A Review of the Application of Meta-Heuristic Algorithms to 2D Strip Packing Problems

This paper is a review of the approachesdeveloped to solve 2D packing problems withmeta-heuristic algorithms. As packing tasks arecombinatorial problems with very large searchspaces, the recent literature encourages theuse of meta-heuristic search methods, inparticular genetic algorithms. The objective ofthis paper is to present and categorise thesolution approaches in the literature for 2Dregular and irregular strip packing problems.The focus is hereby on the analysis of themethods involving genetic algorithms. Anoverview of the methods applying othermeta-heuristic algorithms including simulatedannealing, tabu search, and artificial neuralnetworks is also given.

[1]  Loris Faina,et al.  An application of simulated annealing to the cutting stock problem , 1999, Eur. J. Oper. Res..

[2]  Emanuel Falkenauer,et al.  A hybrid grouping genetic algorithm for bin packing , 1996, J. Heuristics.

[3]  T. Kampke Simulated annealing: Use of a new tool in bin packing , 1988 .

[4]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[5]  K.K.B. Hon,et al.  The Nesting of Two-Dimensional Shapes Using Genetic Algorithms , 1995 .

[6]  Kathryn A. Dowsland,et al.  A family of genetic algorithms for the pallet loading problem , 1996, Ann. Oper. Res..

[7]  Peter Andras,et al.  A Genetic Solution for the Cutting Stock Problem , 1996 .

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

[9]  A. M. Gomes,et al.  A New Constructive Algorithm for Nesting Problems , 2001 .

[10]  Antonio Albano,et al.  NESTING TWO-DIMENSIONAL SHAPES IN RECTANGULAR MODULES , 1976 .

[11]  Vassilios E. Theodoracatos,et al.  The optimal packing of arbitrarily-shaped polygons using simulated annealing and polynomial-time cooling schedules , 1995 .

[12]  Paolo Prinetto,et al.  Optimizing area loss in flat glass cutting , 1997 .

[13]  Robert J. Fowler,et al.  Optimal Packing and Covering in the Plane are NP-Complete , 1981, Inf. Process. Lett..

[14]  Patrick Healy,et al.  A Local Optimization-based Solution to the Rectangle Layout Problem , 1996 .

[15]  A. I. Hinxman The trim-loss and assortment problems: A survey , 1980 .

[16]  José Fernando Oliveira,et al.  TOPOS – A new constructive algorithm for nesting problems , 2000, OR Spectr..

[17]  Oliver Vornberger,et al.  Genetic packing of rectangles on transputers , 1991 .

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

[19]  Marvin D. Troutt,et al.  Applications of genetic search and simulated annealing to the two-dimensional non-guillotine cutting stock problem , 2001 .

[20]  Paul F. Whelan,et al.  Automated packing systems: review of industrial implementations , 1993, Other Conferences.

[21]  E. Hopper,et al.  A genetic algorithm for a 2D industrial packing problem , 1999 .

[22]  William B. Dowsland On a Research Bibliography for Cutting and Packing Problems , 1992 .

[23]  Richard W. Eglese,et al.  Simulated annealing: A tool for operational research , 1990 .

[24]  W. Dowsland Three-dimensional packing—solution approaches and heuristic development , 1991 .

[25]  Mark J. Jakiela,et al.  Solving Pattern Nesting Problems with Genetic Algorithms Employing Task Decomposition and Contact Detection , 1995, Evolutionary Computation.

[26]  Harald Dyckhoff,et al.  Cutting and Packing in Production and Distribution , 1992 .

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

[28]  S. Maouche,et al.  Irregular shape nesting and placing with evolutionary approach , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

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

[30]  Suck-Joo Na,et al.  Two-Stage Approach for Nesting in Two-Dimensional Cutting Problems Using Neural Network and Simulated Annealing , 1996 .

[31]  N. Ono,et al.  An evolutionary approach to two-dimensional guillotine cutting problem , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[32]  S. Maouche,et al.  Evolutionary search techniques application in automated layout-planning optimization problem , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

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

[34]  Vassilios Petridis,et al.  Varying quality function in genetic algorithms and the cutting problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[35]  K. Dowsland,et al.  Solution approaches to irregular nesting problems , 1995 .

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

[37]  R. P. Pargas,et al.  A parallel stochastic optimization algorithm for solving 2D bin packing problems , 1993, Proceedings of 9th IEEE Conference on Artificial Intelligence for Applications.

[38]  Dirk Van Oudheusden Deterministic scheduling theory , 1997 .

[39]  Oliver Vornberger,et al.  Parallel Genetic Packing of Rectangles , 1990, PPSN.

[40]  David S. Johnson,et al.  Approximation Algorithms for Bin-Packing — An Updated Survey , 1984 .

[41]  H. Gea,et al.  Two-dimensional packing problems using genetic algorithms , 2005, Engineering with Computers.

[42]  Derek Smith,et al.  Bin Packing with Adaptive Search , 1985, ICGA.

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

[44]  B. H. Gwee,et al.  Polyominoes tiling by a genetic algorithm , 1996, Comput. Optim. Appl..

[45]  Kikuo Fujita,et al.  Hybrid Approach for Optimal Nesting Using a Genetic Algorithm and a Local Minimization Algorithm , 1998 .

[46]  Edward G. Coffman,et al.  Average-case analysis of cutting and packing in two dimensions , 1990 .

[47]  J.J.S. Sentieiro,et al.  A system for the compaction of two-dimensional irregular shapes based on simulated annealing , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[48]  Antonio Albano,et al.  Optimal Allocation of Two-Dimensional Irregular Shapes Using Heuristic Search Methods , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[49]  Cheng-Yan Kao,et al.  On solving rectangle bin packing problems using genetic algorithms , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[50]  Eva Hopper,et al.  Two-dimensional Packing utilising Evolutionary Algorithms and other Meta-Heuristic Methods , 2002 .

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

[52]  T. Kampke Simulated Annealing: use of new tool in bin packing , 1988 .

[53]  B. Golden Approaches to the Cutting Stock Problem , 1976 .

[54]  B. Kröger Guillotineable bin packing: A genetic approach , 1995 .

[55]  Graham Kendall,et al.  Applying Simulated Annealing and the No Fit Polygon to the Nesting Problem , 2000 .

[56]  S. C. Sarin Two-Dimensional Stock Cutting Problems and Solution Methodologies , 1983 .

[57]  Paul E. Sweeney,et al.  Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography , 1992 .

[58]  Jacek Blazewicz,et al.  Using a tabu search approach for solving the two-dimensional irregular cutting problem , 1993, Ann. Oper. Res..

[59]  K.K.B. Hon,et al.  New approaches for the nesting of two-dimensional shapes for press tool design , 1992 .

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

[61]  J. A. George,et al.  Packing different-sized circles into a rectangular container , 1995 .

[62]  P. Jain,et al.  Optimal Blank Nesting Using Simulated Annealing , 1992 .

[63]  E. Hopper,et al.  Application of Genetic Algorithms to Packing Problems — A Review , 1998 .

[64]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .