Guided Local Search for the Three-Dimensional Bin-Packing Problem

The three-dimensional bin packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on Guided Local Search (GLS). Starting with an upper bound on the number of bins obtained by a greedy heuristic, the presented algorithm iteratively decreases the number of bins, each time searching for a feasible packing of the boxes using GLS. The process terminates when a given time limit has been reached or the upper bound matches a precomputed lower bound. The algorithm can also be applied to two-dimensional bin packing problems by having a constant depth for all boxes and bins. Computational experiments are reported for two-and three-dimensional instances with up to 200 boxes, and the results are compared with those obtained by heuristics and exact methods from the literature.