Constraints relaxation allows generator to partially violate some constraints in order to fully generate the timetable.
With constraints relaxation enabled, program tries to fulfil all the constraints, but if it gets in some bigger trouble with some card, it will put it into timetable even if it means that some constraints will be broken. Of course, it tries to create timetable that most closely matches your constraints.
Constraints relaxation can help you in two ways:
1. It can help you with identifying what can be the problem with your timetable and which constraints are probably too hard. If you generate your timetable with relaxation turned on, there is a higher chance that timetable will be generated. Then you can check which constraints were relaxed and think if they are realistic. Or you might consider changing settings of some constraints to some easier values.
2. It can help you to find the final timetable with only some constraints relaxed.
If you turn the constraints relaxation to strict, then no constraints can be relaxed and only those timetables that are fully complient with your requirements are accepted. The software will generate until it finds such, or may leave some unset cards in case such a timetable doesn't exist.
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