Convex Optimization 2026, 36 - Floor Planning

A floor planning problem extends a placement problem in that the nodes have physical dimension and must not overlap and can be reconfigured within limits. The objective is then usually to minimize the size of the bounding box. The general form of this problem is considered complicated, but if the relative positioning of the boxes is specified, it becomes at least a convex optimization problem (p. 438). The problem is expressed into a series of inequalities (Eq. 8.32), which can be adapted to make create the relative positioning constraints (Eq. 8.33) (8.8.1). Some convex optimization floor planning problems include the minimum spacing problem, the minimum cell area problem, and those including only constraints on aspect ratio, alignment, symmetry, similarity, containment and distance (8.8.2). Floor planning problems can be written as geometric programs in the object parameters and the bounding box. The constraints on the bounding box and the relative positioning constraints are posynomial inequalities and monomial, so dividing them by the righthand side yields standard posynomial inequalities. Some constraints can't be handled this way (8.8.3).