A comparative review of 3D container loading algorithms

Three-dimensional cutting and packing problems have a range of important applications and are of par- ticular relevance to the transportation of cargo in the form of container loading problems. Recent years has seen a marked increase in the number of papers examining a variant of the container loading problem ranging from largely theoretical to implementations that focus on meeting the many critical real world constraints. In this paper we review the literature focusing on the solution methodologies employed by researchers, with the aim of providing insight into some of the critical algorithmic design issues. In addition we provide an extensive comparison of algorithm performance across the benchmark literature

[1]  Chen-Fu Chien,et al.  A recursive computational procedure for container loading , 1998 .

[2]  Kun He,et al.  An efficient placement heuristic for three-dimensional rectangular packing , 2011, Comput. Oper. Res..

[3]  Eberhard E. Bischoff,et al.  A comparative evaluation of heuristics for container loading , 1990 .

[4]  Andreas Bortfeldt,et al.  Constraints in container loading - A state-of-the-art review , 2013, Eur. J. Oper. Res..

[5]  Reinaldo Morabito,et al.  An AND/OR-graph Approach to the Container Loading Problem , 1994 .

[6]  Türkay Dereli,et al.  A hybrid 'bee(s) algorithm' for solving container loading problems , 2011, Appl. Soft Comput..

[7]  Graham Kendall,et al.  A hybrid placement strategy for the three-dimensional strip packing problem , 2011, Eur. J. Oper. Res..

[8]  Andreas Bortfeldt,et al.  A Tree Search Algorithm for Solving the Container Loading Problem , 2010, INFORMS J. Comput..

[9]  Gi-Tae Yeo,et al.  An effective evolutionary algorithm for the multiple container packing problem , 2008 .

[10]  Philippe Grégoire,et al.  A General Purpose Algorithm for Three-Dimensional Packing , 2005, INFORMS J. Comput..

[11]  Guntram Scheithauer A Three-dimensional Bin Packing Algorithm , 1991, J. Inf. Process. Cybern..

[12]  Daniele Vigo,et al.  The Three-Dimensional Bin Packing Problem , 2000, Oper. Res..

[13]  Andrew Lim,et al.  3-D Container Packing Heuristics , 2005, Applied Intelligence.

[14]  Daniele Vigo,et al.  Heuristic algorithms for the three-dimensional bin packing problem , 2002, Eur. J. Oper. Res..

[15]  Andrew Lim,et al.  A prototype column generation strategy for the multiple container loading problem , 2012, Eur. J. Oper. Res..

[16]  Michael Eley,et al.  Solving container loading problems by block arrangement , 2002, Eur. J. Oper. Res..

[17]  David Pisinger,et al.  Heuristics for the container loading problem , 2002, Eur. J. Oper. Res..

[18]  Pupong Pongcharoen,et al.  Development of a stochastic optimisation tool for solving the multiple container packing problems. , 2012 .

[19]  Yoshiko Wakabayashi,et al.  Approximation Algorithms for the Orthogonal Z-Oriented Three-Dimensional Packing Problem , 1999, SIAM J. Comput..

[20]  David Pisinger,et al.  Multi-dimensional bin packing problems with guillotine constraints , 2010, Comput. Oper. Res..

[21]  Reinaldo Morabito,et al.  An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container , 2002, Eur. J. Oper. Res..

[22]  Hermann Gehring,et al.  A Parallel Genetic Algorithm for Solving the Container Loading Problem , 2002 .

[23]  Jing Xu,et al.  An iterated construction approach with dynamic prioritization for solving the container loading problems , 2012, Expert Syst. Appl..

[24]  Shih-Wei Huang,et al.  A Hybrid Meta-Heuristic for the Container Loading Problem , 2007 .

[25]  J. A. George,et al.  A heuristic for packing boxes into a container , 1980, Comput. Oper. Res..

[26]  M. Meyer,et al.  A computer-based heuristic for packing pooled shipment containers , 1990 .

[27]  Daniel Mack,et al.  A parallel tabu search algorithm for solving the container loading problem , 2003, Parallel Comput..

[28]  Andrew Lim,et al.  The container loading problem , 2005, SAC '05.

[29]  Katsuhisa Ohno,et al.  The Three-Dimensional Bin Packing Problem and Its Practical Algorithm , 2003 .

[30]  Anna Sciomachen,et al.  A 3D-BPP approach for optimising stowage plans and terminal productivity , 2007, Eur. J. Oper. Res..

[31]  Bryan Kok Ann Ngoi,et al.  Applying spatial representation techniques to the container packing problem , 1994 .

[32]  Yong Wu,et al.  A global search framework for practical three-dimensional packing with variable carton orientations , 2012, Comput. Oper. Res..

[33]  Teodor Gabriel Crainic,et al.  Extreme Point-Based Heuristics for Three-Dimensional Bin Packing , 2008, INFORMS J. Comput..

[34]  Eberhard E. Bischoff,et al.  Allowing for weight considerations in container loading , 1998 .

[35]  Andreas Bortfeldt,et al.  Eine Heuristik für Multiple Containerladeprobleme , 2000, OR Spectr..

