Two-dimensional residual-space-maximized packing

Only a single heuristic policy required during packing.Best results obtained in large-scale problem.Fast computational speed. Many approaches exist for solving two dimensional rectangle-packing problems. Some rely on multiple heuristic policies to detect suitable packing positions. Others resort to searching for a sound packing sequence from a great number of variations. This paper describes a heuristic algorithm with only a single policy: maximize the residual space during packing, which ensures that rectangles to be packed will fit into the space with maximum likelihood. An efficient implementation is proposed to realize the policy. Experimental results based on openly available datasets demonstrate that the proposed algorithm is comparable to most state-of-the-art algorithms in space efficiency while is significantly faster in data processing. In the case of large-scale problems tested, it is the best by both evaluation metrics.

[1]  C. Potts,et al.  A genetic algorithm for two-dimensional bin packing with due dates , 2013 .

[2]  Daniele Vigo,et al.  A lower bound for the non-oriented two-dimensional bin packing problem , 2002, Discret. Appl. Math..

[3]  Bernard Chazelle,et al.  The Bottomn-Left Bin-Packing Heuristic: An Efficient Implementation , 1983, IEEE Transactions on Computers.

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

[5]  José Fernando Gonçalves,et al.  A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem , 2007, Eur. J. Oper. Res..

[6]  Lijun Wei,et al.  A Binary Search Heuristic Algorithm Based on Randomized Local Search for the Rectangular Strip-Packing Problem , 2013, INFORMS J. Comput..

[7]  Graham Kendall,et al.  A New Placement Heuristic for the Orthogonal Stock-Cutting Problem , 2004, Oper. Res..

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Cihan H. Dagli,et al.  New approaches to nesting rectangular patterns , 1997, J. Intell. Manuf..

[10]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

[11]  Marco A. Boschetti,et al.  The Two-Dimensional Finite Bin Packing Problem. Part II: New lower and upper bounds , 2003, 4OR.

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

[13]  Ender Özcan,et al.  Bidirectional best-fit heuristic for orthogonal rectangular strip packing , 2009, Ann. Oper. Res..

[14]  L. Fogel,et al.  European Journal Ofoperational Research on Genetic Algorithms for the Packing of Polygons , 1996 .

[15]  Gleb Belov,et al.  One-dimensional heuristics adapted for two-dimensional rectangular strip packing , 2008, J. Oper. Res. Soc..

[16]  Aziz Moukrim,et al.  New resolution algorithm and pretreatments for the two-dimensional bin-packing problem , 2008, Comput. Oper. Res..

[17]  Andrew Lim,et al.  A skyline heuristic for the 2D rectangular packing and strip packing problems , 2011, Eur. J. Oper. Res..

[18]  J. W. Barnes,et al.  An Adaptive Tabu Search Approach for 2-Dimensional Orthogonal Packing Problems , 2006 .

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

[20]  Ramón Alvarez-Valdés,et al.  A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems , 2005, J. Oper. Res. Soc..

[21]  E. Hopper,et al.  An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem , 2001, Eur. J. Oper. Res..

[22]  Kai Zhang,et al.  Bidirectional best-fit heuristic considering compound placement for two dimensional orthogonal rectangular strip packing , 2013, Expert Syst. Appl..

[23]  Hongfei Teng,et al.  An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles , 1999, Eur. J. Oper. Res..

[24]  K. Dowsland Some experiments with simulated annealing techniques for packing problems , 1993 .

[25]  Daniele Vigo,et al.  Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems , 1999, INFORMS J. Comput..

[26]  J. O. Berkey,et al.  Two-Dimensional Finite Bin-Packing Algorithms , 1987 .

[27]  Stephen C. H. Leung,et al.  A fast layer-based heuristic for non-guillotine strip packing , 2011, Expert Syst. Appl..

[28]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[29]  S. Martello,et al.  Exact Solution of the Two-Dimensional Finite Bon Packing Problem , 1998 .

[30]  Ronald L. Rivest,et al.  Orthogonal Packings in Two Dimensions , 1980, SIAM J. Comput..