Skip to main content
SpringerLink
Log in

A Hybrid Improvement Heuristic for the One-Dimensional Bin Packing Problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

We propose in this work a hybrid improvement procedure for the bin packing problem. This heuristic has several features: the use of lower bounding strategies; the generation of initial solutions by reference to the dual min-max problem; the use of load redistribution based on dominance, differencing, and unbalancing; and the inclusion of an improvement process utilizing tabu search. Encouraging results have been obtained for a very wide range of benchmark instances, illustrating the robustness of the algorithm. The hybrid improvement procedure compares favourably with all other heuristics in the literature. It improved the best known solutions for many of the benchmark instances and found the largest number of optimal solutions with respect to the other available approximate algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alvim, A.C.F., F. Glover, C.C. Ribeiro, and D.J. Aloise. (1999). “Local Search for the Bin Packing Problem.” In Extended Abstracts of the 3rd Metaheuristics International Conference, Angra dos Reis, pp. 7-12.

  • Alvim A.C.F., D.J. Aloise, F. Glover, and C.C. Ribeiro. (2001). “A Hybrid Improvement Heuristic for the Bin Packing Problem.” In Extended Abstracts of the 4th Metaheuristics International Conference, Porto, pp. 63-68.

  • Dell'Amico, M. and S. Martello. (1995). “Optimal Scheduling of Tasks on Identical Parallel Processors.” ORSA Journal on Computing 7, 191–200.

    Google Scholar 

  • Argüello, M.F., T.A. Feo, and O. Goldschmidt. (1996). “Randomized Methods for the Number Partitioning Problem.” Computers and Operations Research 23, 103–111.

    Google Scholar 

  • Coffman, E.G. Jr., M.R. Garey, and D.S. Johnson. (1997). “Approximation Algorithms for Bin Packing:ASurvey.” In D. Hochbaum (ed.), Approximation Algorithms for NP-Hard Problems. PWS Publishing, pp. 46-93.

  • Dyckhoff, H. (1990). “A Typology of Cutting and Packing Problems.” European Journal of Operational Research 44, 145–159.

    Google Scholar 

  • Falkenauer, E. (1996). “A Hybrid Grouping Genetic Algorithm for Bin Packing.” Journal of Heuristics 2, 5–30.

    Google Scholar 

  • Fekete, S.P. and J. Schepers. (2001). “New Classes of Fast Lower Bounds for Bin Packing Problems.” Mathematical Programming 91(1), 11–31.

    Google Scholar 

  • Fleszar, K. and K. Hindi. (2002). “New Heuristics for One-Dimensional Bin Packing.” Computers and Operations Research 29(7), 821–839.

    Google Scholar 

  • Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company.

  • Gent, I. (1998). “Heuristic Solution of Open Bin Packing Problems.” Journal of Heuristics 3, 299–304.

    Google Scholar 

  • Glover, F. and M. Laguna. (1997). Tabu Search. Kluwer Academic Publishers.

  • Graham, R.L. (1969). “Bounds on Multiprocessing Timing Anomalies.” SIAM Journal of Applied Mathematics 17, 416–429.

    Google Scholar 

  • Hackman, S.T., M. Magazine, and T. Wee. (1989). “Fast, Effective Algorithms for Simple Assembly Line Balancing Problems.” Operations Research 37, 916–924.

    Google Scholar 

  • Hansen, P. and N. Mladenovi?. (1999). “An Introduction to Variable Neighbourhood Search.” In S. Voss, S. Martello, I.H. Osman, and C. Roucairol (eds.), Metaheuristics: Advances and Trends in Local Search Procedures for Optimization. Kluwer, pp. 433-458.

  • Hübscher, R. and F. Glover. (1994). “Applying Tabu Search with Influential Diversification to Multiprocessor Scheduling.” Computers and Operations Research 21, 877–884.

    Google Scholar 

  • Karmarkar, N. and R.M. Karp. (1982a). “The Differencing Method of Set Partitioning.” Report UCB/CSD 82/113, Computer Science Division, University of California, Berkeley.

