Improved metaheuristics for the two-dimensional strip packing problem

Abstract Given a fixed set of rectangular items and a single rectangular object of fixed width and unlimited height, the two-dimensional strip packing problem consists of packing all the items into the object in a non-overlapping manner, such that the resulting packing height is a minimum. Two improved strip packing metaheuristics are proposed in this paper. The first algorithm is a hybrid approach in which the method of simulated annealing is combined with a heuristic construction algorithm, while the second algorithm involves application of the method of simulated annealing directly in the space of completely defined packing layouts, without an encoding of solutions. These two algorithms are compared with a representative sample of metaheuristics from the literature in terms of solution quality achieved in the context of a large set of 1 718 benchmark instances, clustered into four sets of test problems, each with differing characteristics. It is found that the new algorithms indeed compare favourably with, and in some cases outperform, existing strip packing metaheuristics in the literature.