A partition-based heuristic algorithm for the rectilinear block packing problem

Abstract

This paper focuses on a two-dimensional strip packing problem where a set of arbitrarily shaped rectilinear blocks need be packed into a larger rectangular container without overlap. A rectilinear block is a polygonal block whose interior angles are either 90°or 270°. This problem involves many industrial applications, such as VLSI design, timber/glass cutting, and newspaper layout. We generalized a bottomleft and a best-fit algorithms to the rectilinear block packing problem in our previous paper. Based on the analysis of the strength and weakness of these algorithms, we propose a new construction heuristic algorithm called the partition-based best-fit algorithm (PBF algorithm), which takes advantages of both the bottomleft and the best-fit algorithms. The basic idea of the PBF algorithm is that it partitions all the items into groups and then packs the items in a group-by-group manner. The best-fit algorithm is taken as the internal tactics for each group. The proposed algorithm is tested on a series of instances, which are generated from benchmark instances. The computational results show that the proposed algorithm significantly improves the performance of the existing construction heuristic algorithms and is especially effective for the instances having large differences in the sizes of given shapes.