### 3.7.115. Heuristics for two-dimensional rectangle placement problems

A constraint for which one of the following heuristics was used in the context of two -dimensional rectangles  placement problems where rectangles should not overlap. For easy instances involving non -overlapping constraints where there is enough room, a standard heuristics where one fixes each rectangle successively by trying out its possible values for its $x$ -coordinate and its $y$ -coordinate will do the job. However, for more difficult problems a less aggressive heuristics is usually required, specially when the filtering algorithms attached to the constraints are weak. The paradox is that less aggressive heuristics sometimes do not find rapidly a first solution to easy instances since they may potentially artificially create infeasible subproblems.