Skip to main content

An Evolutionary Algorithm for the Unconstrained Binary Quadratic Problems

  • Conference paper

Part of the book series: Advances in Soft Computing ((AINSC,volume 33))

Abstract

In this paper a new evolutionary algorithm (EA) is described for the unconstrained Binary Quadratic Problem, which is to be used with small, medium and large scale problems as well. This method can be divided into two stages, where each stage is a steady-state EA. The first stage improves the quality of the initial population. The second stage uses concatenated, complex neighbourhood structures for the mutations and improves the quality of the solutions with a randomized k-opt local search procedure. The bit selection by mutation is based on an explicit collective memory (EC-memory) that is a modification of the flee-mutation operator (Sebag et al. 1997). We tested our algorithm on all the benchmark problems of the OR-Library. Comparing the results with other heuristic methods, we can conclude that our algorithm belongs to the best methods of this problem scope.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beasley JE (1999) Heuristic algorithm for the unconstrained binary quadratic programming problem, Working Paper, Imperial College.

    Google Scholar 

  2. Bjorndal MH, Caprara A, Cowling PI, Della Crosce F, Lourenço H, Malucelli F, Orman AJ, Pisinger D, Rego C, Salazar JJ (1995) Some thoughts on combinatorial optimization. European Journal of Operational Research 83: 153–170.

    Article  Google Scholar 

  3. Glover F (1997) A template for scatter search and path relinking. In: Hao JK, Lutton E, Ronald E, Schoenauer D, Snyers D (eds) Artificial Evolution, Lecture Notes in Computer Science, 1363. Heidelberg, pp 13–54.

    Google Scholar 

  4. Glover F, Kochenberger GA, Alidaee B (1998) Adaptive memory tabu search for binary quadratic programs, Management Science. 44.(3): 336–345.

    Article  MATH  Google Scholar 

  5. Glover F, Alidaee B, Rego C, Kochenberger GA (2002) One-pass heuristics for large-scale unconstrained binary quadratic problems, European Journal of Operational Research 137: 272–287.

    Article  MATH  MathSciNet  Google Scholar 

  6. Helmberg C, Rendl F (1998) Solving quadratic (0,1)-problem by semidefinite programs and cutting planes, Mathematical Programming 82: 388–399.

    MathSciNet  Google Scholar 

  7. Horst R, Pardalos PM, Thoai NV (2000) Introduction to Global Optimization 2nd Edition, Kluwer Ac. Pub. Dordrecht

    MATH  Google Scholar 

  8. Katayama K, Narihisa H (2001) Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem, European Journal of Operational Research 134: 103–119.

    Article  MATH  MathSciNet  Google Scholar 

  9. Katayama K, Narihisa H (2001a) On Fundamental Design of Parthenogenetic Algorithm for the Binary Quadratic Programming Problem, Proceeding of the 2001 Congress on Evolutionary Computing. Seoul. Vol. 1: 356–363.

    Article  Google Scholar 

  10. Lodi A, Allemand K, Liebling M (1999) An evolutionary heuristic for quadratic 0–1 programming, European Journal of Operational Research 119: 662–670.

    Article  MATH  Google Scholar 

  11. Merz P, Freisleben B (1999) Genetic algorithm for binary quadratic programming, in: Proceeding of the 1999 international Genetic and Evolutionary Computation Conference, Morgan Kaufmann, Los Altos, CA, pp 417–424.

    Google Scholar 

  12. Merz P, Freisleben B (2002) Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming. Journal of Heuristics, vol. 8, no.2, pp 197–213.

    Article  MATH  Google Scholar 

  13. Merz P, Katayama K (2001) A Hybrid Evolutionary Local Search Approach for the Unconstrained Binary Quadratic Programming Problem. Tech. Rep., Department of Computer Science, University of Tübingen, Germany. Accepted for publication in Bio Systems.

    Google Scholar 

  14. Pardalos PM, Rodgers GP (1990) Computational aspects of a branch and bound algorithm for quadratic zero-one programming, Computing 45: 131–144.

    Article  MATH  MathSciNet  Google Scholar 

  15. Sebag M, Schoenauer M, Ravisé C (1997) Toward Civilized Evolution: Developing Inhibitions. In: Bäck T (ed): Proc. of the 7th International Conference on Genetic Algorithm. Morgan Kaufmann Pub. San Francisco, pp 291–298.

    Google Scholar 

  16. Sherali HD, Adams WP (1998) A reformulation-linearization technique for solving discrete and continuous nonconvex problems, Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  17. Shor NZ (1998) Nondifferentiable Optimization and Polynomial Problems, Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Borgulya, I. (2005). An Evolutionary Algorithm for the Unconstrained Binary Quadratic Problems. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-31182-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22807-3

  • Online ISBN: 978-3-540-31182-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics