  Floor planning is an important and difficult task in architecture. When
planning office buildings, rooms that belong to the same organisational unit
should be placed close to each other. This leads to the following NP-hard
mathematical optimization problem. Given the outline of each floor, a list of
room sizes, and, for each room, the unit to which it belongs, the aim is to
compute floor plans such that each room is placed on some floor and the total
distance of the rooms within each unit is minimized.
  The problem can be formulated as an integer linear program (ILP). Commercial
ILP solvers exist, but due to the difficulty of the problem, only small to
medium instances can be solved to (near-) optimality. For solving larger
instances, we propose to split the problem into two subproblems; floor
assignment and planning single floors. We formulate both subproblems as ILPs
and solve realistic problem instances. Our experimental study shows that the
problem helps to reduce the computation time considerably. Where we were able
to compute the global optimum, the solution cost of the combined approach
increased very little.
