A new solution representation for the rectilinear block packing problem

Abstract

The rectilinear block packing problem is a problem of packing a set of rectilinear blocks into a larger rectangular container, where a rectilinear block is a polygonal block whose interior angles are either 90° or 270°. This problem has many applications, such as VLSI design and timber cutting. In this paper, we propose a new solution representation, based on an order of items, to decide a layout of rectilinear blocks whose x-coordinates are fixed. When the shapes of given items have certain characteristics, our representation guarantees optimality. We also generalize this result to the case of general shapes. We then propose an exact algorithm that iteratively generates x-coordinates of items and finds the corresponding optimal layout. The computational results show that our algorithm obtains five exact and one heuristic solutions for six instances and it improves the running time of an existing algorithm.