A New Search Procedure for the Two-dimensional Orthogonal Packing Problem

Abstract

In this paper we propose a new exact procedure for the two-dimensional orthog- onal packing problem, based on F. Clautiaux et al. approach (Clautiaux et al. Eur. J. Oper. Res. 183(3), 1196-1211, 2007). The principle consists in searching first the positions of the items on the horizontal axis, so as that, at each position, the sum of the heights of the items does not exceed the height of the bin. Each time a valid placement of all the items is encountered, another procedure determines if it can be extended to a solution of the pack- ing problem, searching the positions of the items on the vertical axis. Novel aspects of our approach include a simple and efficient search procedure, which only generates restricted placements, at least in a first stage, in order to reduce the search space, and the memoriza- tion of unsuccessful configurations, which are then used to detect dead-ends. We tested our implementation on a selection of orthogonal packing problems and strip packing problems, and we compared our results with those of recent successful approaches.