Abstract
The bin-packing problem is a well known NP-Hard optimisation problem, and, over the years, many heuristics have been developed to generate good quality solutions. This paper outlines a genetic programming system which evolves a heuristic that decides whether to put a piece in a bin when presented with the sum of the pieces already in the bin and the size of the piece that is about to be packed. This heuristic operates in a fixed framework that iterates through the open bins, applying the heuristic to each one, before deciding which bin to use. The best evolved programs emulate the functionality of the human designed ‘first-fit’ heuristic. Thus, the contribution of this paper is to demonstrate that genetic programming can be employed to automatically evolve bin packing heuristics which are the same as high quality heuristics which have been designed by humans.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. The MIT Press, Cambridge, Massachusetts (1994)
Koza, J.R., Bennett III, F.H., Andre, D., Keane, M.A.: Genetic Programming III: Darwinian Invention and Problem solving. Morgan Kaufmann, San Francisco (1999)
Koza, J.R.: Genetic Programming: on the Programming of Computers by Means of Natural Selection. The MIT Press, Boston, Massachusetts (1992)
Ross, P.: Hyper-heuristics. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 529–556. Kluwer, Boston (2005)
Burke, E.K., Hart, E., Kendall, G., Newall, J., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern search technology. In: Glover, F., Kochenberger, G. (eds.) Handbook of Meta-Heuristics, pp. 457–474. Kluwer, Dordrecht (2003)
Soubeiga, E.: Development and Application of Hyperheuristics to Personnel Scheduling. PhD thesis, Univesity of Nottingham, School of Computer Science (2003)
Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 4, 67–82 (1997)
Whitley, D., Watson, J.P.: Complexity theory and the no free lunch theorem. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 317–339. Kluwer, Boston (2005)
Ross, P., Schulenburg, S., Marin-Blazquez, J.G., Hart, E.: Hyper heuristics: Learning to combine simple heuristics in bin packing problems. In: Proceedings of the Genetic and Evolutionary Computation Conference 2002 (GECCO 2002), pp. 942–948 (2002)
Ross, P., Marin-Blazquez, J.G., Schulenburg, S., Hart, E.: Learning a procedure that can solve hard bin-packing problems: A new ga-based approach to hyperheurstics. In: Proceedings of the Genetic and Evolutionary Computation Conference 2003 (GECCO 2003), Chicago, Illinois, pp. 1295–1306 (2003)
Burke, E.K., Kendall, G., Landa Silva, J.D., O’Brien, R.F.J., Soubeiga, E.: An ant algorithm hyperheuristic for the project presentation scheduling problem. In: Proceedings of the Congress on Evolutionary Computation 2005 (CEC 2005), Edinburgh, U.K., vol. 3, pp. 2263–2270 (2005)
Burke, E.K., Kendall, G., Soubeiga, E.: A tabu-search hyper-heuristic for timetabling and rostering. Journal of Heuristics 9, 451–470 (2003)
Cowling, P., Kendall, G., Soubeiga, E.: A hyperheuristic approach to scheduling a sales summit. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 176–190. Springer, Heidelberg (2001)
Burke, E.K., Landa Silva, J.D., Soubeiga, E.: Multi-objective hyper-heuristic approaches for space allocation and timetabling. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Meta-heuristics: Progress as Real Problem Solvers, Selected Papers from the 5th Metaheuristics International Conference (MIC 2003), pp. 129–158. Springer, Heidelberg (2005)
Burke, E.K., McCollum, B., Meisels, A., Petrovic, S., Qu, R.: A graph-based hyper heuristic for educational timetabling problems. European Journal of Operational Research (in press, to appear 2006, available online November 21, 2005)
Burke, E.K., Petrovic, S., Qu, R.: Case based heuristic selection for timetabling problems. Journal of Scheduling 9, 115–132 (2006)
Dowsland, K., Soubeiga, E., Burke, E.K.: A simulated annealing hyper-heuristic for determining shipper sizes. European Journal of Operational Research (in press, to appear 2006, available online November 29, 2005) (accepted)
Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. John Wiley and Sons, Chichester (1990)
Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. Journal of Heuristics 2, 5–30 (1996)
Beasley, J.E.: Binpacking benchmark data, at the brunell university or-library. (Last modified: 07-09-2004) [accessed March 1, 2006], Available at: http://people.brunel.ac.uk/~mastjjb/jeb/orlib/binpackinfo.html
Coffman Jr., E.G., Galambos, G., Martello, S., Vigo, D.: Bin packing approximation algorithms: Combinatorial analysis. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, Kluwer, Dordrecht (1998)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Fransisco (1979)
Rhee, W.T., Talagrand, M.: On line bin packing with items of random size. Math. Oper. Res. 18, 438–445 (1993)
Johnson, D., Demers, A., Ullman, J., Garey, M., Graham, R.: Worst-case performance bounds for simple one-dimensional packaging algorithms. SIAM Journal on Computing 3, 299–325 (1974)
Koza, J.R., Poli, R.: Genetic programming. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 127–164. Kluwer, Boston (2005)
Bernstein, Y., Li, X., Ciesielski, V., Song, A.: Multiobjective parsimony enforcement for superior generalisation performance. In: Proceedings of the Congress for Evolutionary Computation 2004 (CEC 2004), Portland, Oregon, pp. 83–89 (2004)
Falkenauer, E., Delchambre, A.: A genetic algorithm for bin packing and line balancing. In: Proceedings of the IEEE 1992 Int. Conference on Robotics and Automation, Nice, France, pp. 1186–1192 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burke, E.K., Hyde, M.R., Kendall, G. (2006). Evolving Bin Packing Heuristics with Genetic Programming. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_87
Download citation
DOI: https://doi.org/10.1007/11844297_87
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
eBook Packages: Computer ScienceComputer Science (R0)