domain according to the supplied arguments.

Use interval variables to model (possibly zero-length) intervals of integers, for example a time to perform some action. Informally saying, an interval variable has unknown start and end such that start ≤ end and non-negative length = end - start. Furthermore an interval variable can be absent to represent the fact that the action was not taken at all. When the interval is present then it cannot be absent (the action must be taken). When the interval is optional then it is up to CP Optimizer to decide whether it will be present or absent in the solution (the action may be taken).

More detailed descriptions of the semantics of the interval variable including intensity, granularity and size can be found in Interval variables in CP Optimizer.

Example

// Present interval variable with length 10 that cannot end after 1000:
a = intervalVar(end=0..1000, length=10);

// Longer way to express the same (domains of variables a and b are the same):
b = intervalVar(present, length=10, start=0..990, end=10..1000);

// Optional action with fixed start time but unknown end time:
c = intervalVar(optional, start=112, end=0..2000);

// A task that takes 6 working days, it is prolonged by weekends.
// Days are counted from 0.
workingDays = stepFunction((intervalmin, 0), (0, 100), (5, 0), (7, 100), (12, 0), (14, 100), (19, 0));
d = intervalVar(size=6, end=0..21, intensity=workingDays);
// Task d cannot start or end during a weekends:
forbidStart(d, workingDays);
forbidEnd(d, workingDays);

// Absent interval variable, trailing comma.
e = intervalVar(absent,);

// None of the interval variables above can overlap:
noOverlap([a, b, c, d, e]);

Notes

• It is not mandatory to assign a name to interval variable, however it is a good practice.
• It is not an error to specify start, end or other parameters when the interval var was set to absent, it is not a good practice though. Those parameters are ignored in this case.
• It is also not an error to specify the parameters in a conflicting way. E.g. start=10 and end=0 would make the interval end before its start. In this case, if the interval variable is optional then it is set to absent. If it is present then the whole problem is insoluble (CP Optimizer reports that there is no solution).
• CP Optimizer is obliged to assign a value to every interval variable when it search for a solution, even if the variable is not used in any constraint or expression. Such variables have no purpose and slow down the search.
• If several interval variables use the same intensity function then it is best to assign a name to that function and then use it repeatedly.