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Hybrid Population-Based Algorithms for the Bi-Objective Quadratic Assignment Problem

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Journal of Mathematical Modelling and Algorithms

Abstract

We present variants of an ant colony optimization (MO-ACO) algorithm and of an evolutionary algorithm (SPEA2) for tackling multi-objective combinatorial optimization problems, hybridized with an iterative improvement algorithm and the robust tabu search algorithm. The performance of the resulting hybrid stochastic local search (SLS) algorithms is experimentally investigated for the bi-objective quadratic assignment problem (bQAP) and compared against repeated applications of the underlying local search algorithms for several scalarizations. The experiments consider structured and unstructured bQAP instances with various degrees of correlation between the flow matrices. We do a systematic experimental analysis of the algorithms using outperformance relations and the attainment functions methodology to asses differences in the performance of the algorithms. The experimental results show the usefulness of the hybrid algorithms if the available computation time is not too limited and identify SPEA2 hybridized with very short tabu search runs as the most promising variant.

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References

  1. Bleuler, S., Laumanns, M., Thiele, L. and Zitzler, E.: PISA – A platform and programming language independent interface for search algorithms in C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb and L. Thiele (eds.), Evolutionary Multi-Criterion Optimization (EMO 2003), Vol. 2632 of Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, 2003, pp. 494–508.

    Google Scholar 

  2. Çela, E.: The Quadratic Assignment Problem: Theory and Algorithms, Kluwer Academic, Dordrecht, The Netherlands, 1998.

    MATH  Google Scholar 

  3. Dorigo, M. and Stützle, T.: Ant Colony Optimization, MIT, Cambridge, Massachusetts, 2004.

    MATH  Google Scholar 

  4. Fleurent, C. and Ferland, J. A.: Genetic hybrids for the quadratic assignment problem, in P. M. Pardalos and H. Wolkowicz (eds.), Quadratic Assignment and Related Problems, Vol. 16 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence, Rhode Island, 1994, pp. 173–187.

    Google Scholar 

  5. Galinier, P. and Hao, J. K.: Hybrid evolutionary algorithms for graph coloring. J. Comb. Optim. 3(4) (1999), 379–397.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gambardella, L. M., Taillard, E. D. and Dorigo, M.: Ant colonies for the quadratic assignment problem. J. Oper. Res. Soc. 50(2) (1999), 167–176.

    Article  MATH  Google Scholar 

  7. Grunert da Fonseca, V., Fonseca, C. M. and Hall, A.: Inferential performance assessment of stochastic optimisers and the attainment function, in E. Zitzler, K. Deb, L. Thiele, C. C. Coello and D. Corne (eds.), Evolutionary Multi-criterion Optimization (EMO 2001), Vol. 1993 of Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, 2001, pp. 213–225.

    Google Scholar 

  8. Hamacher, H., Nickel, S. and Tenfelde-Podehl, D.: Facilities layout for social institutions, in Operation Research Proceedings 2001, Selected Papers of the International Conference on Operations Research (OR2001), Springer, Berlin Heidelberg New York, 2001, pp. 229–236.

    Google Scholar 

  9. Hansen, M. P. and Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, 1998.

  10. Hoos, H. and Stützle, T.: Stochastic Local Search – Foundations and Applications, Morgan Kaufmann, San Francisco, California, 2004.

    Google Scholar 

  11. Iredi, S., Merkle, D. and Middendorf, M.: Bi-Criterion optimization with multi colony ant algorithms, in E. Zitzler, K. Deb, L. Thiele, C. C. Coello and D. Corne (eds.), First International Conference on Evolutionary Multi-Criterion Optimization, (EMO'01), Vol. 1993 of Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, 2001, pp. 359–372.

    Google Scholar 

  12. Ishibuchi, H., Yoshida, T. and Murata, T.: Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Trans. Evol. Comput. 7(2) (2003), 204–223.

    Article  Google Scholar 

  13. Jaszkiewicz, A.: Genetic local search for multiple objective combinatorial optimization. Eur. J. Oper. Res. 137(1) (2002), 50–71.

    Article  MATH  MathSciNet  Google Scholar 

  14. Knowles, J. and Corne, D.: The pareto archived evolution strategy: a new baseline algorithm for pareto multiobjective optimisation, in Proceedings of 1999 Congress on Evolutionary Computation (CEC'99), Vol. 1. 1999, pp. 98–105.

  15. Knowles, J. and Corne, D.: Towards landscape analyses to inform the design of a hybrid local search for the multiobjective quadratic assignment problem, in A. Abraham, J. R. del Solar and M. Koppen (eds.), Soft Computing Systems: Design, Management and Applications, IOS, 2002, pp. 271–279.

