Metaheuristic Algorithms for the Strip Packing Problem

Given a set of rectangular items and a strip of given width, we consider the problem of allocating all the items to a minimum height strip. We present a Tabu search algorithm, a genetic algorithm and we combine the two into a hybrid approach. The performance of the proposed algorithms is evaluated through extensive computational experiments on instances from the literature and on randomly generated instances.

[1]  S. Jakobs,et al.  European Journal Ofoperational Research on Genetic Algorithms for the Packing of Polygons , 2022 .

[2]  Brenda S. Baker,et al.  Shelf Algorithms for Two-Dimensional Packing Problems , 1983, SIAM J. Comput..

[3]  Andrea Lodi,et al.  Two-dimensional packing problems: A survey , 2002, Eur. J. Oper. Res..

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

[5]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

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

[7]  Sven-Olai Høyland Bin-Packing in 1.5 Dimension , 1988, SWAT.

[8]  Daniel Dominic Sleator,et al.  A 2.5 Times Optimal Algorithm for Packing in Two Dimensions , 1980, Inf. Process. Lett..

[9]  Daniele Vigo,et al.  An Exact Approach to the Strip-Packing Problem , 2003, INFORMS J. Comput..

[10]  Bengt-Erik Bengtsson,et al.  Packing Rectangular Pieces - A Heuristic Approach , 1982, Comput. J..

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

[12]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[13]  P. W. Poon,et al.  Genetic algorithm crossover operators for ordering applications , 1995, Comput. Oper. Res..

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

[15]  Daniele Vigo,et al.  Neighborhood Search Algorithm for the Guillotine Non-Oriented Two-Dimensional Bin Packing Problem , 1999 .

[16]  John E. Beasley,et al.  Algorithms for Unconstrained Two-Dimensional Guillotine Cutting , 1985 .

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

[18]  Mauro Dell'Amico,et al.  Annotated Bibliographies in Combinatorial Optimization , 1997 .

[19]  Daniele Vigo,et al.  Approximation algorithms for the oriented two-dimensional bin packing problem , 1999, Eur. J. Oper. Res..

[20]  Nicos Christofides,et al.  An Algorithm for Two-Dimensional Cutting Problems , 1977, Oper. Res..

[21]  Chuan Yi Tang,et al.  A 2.|E|-Bit Distributed Algorithm for the Directed Euler Trail Problem , 1993, Inf. Process. Lett..

[22]  Robert E. Tarjan,et al.  Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms , 1980, SIAM J. Comput..

[23]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[24]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[25]  Igal Golan,et al.  Performance Bounds for Orthogonal Oriented Two-Dimensional Packing Algorithms , 1981, SIAM J. Comput..

[26]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[27]  Lawrence Davis,et al.  Applying Adaptive Algorithms to Epistatic Domains , 1985, IJCAI.

[28]  Brenda S. Baker,et al.  A 5/4 Algorithm for Two-Dimensional Packing , 1981, J. Algorithms.

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

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

[31]  Colin Reeves,et al.  Hybrid genetic algorithms for bin-packing and related problems , 1996, Ann. Oper. Res..

[32]  Gerhard Wäscher,et al.  Cutting and packing , 1995, Eur. J. Oper. Res..

[33]  C. Reeves Modern heuristic techniques for combinatorial problems , 1993 .

[34]  David de la Fuente,et al.  Resolution of strip-packing problems with genetic algorithms , 2000, J. Oper. Res. Soc..

[35]  A. Steinberg,et al.  A Strip-Packing Algorithm with Absolute Performance Bound 2 , 1997, SIAM J. Comput..

[36]  Daniele Vigo,et al.  Recent advances on two-dimensional bin packing problems , 2002, Discret. Appl. Math..

[37]  Donna J. Brown,et al.  An Improved BL Lower Bound , 1980, Inf. Process. Lett..