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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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.
Çela, E.: The Quadratic Assignment Problem: Theory and Algorithms, Kluwer Academic, Dordrecht, The Netherlands, 1998.
Dorigo, M. and Stützle, T.: Ant Colony Optimization, MIT, Cambridge, Massachusetts, 2004.
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.
Galinier, P. and Hao, J. K.: Hybrid evolutionary algorithms for graph coloring. J. Comb. Optim. 3(4) (1999), 379–397.
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.
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.
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.
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.
Hoos, H. and Stützle, T.: Stochastic Local Search – Foundations and Applications, Morgan Kaufmann, San Francisco, California, 2004.
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.
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.
Jaszkiewicz, A.: Genetic local search for multiple objective combinatorial optimization. Eur. J. Oper. Res. 137(1) (2002), 50–71.
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.
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.
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.
López-Ibáñez, M.: Multi-objective ant colony optimization. Diploma thesis, Intellectics Group, Computer Science Department, Technische Universität Darmstadt, Germany, 2004.
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.
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.
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.
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.
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.
Sahni, S. and Gonzalez, T.: P-complete approximation problems. J. ACM 23 (1976), 555–565.
Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation and Application, Wiley Series in Probability and Mathematical Statistics, Wiley, New York, 1986.
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.
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.
Taillard, É. D.: Robust taboo search for the quadratic assignment problem. Parallel Comput. 17 (1991), 443–455.
Taillard, É. D.: Comparison of iterative searches for the quadratic assignment problem. Location Sci. 3 (1995), 87–105.
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.
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.
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.
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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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DOI: https://doi.org/10.1007/s10852-005-9034-x