Practical Algorithms for Two-Dimensional Packing of Rectangles

This chapter discusses the rectangle packing problem and its variations and introduces coding schemes for the rectangle packing problem, which are used to represent solutions. It presents heuristic algorithms, from the traditional to the latest ones, for the rectangle packing problem. The chapter also introduces techniques to enumerate all the bottom-left stable positions in a layout. It also discusses metaheuristic algorithms for the rectangle packing problem and explores various schemes used to represent solutions to the rectangle packing problem and explains algorithms based on these coding schemes. The chapter considers the following two-dimensional rectangle packing problem. For some packing problems including the two-dimensional irregular packing problem, algorithms with compaction and separation operations were proposed. Cutting and packing problems can be classified using different criteria. F. G. Ortmann et al. proposed several new and improved level algorithms for the strip packing problem and a bin packing problem with different-sized bins.