[36]  Chen-Fu Chien,et al.  A container packing support system for determining and visualizing container packing patterns , 2004, Decis. Support Syst..

[37]  Jiamin Liu,et al.  A novel hybrid tabu search approach to container loading , 2011, Comput. Oper. Res..

[38]  Kin Keung Lai,et al.  Effective methods for a container packing operation , 1997 .

[39]  Eberhard E. Bischoff,et al.  Weight distribution considerations in container loading , 1999, Eur. J. Oper. Res..

[40]  Nelson Maculan,et al.  A greedy search for the three‐dimensional bin packing problem: the packing static stability case , 2003 .

[41]  Søren Gram Christensen,et al.  Container loading with multi-drop constraints , 2009, Int. Trans. Oper. Res..

[42]  Marisa B. Figueiredo,et al.  A particular approach for the Three-dimensional Packing Problem with additional constraints , 2010, Comput. Oper. Res..

[43]  Sándor P. Fekete,et al.  A New Exact Algorithm for General Orthogonal D-Dimensional Knapsack Problems , 1997, ESA.

[44]  Kamlesh Mathur,et al.  Value considerations in three-dimensional packing -- A heuristic procedure using the fractional knapsack problem , 1994 .

[45]  Leah Epstein,et al.  Dynamic multi-dimensional bin packing , 2010, J. Discrete Algorithms.

[46]  Ramón Alvarez-Valdés,et al.  Neighborhood structures for the container loading problem: a VNS implementation , 2010, J. Heuristics.

[47]  Gerhard Wäscher,et al.  An improved typology of cutting and packing problems , 2007, Eur. J. Oper. Res..

[48]  Kun He,et al.  A new heuristic algorithm for cuboids packing with no orientation constraints , 2009, Comput. Oper. Res..

[49]  Hermann Gehring,et al.  Applying Tabu Search to Container Loading Problems , 1998 .

[50]  Shigeyuki Takahara,et al.  A Multi-start Local Search Approach to the Multiple Container Loading Problem , 2008 .

[51]  Mauricio G. C. Resende,et al.  A parallel multi-population biased random-key genetic algorithm for a container loading problem , 2012, Comput. Oper. Res..

[52]  D. Mack,et al.  A parallel hybrid local search algorithm for the container loading problem , 2004 .

[53]  Hamadi Hasni,et al.  On a Hybrid Genetic Algorithm for Solving the Container Loading Problem with no Orientation Constraints , 2013, J. Math. Model. Algorithms.

[54]  Zhou-Jing Wang,et al.  A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach , 2008, Eur. J. Oper. Res..

[55]  J. A. George,et al.  A Method for Solving Container Packing for a Single Size of Box , 1992 .

[56]  John Y. Cheung,et al.  Hybrid genetic algorithm for container packing in three dimensions , 1993, Proceedings of 9th IEEE Conference on Artificial Intelligence for Applications.

[57]  Yoshiko Wakabayashi,et al.  Three-dimensional packings with rotations , 2009, Comput. Oper. Res..

[58]  Chun-Cheng Lin,et al.  On the Three-Dimensional Container Packing Problem under Home Delivery Service , 2011, Asia Pac. J. Oper. Res..

[59]  Lei Wu,et al.  A Linear Programming Approach for the Three-Dimensional Bin-Packing Problem , 2010, Electron. Notes Discret. Math..

[60]  E. E. Bischoff,et al.  Three-dimensional packing of items with limited load bearing strength , 2006, Eur. J. Oper. Res..

[61]  Mark Goh,et al.  Three-dimensional bin packing problem with variable bin height , 2010, Eur. J. Oper. Res..

[62]  Edmund K. Burke,et al.  A space-indexed formulation of packing boxes into a larger box , 2012, Oper. Res. Lett..

[63]  Graham Kendall,et al.  Automating the Packing Heuristic Design Process with Genetic Programming , 2012, Evolutionary Computation.

[64]  Mhand Hifi,et al.  Approximate algorithms for the container loading problem , 2002 .

[65]  Marco A. Boschetti New lower bounds for the three-dimensional finite bin packing problem , 2004, Discret. Appl. Math..

[66]  Kin Keung Lai,et al.  Container packing in a multi-customer delivering operation , 1998 .

[67]  Wenbin Zhu,et al.  A new iterative-doubling Greedy-Lookahead algorithm for the single container loading problem , 2012, Eur. J. Oper. Res..

[68]  Pius J. Egbelu,et al.  A heuristic approach to the three-dimensional cargo-loading problem , 1989 .

[69]  Manfred W. Padberg,et al.  Packing small boxes into a big box , 2000, Math. Methods Oper. Res..

[70]  David Pisinger,et al.  Guided Local Search for the Three-Dimensional Bin-Packing Problem , 2003, INFORMS J. Comput..

[71]  Robert W. Haessler,et al.  Load planning for shipments of low density products , 1990 .

[72]  Reinaldo Morabito,et al.  Three-dimensional container loading models with cargo stability and load bearing constraints , 2012, Comput. Oper. Res..

[73]  Hermann Gehring,et al.  A Genetic Algorithm for Solving the Container Loading Problem , 1997 .

