Floorplanning apartments

Imagine that you have an apartment with a surface of 96 m2, with dimensions 12m⨯8m. You would like to design the floor-plan of the apartment according to some preferences and constraints. For example:

The project consists of generating different floor-plans for the apartment that meet certain design constraints, similar to the ones presented above. The specification of the constraints and preferences should be done using some simple user-friendly language. For solving the problem, algorithms typically used for floor-planning VLSI chips will be used.

The figure below shows the similarity between floor-planning an apartment and floor-planning a VLSI chip. Much of the knowledge acquired for chip floor-planning can be reused for apartment floor-planning.

      

For this project, the initial placement will be generated by other methods (e.g., spectral algorithms). Mathematical optimization will be used to legalize the position of the rooms while keeping the cost function as low as possible.

Floorplanning can be posed as a non-convex mathematical optimization problem. The initial positions of the rooms and the target area are known. The optimizer can reshape the rooms until a legal location is found as close as possible to the original location.

The following video, taken from the floorplan of a VLSI chip, illustrates how the configuration of the layout could evolve during the optimization process.


References