Strategy E is a genetic algorithm which involves a huge amount of computations and provides excellent results.
First, Untis calculates a series of timetables. On contrary to strategy B, where only one timetable is the base of new series, this strategy uses two timetables (mother and father timetable) as the base for new series.
You should use this strategy if you have got already good results with other strategies. Usually strategy E can still improve the result. The length of the optimisation depends on the size of the school, the number of timetables to be calculated, the optimisation level and the performance of your computer. This can take "overnight", indeed.