[74]  Sándor P. Fekete,et al.  A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing , 2003, Math. Oper. Res..

[75]  Ramón Alvarez-Valdés,et al.  A Maximal-Space Algorithm for the Container Loading Problem , 2008, INFORMS J. Comput..

[76]  Jens Egeblad,et al.  Heuristic approaches for the two- and three-dimensional knapsack packing problem , 2009, Comput. Oper. Res..

[77]  Andrew Lim,et al.  The multiple container loading cost minimization problem , 2011, Eur. J. Oper. Res..

[78]  C. K. Chua,et al.  Constraint‐based spatial representation technique for the container packing problem , 1998 .

[79]  Sara Ceschia,et al.  Local search for a multi-drop multi-container loading problem , 2013, J. Heuristics.

[80]  Jong Mau Yeh,et al.  Applying genetic algorithms and neural networks to the container loading problem , 2003 .

[81]  Shigeyuki Takahara A Simple Meta-heuristic Approach for the Multiple Container Loading Problem , 2006, 2006 IEEE International Conference on Systems, Man and Cybernetics.

[82]  Chen-Fu Chien,et al.  An efficient computational procedure for determining the container-loading pattern , 2009, Comput. Ind. Eng..

[83]  Keisuke Ishihara,et al.  A Tree Based Novel Representation for 3D-Block Packing , 2009, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[84]  Andrew Lim,et al.  A multi-faced buildup algorithm for three-dimensional packing problems , 2003 .

[85]  Loris Faina A global optimization algorithm for the three-dimensional packing problem , 2000, Eur. J. Oper. Res..

[86]  Nancy J. Ivancic An Integer Programming Based Heuristic Approach to the Three Dimensional Packing Problem , 1988 .

[87]  M.-K. Kang,et al.  Heuristics with a new block strategy for the single and multiple containers loading problems , 2010, J. Oper. Res. Soc..

[88]  Chin-Sheng Chen,et al.  An analytical model for the container loading problem , 1995 .

[89]  Mauricio G. C. Resende,et al.  A biased random key genetic algorithm for 2D and 3D bin packing problems , 2013 .

[90]  K. Lai,et al.  Developing a simulated annealing algorithm for the cutting stock problem , 1997 .

[91]  Hermann Gehring,et al.  A hybrid genetic algorithm for the container loading problem , 2001, Eur. J. Oper. Res..

[92]  Wallace Kit-Sang Tang,et al.  A hybrid genetic approach for container loading in logistics industry , 2005, IEEE Transactions on Industrial Electronics.

[93]  Kun He,et al.  A caving degree based flake arrangement approach for the container loading problem , 2010, Comput. Ind. Eng..

[94]  Hongfeng Wang,et al.  A hybrid genetic algorithm with a new packing strategy for the three-dimensional bin packing problem , 2012, Appl. Math. Comput..

[95]  Yu Peng,et al.  A heuristic block-loading algorithm based on multi-layer search for the container loading problem , 2012, Comput. Oper. Res..

[96]  Tetsuo Sawaragi,et al.  A tree search method for the container loading problem with shipment priority , 2011, Eur. J. Oper. Res..

[97]  Reinaldo Morabito,et al.  MIP-based approaches for the container loading problem with multi-drop constraints , 2012, Ann. Oper. Res..

[98]  Andrew Lim,et al.  The six elements to block-building approaches for the single container loading problem , 2012, Applied Intelligence.

[99]  A. Moura,et al.  A GRASP approach to the container-loading problem , 2005, IEEE Intelligent Systems.

[100]  Sándor P. Fekete,et al.  An Exact Algorithm for Higher-Dimensional Orthogonal Packing , 2006, Oper. Res..

[101]  Daniel Mack,et al.  A heuristic for the three-dimensional strip packing problem , 2007, Eur. J. Oper. Res..

[102]  Guntram Scheithauer Algorithms for the Container Loading Problem , 1992 .

[103]  E. E. Bischoff,et al.  Issues in the development of approaches to container loading , 1995 .

[104]  Ignacio Araya,et al.  A beam search approach to the container loading problem , 2014, Comput. Oper. Res..

[105]  Yoshiko Wakabayashi,et al.  An algorithm for the three-dimensional packing problem with asymptotic performance analysis , 1997, Algorithmica.

[106]  M. K. Lim,et al.  Integrated Manufacturing Systems Control Using a Multi-Agent System , 2000 .

[107]  Daniele Vigo,et al.  TSpack: A Unified Tabu Search Code for Multi-Dimensional Bin Packing Problems , 2004, Ann. Oper. Res..

[108]  Teodor Gabriel Crainic,et al.  TS2PACK: A two-level tabu search for the three-dimensional bin packing problem , 2009, Eur. J. Oper. Res..

[109]  Kun He,et al.  A caving degree approach for the single container loading problem , 2009, Eur. J. Oper. Res..

[110]  Chen-Fu Chien,et al.  A framework of modularized heuristics for determining the container loading patterns , 1999 .

[111]  Andrew Lim,et al.  A Heuristic for the Multiple Container Loading Cost Minimization Problem , 2011, IEA/AIE.