    Google Scholar 

  • Karmarkar, N. and R.M. Karp. (1982). “An Efficient Approximation Scheme for the One-Dimensional Bin Packing Problem.” In Proceedings of the 23rd Symposium on Foundations of Computer Science. IEEE Computer Society, pp. 312-320.

  • Karp, R.M. (1972). “Reducibility Among Combinatorial Problems.” In R.E. Miller and J.M. Thatcher (eds.), Complexity of Computer Computations. Plenum Press, pp. 85-103.

  • Martello, S. and P. Toth. (1990a). Knapsack Problems: Algorithms and Computer Implementations. Wiley.

  • Martello, S. and P. Toth. (1990). “Lower Bounds and Reduction Procedures for the Bin Packing Problem.” Discrete Applied Mathematics 28, 59–70.

    Google Scholar 

  • Schoenfield, J.E. (2002). “Fast, Exact Solution of Open Bin Packing Problems Without Linear Programming.” Working paper.

  • Scholl, A. (2003). Online document at http://www.bwl.tu-darmstadt.de/bwl3/forsch/projekte/binpp/index.htm, last visited on April 13.

  • Scholl, A., R. Klein, and C. Jürgens. (1997). “BISON: A Fast Hybrid Procedure for Exactly Solving the One-Dimensional Bin Packing Problem.” Computers and Operations Research 24, 627–645.

    Google Scholar 

  • Scholl, A. and S. Voss. (1996). “Simple Assembly Line Balancing-Heuristic Approaches.” Journal of Heuristics 2, 217–244.

    Google Scholar 

  • Schwerin, P. and G. Wäscher. (1997). “The Bin-Packing Problem: A Problem Generator and Some Numerical Experiments with FFD Packing and MTP.” International Transactions in Operational Research 4, 377–389.

    Google Scholar 

  • Schwerin, P. and G. Wäscher. (1999). “A New Lower Bound for the Bin-Packing Problem and its Integration into MTP.” Pesquisa Operacional 19, 111–129.

    Google Scholar 

  • Soma, N.Y., H.H. Yanasse, and N. Maculan. (1999). “A Heuristic for the Bin Packing Problem.” Presented at the IFORS Triennial Conference, Beijing.

  • Special Interest Group on Cutting and Packing. (2003). Online document at http://www.apdio.pt/sicup/Sicuphomepage/research.htm, last visited on April 13.

  • Valério de Carvalho, J.M. (1999). “Exact Solution of Bin-Packing Problems Using Column Generation and Branch-and-Bound.” Annals of Operations Research 86, 629–659.

    Google Scholar 

  • Vanderbeck, F. (1999). “Computational Study of a Column Generation Algorithm for Bin Packing and Cutting Stock Problems.” Mathematical Programming 86, 565–594.

    Google Scholar 

  • Wäscher, G. and T. Gau. (1996). “Heuristics for the Integer One-Dimensional Cutting Stock Problem: A Computational Study.” OR Spektrum 18, 131–144.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Catholic University of Rio de Janeiro, Rua Marquês de São Vicente 225, Rio de Janeiro, 22453-900, Brazil

    Adriana C.F. Alvim & Celso C. Ribeiro

  2. Leeds School of Business, University of Colorado at Boulder, Boulder, CO, 80309-0419, US

    Fred Glover

  3. Department of Computer Science and Applied Mathematics, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil

    Dario J. Aloise

Authors
  1. Adriana C.F. Alvim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Celso C. Ribeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fred Glover
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dario J. Aloise
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alvim, A.C., Ribeiro, C.C., Glover, F. et al. A Hybrid Improvement Heuristic for the One-Dimensional Bin Packing Problem. Journal of Heuristics 10, 205–229 (2004). https://doi.org/10.1023/B:HEUR.0000026267.44673.ed

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:HEUR.0000026267.44673.ed

Search

Navigation