Location (value, i.e., a single placement of the rectangle).
Resource constraint (rectangular area where the rectangles are to be placed).
Package org.cpsolver.ifs.example.rpp Description
Random Placement Problem.
The random placement problem (RPP; for more details, see
seeks to place a set of randomly generated rectangles (called objects)
of different sizes into a larger rectangle (called placement area) in
such a way that no objects overlap and all objects' borders are
parallel to the border of the placement area. In addition, a set of
allowable placements can be randomly generated for each object. The
ratio between the total area of all objects and the size of the
placement area will be denoted as the filled area ratio.
RPP allows us to generate various instances of the problem similar to
a trivial timetabling problem. The correspondence is as follows: the
object corresponds to a course to be timetabled; the x-coordinate to
its time, the y-coordinate to its classroom. For example, a course
taking three hours corresponds to an object with dimensions 3x1 (the
course should be taught in one classroom only). Each course can be
placed only in a classroom of sufficient capacity; we can expect that
the classrooms are ordered increasingly in their size so each object
will have a lower bound on its y-coordinate.
MPP instances were generated as follows: First, the initial solution
was computed. The changed problem differs from the initial problem by
input perturbations. An input perturbation means that both x
coordinate and y coordinate of a rectangle must differ from the
initial values, i.e., x!=xinitial and y!=yinitial. For a single initial
problem and for a given number of input perturbations, we can randomly
generate various changed problems. In particular, for a given number
of input perturbations, we randomly select a set of objects which
should have input perturbations. The solution to MPP can be evaluated
by the number of additional perturbations. They are given by
subtraction of the final number of perturbations and the number of