The floorplanning (or facility layout) problem consists in finding the optimal positions for a given set of modules of fixed area (but perhaps varying dimensions) within a facility such that the distances between pairs of modules that have a positive connection cost are minimized. This is a hard discrete optimization problem; even the restricted version where the shapes of the modules are fixed and the optimization is taken over a fixed finite set of possible module locations is NP-hard. In this paper, we extend the concept of target distance introduced by Etawil and Vannelli and apply it to derive the AR (Attractor-Repeller) model which is designed to improve upon the NLT method of van Camp et al. This new model is designed to find a good initial point for the Stage-3 NLT solver and has the advantage that it can be solved very efficiently using a suitable optimization algorithm. Because the AR model is not a convex optimization problem, we also derive a convex version of the model and explore the generalized target distance that arises in this derivation. Numerical results demonstrating the potential of our approach are presented.
Mathematical Methods of Operations Research, Vol. 56(1):3-27, 2002.