Choosing the right heuristics

This is a very complex issue: in interval analysis we use a lot of heuristics but it is quite difficult to determine what is the right combination that will be the most efficient to solve a problem. And choosing the right parameters for these heuristics may have a very large influence on the computation time (and we mean a really large with a decrease factor of the computation time that may be $10^4$).

Usually it is good policy to use filters that may be generated with simplification procedures (see section 4.2). For example the 2B-consistency, see the Hull_Consistency procedure, section 4.2.1) with a repeat factor $f$ that is about the diameter of the initial range divided by 1000. Similarly it is good policy to use the 3B method (see section 4.5) with an `ALIAS/Delta3B` value similar to the $f$ factor. You may also consider looking at the ALIAS-C++ library that provide specific filters (not all of them are incorporated in ALIAS-Maple) that you may use to write your own specific simplification procedure.