Abstract
This paper deals with the three-dimensional container packing problem (3 DCPP) in which a number of items are orthogonally packed onto a rectangular container so that the utilization rate of the container space or the total value of loaded items is maximized. Besides the above objectives, some other practical constraints such as loading stability, the rotation of items about the height direction and the fixed loading (unloading) orders must be considered for real-life 3 DCPP. Firstly, a concept of sub-volumes, similar to sub-areas in the two-dimension problem, and two basic operations between them are proposed. Based upon the generating scheme of the sub-volumes, the packing pattern and its finite enumeration scheme are described. Then, a sub-volume based simulated annealing (SVBSA) algorithm is proposed, which aims at generating flexible and efficient packing patterns and providing a high degree of inherent stability at the same time. Computational experiments on benchmark problems from ORLIBRARY (URL : http://www.ms.ic.ac.uk/info.html) show its efficiency. Although, in theory, the SVBSA algorithm can converge to an optimal packing pattern with probability one after infinite numbers of state transitions, it is not easy to determine an appropriate stopping criterion for each real-life problem. Therefore, an on-line visual representation of the packing pattern is developed in order to trace the search process and stop the algorithm when a satisfactory packing pattern is obtained. Furthermore, for the fixed loading (unloading) order problems the SVBSA algorithm can be simplified into a sub-volume based iterative procedure.
