A Heuristic Algorithm for the Offline One-Dimensional Bin Packing Problem Inspired by the Point Jacobi Matrix Iterative Method

The bin packing problem is a well known NP-hard problem that consists in placing a set of items of different sizes in a mimimum number of bins. An iterative algorithm for the one-dimensional offline bin packing problem is presented whose number of iterations needed to reach an unchanging partition when faced to a particular instance is bounded by the performance of the point Jacobi method on the problem taken as a matrix relaxation one. The algorithm was tested on a large widely used benchmark instances from the literature and behaved very successfully on a class considered as very difficult.