The effects of combining search and modelling techniques can be complex and
unpredictable, so guidelines are very important for the design and development of
effective and robust solvers. This is an issue not only for exact solvers, but also
for approximate techniques, such as local search. A recently observed phenomenon is
the negative effect of symmetry breaking constraints on local search performance.
The reasons for this are poorly understood and they are likely to be  found  in  the
structure of the search space, mainly in the reachability of solutions. In this
talk, we discuss the current conjectures on this phenomenon and propose a new
hypothesis based on the concept of basin of attraction of solutions, that can be
seen as a generalization of previous conjectures. This approach can also be
generalized to study other related phenomena, such as the effect of redundant
constraints and constraint-based neighborhoods.