In this paper, we present a review of the recent approaches proposed in the literature for strip-packing problems. Many of them have been concurrently published, given some similar results for the same set of benchmarks. Due to the quantity of published papers, it is difficult to ascertain the level of current research in this area. & 2008 Published by Elsevier Ltd.

We show that a modification of the Kenyon-Remila algorithm for the strip-packing problem yields an improved bound on the value of the approximate solution. As a corollary we derive that there exists a polynomial-time algorithm that always finds a solution of value OPT +O( √ OPT logOPT ) where OPT is the optimal value.

In this paper a hybrid algorithm to solve Irregular Strip Packing problems is presented. The metaheuristic simulated annealing is used to guide the search over the solution space while linear programming models are solved to generate neighbourhoods during the search process. These linear programming models, which are used to locally optimise the layouts, derive from the application of compactio...

A new meta-heuristic algorithm to find the minimum height for twodimensional strip rectangular packing problem is presented. This algorithm is mainly based on the heuristic recursive strategy and simulated annealing algorithm. The computational results on a class of benchmark problems have shown that this algorithm not only finds shorter height than known meta-heuristic but also runs in shorter...

Object packing by autonomous robots is an important challenge in warehouses and logistics industry. Most conventional data-driven planning approaches focus on regular cuboid packing, which are usually heuristic limit the practical use realistic applications with everyday objects. In this paper, we propose a deep hierarchical reinforcement learning approach to simultaneously plan sequence placem...

We present approximation algorithms for the three-dimensional strip packing problem, and the three-dimensional bin packing problem. We consider orthogonal packings where ninety-degree rotations are allowed. The algorithms we show for these problems have asymptotic performance bounds 2.64, and 4.89, respectively. These algorithms are for the more general case in which the bounded dimensions of t...

The problem of rectangular objects packing into a semi-endless strip is under consideration. Here we propose to solve this problem by linear cutting approximation that may be presented as block structure of packing. Sometimes it becomes necessary to rearrange elements inside linear cutting blocks. The determined method of “reconstruction”(REC) proposed below helps to get solutions close to opti...

This paper considers packing problems with balancing conditions and items consisting of clusters of parallelepipeds (mutually orthogonal, i.e. tetris-like items). This issue is quite frequent in space engineering and a real-world application deals with the Automated Transfer Vehicle project (funded by the European Space Agency), at present under development. A Mixed Integer Programming (MIP) ap...

We consider two-dimensional bin packing and strip packing problems where the items have to be packed by levels. We introduce new mathematical models involving a polynomial number of variables and constraints, and show that their LP relaxations dominate the standard area relaxations. We then propose new (combinatorial) bounds that can be computed in O(n log n) time. We show that they dominate th...

We consider three connected resource-constrained optimization problems: 1D bin packing (BPP), resource-constrained project scheduling (PSP), and 2D strip packing without rotation (SPP). In the context of SPP, BPP is also known as the 1D bar relaxation and PSP as the 1D contiguous relaxation. It is easy to see that SPP can be relaxed in two different ways down to a PSP: horizontal and vertical s...