Abstract
Stochastic Local Search (SLS) algorithms can be seen as being composed of several algorithmic components, each playing some specific role with respect to overall performance. This article explores the application of experimental design techniques to analyze the effect of components of SLS algorithms for Multiobjective Combinatorial Optimization problems, in particular for the Biobjective Quadratic Assignment Problem. The analysis shows that there exists a strong dependence between the choices for these components and various instance features, such as the structure of the input data and the correlation between the objectives.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Andersen, K. Jörnsten, and M. Lind. On bicriterion minimal spanning trees: An approximation. Computers & Operations Research, 23(12):1171–1182, 1996.
J. Conover. Pratical Nonparametric Statistics. John Wiley & Sons, New York, NY, 1980.
P. Czyzak and A. Jaszkiewicz. Pareto simulated annealing - a metaheuristic technique for multiple objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7:34–47, 1998.
A. Dean and D. Voss. Design and Analysis of Experiments. Springer Verlag, New York, NY, 1999.
C. M. Fonseca and P. Fleming. On the performance assessment and comparison of stochastic multiobjective optimizers. In H. M. Voigt et al., editors, Proceedings of PPSN-IV, Fourth International Conference on Parallel Problem Solving from Nature, volume 1141 of LNCS, pages 584–593. Springer Verlag, Berlin, Germany, 1996.
C. M. Fonseca, V. Grunert da Fonseca, and L. Paquete. Exploring the performance of stochastic multiobjective optimisers with the second-order attainment function. In C. C. Coello, A. H. Aguirre, and E. Zitzler, editors, Evolutionary Multi-criterion Optimization (EMO 2005), volume 3410 of LNCS, pages 250–264. Springer Verlag, Berlin, Germany, 2005.
X. Gandibleux and M. Ehrgott. 20 years of multiobjective metaheuristics. But what about the solution of combinatorial problems with multiple objectives? In C. C. Coello, A. H. Aguirre, and E. Zitzler, editors, Evolutionary Multi-criterion Optimization (EMO 2005), volume 3410 of LNCS, pages 33–46. Springer Verlag, Berlin, Germany, 2005.
X. Gandibleux, N. Mezdaoui, and A. Fréville. A tabu search procedure to solve multiobjective combinatorial optimization problems. In R. Caballero, F. Ruiz, and R. Steuer, editors, Advances in Multiple Objective and Goal Programming, volume 455 of LNEMS, pages 291–300. Springer Verlag, 1997.
X. Gandibleux, H. Morita, and N. Katoh. Use of a genetic heritage for solving the assignment problem. In C. M. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors, Evolutionary Multi-criterion Optimization (EMO 2003), volume 2632 of LNCS, pages 43–57. Springer Verlag, Berlin, Germany, 2003.
P. I. Good. Permutation Tests: A pratical guide to resampling methods for testing hypothesis. Springer Verlag, New York, USA, 2nd edition, 2000.
V. Grunert da Fonseca, C. M. Fonseca, and A. Hall. Inferential performance assessment of stochastic optimizers and the attainment function. In E. Zitzler, K. Deb, L. Thiele, C. C. Coello, and D. Corne, editors, Evolutionary Multi-criterion Optimization (EMO 2001), volume 1993 of LNCS, pages 213–225. Springer Verlag, Berlin, Germany, 2001.
H. V. Hamacher, M. Labbé, and S. Nickel. Multicriteria network location problems with sum objectives. Networks, 33:79–92, 1999.
M. P. Hansen and A. Jaszkiewicz. 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.
H. Hoos and T. Stützle. Stochastic Local Search – Foundations and Applications. Morgan Kaufmann Publishers, San Francisco, CA, 2004.
J. Hsu. Multiple Comparisons - Theory and Methods. Chapman & Hall/CRC, 1996.
A. Jaszkiewicz. Genetic local search for multiple objective combinatorial optimization. Technical Report RA-014/98, Institute of Computing Science, Pozna’n University of Technology, Poznań, Poland, 1998.
P. Klingsberg. A gray code for compositions. Journal of Algorithms, 3:41–44, 1982.
J. Knowles and D. Corne. Instance generators and test suites for the multiobjective quadratic assignment problem. In C. M. Fonseca et al., editors, Evolutionary Multi-criterion Optimization (2003), volume 2632 of LNCS, pages 295–310. Springer Verlag, Berlin, Germany, 2003.
Manuel López-Ibáñez, Luis Paquete, and Thomas Stützle. Hybrid population-based algorithms for the bi-objective quadratic assignment problem. Journal of Mathematical Modelling and Algorithms, 5(1):111–137, 2006.
L. Paquete. Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: Methodology and Analysis. PhD thesis, Fachbereich Informatik, Technische Universität Darmstadt, 2005.
L. Paquete and C. Fonseca. A study of examination timetabling with multiobjective evolutionary algorithms. In Proceedings of the 4th Metaheuristics International Conference (MIC 2001), pages 149–154, Porto, Portugal, 2001.
L. Paquete and T. Stützle. A two-phase local search for the biobjective traveling salesman problem. In C. M. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors, Proceedings of the Evolutionary Multi-criterion Optimization (EMO 2003), volume 2632 of LNCS, pages 479–493. Springer Verlag, Berlin, Germany, 2003.
L. Paquete and T. Stützle. Stochatic local search for multiobjective optimization problems. In T. F. Gonzalez, editor, Approximation Algorithms and Metaheuristics. Chapman & Hall / CRC, In press.
K. J. Shaw, C. M. Fonseca, A. L. Nortcliffe, M. Thompson, J. Love, and P. J. Fleming. Assessing the performance of multiobjective genetic algorithms for optimization of a batch process scheduling problem. In Proceedings of the 1999 Congress on Evolutionary Computation (CEC’99), volume 1, pages 34–75, 1999.
R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York, NY, 1986.
T. Stützle. Iterated local search for the quadratic assignment problem. European Journal of Operational Research, 2006. In press.
É. D. Taillard. Robust taboo search for the quadratic assignment problem. Parallel Computing, 17:443–455, 1991.
É. D. Taillard. Comparison of iterative searches for the quadratic assignment problem. Location Science, 3:87–105, 1995.
E. G. Talbi. A hybrid evolutionary approach for multicriteria optimization problems: Application to the flow shop. In E. Zitzler, K. Deb, L. Thiele, C. C. Coello, and D. Corne, editors, Evolutionary Multi-criterion Optimization (EMO 2001), volume 1993 of LNCS, pages 416–428. Springer Verlag, Berlin, Germany, 2001.
E. L. Ulungu. Optimisation combinatoire multicritére: Détermination de l’ensemble des solutions efficaces et méthodes interactives. PhD thesis, Université de Mons-Hainaut, Mons, Belgium, 1993.
E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. Grunert da Fonseca. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117–132, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Paquete, L., Stützle, T., López-Ibáñez, M. (2007). Using Experimental Design to Analyze Stochastic Local Search Algorithms for Multiobjective Problems. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W., Hartl, R.F., Reimann, M. (eds) Metaheuristics. Operations Research/Computer Science Interfaces Series, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71921-4_17
Download citation
DOI: https://doi.org/10.1007/978-0-387-71921-4_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-71919-1
Online ISBN: 978-0-387-71921-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)