  16. Knowles, J. and Corne, D.: Instance generators and test suites for the multiobjective quadratic assignment problem, in C. M. Fonseca, P. Fleming, E. Zitzler, K. Deb and L. Thiele (eds.), Evolutionary Multi-criterion Optimization (EMO 2003), Vol. 2632 of Lecture Notes in Computer Sience, Springer, Berlin Heidelberg New York, 2003, pp. 295–310.

    Google Scholar 

  17. López-Ibáñez, M.: Multi-objective ant colony optimization. Diploma thesis, Intellectics Group, Computer Science Department, Technische Universität Darmstadt, Germany, 2004.

  18. López-Ibáñez, M., Paquete, L. and Stützle, T.: On the design of ACO for the biobjective quadratic assignment problem, in M. Dorigo, L. Gambardella, F. Mondada, T. Stützle, M. Birratari and C. Blum (eds.), ANTS'2004, Fourth International Workshop on Ant Algorithms and Swarm Intelligence, Vol. 3172 of Lecture Notes in Computer Science, Springer, Berlin Heidelberg New York, 2004, pp. 214–225.

    Google Scholar 

  19. Merz, P.: Memetic algorithms for combinatorial optimization problems: fitness landscapes and effective search strategies. PhD thesis, Department of Electrical Engineering and Computer Science, University of Siegen, Germany, 2000.

  20. Merz, P. and Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans. Evol Comput. 4(4) (2000), 337–352.

    Article  Google Scholar 

  21. Paquete, L., Chiarandini, M. and Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: an experimental study, in X. Gandibleux, M. Sevaux, K. Sörensen and V. T'kindt (eds.), Metaheuristics for Multiobjective Optimisation, Vol. 535 of Lecture Notes in Economics and Mathematical Systems, Springer, Berlin Heidelberg New York, 2004, pp. 177–200.

    Google Scholar 

  22. Paquete, L. and Stützle, T.: A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. Eur. J. Oper. Res. 169(3) (2006), 943–959.

    Article  MATH  Google Scholar 

  23. Sahni, S. and Gonzalez, T.: P-complete approximation problems. J. ACM 23 (1976), 555–565.

    Article  MATH  MathSciNet  Google Scholar 

  24. Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation and Application, Wiley Series in Probability and Mathematical Statistics, Wiley, New York, 1986.

    Google Scholar 

  25. Stützle, T. and Dorigo, M.: ACO algorithms for the quadratic assignment problem, in D. Corne, M. Dorigo and F. Glover (eds.), New Ideas in Optimization, McGraw Hill, London, UK, 1999, pp. 33–50.

    Google Scholar 

  26. Stützle, T. and Hoos, H. H.: \( {\user1{\mathcal{M}\mathcal{A}\mathcal{X}}} \)-\({\user1{\mathcal{M}\mathcal{I}\mathcal{N}}}\) ant system. Future Gener. Comput. Syst. 16(8) (2000), 889–914.

    Article  Google Scholar 

  27. Taillard, É. D.: Robust taboo search for the quadratic assignment problem. Parallel Comput. 17 (1991), 443–455.

    Article  MathSciNet  Google Scholar 

  28. Taillard, É. D.: Comparison of iterative searches for the quadratic assignment problem. Location Sci. 3 (1995), 87–105.

    Article  MATH  Google Scholar 

  29. Zitzler, E., Laumanns, M. and Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization, in K. Giannakoglou, D. Tsahalis, J. Periaux, K. Papaliliou and T. Fogarty (eds.), Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems. Proceedings of the EUROGEN2001 Conference, International Center for Numerical Methods in Engineering (CIMNE), 2002, pp. 95–100.

  30. Zitzler, E. and Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 4(3) (1999), 257–271.

    Article  Google Scholar 

  31. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C. M. and Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2) (2003), 117–132.

    Article  Google Scholar 

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Authors and Affiliations

  1. Centre for Emergent Computing, School of the Built Environment, Napier University, 10 Colinton Rd, Edinburgh, EH10 5DT, UK

    Manuel López-Ibáñez

  2. Faculdade de Economia and Centro de Sistemas Inteligentes, Universidade do Algarve, 8005-139, Faro, Portugal

    Luís Paquete

  3. Université Libre de Bruxelles, IRIDIA, Avenue Franklin Roosevelt 50, 1050, Brussels, Belgium

    Thomas Stützle

Authors
  1. Manuel López-Ibáñez
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  2. Luís Paquete
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  3. Thomas Stützle
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Correspondence to Manuel López-Ibáñez.

Additional information

This research was mainly done while Luís Paquete and Thomas Stützle were with the Intellectics Group at the Computer Science Department of Darmstadt University of Technology, Germany

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López-Ibáñez, M., Paquete, L. & Stützle, T. Hybrid Population-Based Algorithms for the Bi-Objective Quadratic Assignment Problem. J Math Model Algor 5, 111–137 (2006). https://doi.org/10.1007/s10852-005-9034-x

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