A GRASP Approach to the Container-Loading Problem

A. Moura, J.F. Oliveira
2005 IEEE Intelligent Systems  
T he container-loading problem aims to determine the arrangement of items in a container. Researchers approach this 3D, NP-hard problem 1 using heuristic methods. Usually, the CLP aims to maximize loading efficiency-that is, the container space use. Here, the problem we address involves only one container with known dimensions, and the cargo varies from weakly to strongly heterogeneous, independent of the total number of boxes. We consider three requirements related to the load's physical
more » ... ement and to the transportation requirements: box orientation (for example, "this side up"), cargo stability, and container volume. Although considering both volume use and cargo stability could lead to a bi-objective CLP, we tackle cargo stability as a constraint in the constructive phase of the algorithm, and we explicitly consider volume use as the only objective in the constructive and local-search phases. In this article, we present GRMODGRASP, a new algorithm for the CLP based on the GRASP (greedy randomized adaptive search procedure) paradigm. 2 We evaluate GRMODGRASP's performance in terms of volume use and load stability and by comparing it with nine well-known algorithms. Our approach produces solutions that surpass other approaches' solutions in terms of volume use and cargo stability. The Modified George and Robinson heuristic We based GRMODGRASP on GRMOD, an improved version of the George and Robinson heuristic. 3 This wall-building heuristic packs boxes in a container, with an opening in the front, from the back to the front along its length. One modification to the George and Robinson heuristic relates to the container length. 4 The original heuristic considers an infinite-length container (the 3D strip-packing problem), but it doesn't guarantee that the resulting packing will have a length equal to or less than the container's length; GRMOD deals with a finite-length container. With this modification, we can eliminate the George and Robinson algorithm's "unsuccessful packing" and "automatic repacking" procedures, which basically compare the final packing length with the container's length and reapply the heuristic with different parameters. Successively executing the George and Robinson heuristic might obtain a feasible solution if the cargo's total volume is equal to or less than the container's volume. Another modification addresses packing the container's final layers. 4 The George and Robinson heuristic uses a minimal-length parameter that inhibits constructing new layers at the end of the packing process. This causes layers with low volume use. In GRMOD (see figure 1) , the layer depth dimension depends on the unpacked boxes' volume. So, the container's final layers have a smaller depth but better volume use. GRMOD incorporates the two modifications just described plus two improvements that we introduced to improve cargo stability. The first deals with new-space generation, and the other relates to the flexible-width value. Constructive heuristic Like the George and Robinson heuristic, the GRMOD constructive heuristic builds on the concept of empty space-a parallelepipedic region without a box packed inside. GRMOD deals with empty spaces in two different ways. When the empty space's height and width equals the container's height and width, GRMODGRASP is a new algorithm for solving the container-loading problem. Based on a wall-building, constructive heuristic, it can achieve high levels of cargo stability without compromising the container's volume use.
doi:10.1109/mis.2005.57 fatcat:aq5wsohmovcjnjxbp62kn54eum