Abstract
The Linear Ordering Problem (LOP) is an NP-hard combinatorial optimization problem that arises in a variety of applications and several algorithmic approaches to its solution have been proposed. However, few details are known about the search space characteristics of LOP instances. In this article we develop a detailed study of the LOP search space. The results indicate that, in general, LOP instances show high fitness-distance correlations and large autocorrelation length but also that there exist significant differences between real-life and randomly generated LOP instances. Because of the limited size of real-world instances, we propose new, randomly generated large real-life like LOP instances which appear to be much harder than other randomly generated instances. Additionally, we propose a rather straightforward Iterated Local Search algorithm, which shows better performance than several state-of-the-art heuristics.
This is a preview of subscription content, log in via an institution to check access.
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
O. Becker. Das Helmstädtersche Reihenfolgeproblem-die Effizienz verschiedener Näherungsverfahren. In Computer uses in the Social Science,Wien, January 1967.
V. Campos, M. Laguna, and R. Martí. Scatter search for the linear ordering problem. In D. Corne et al., editor, New Ideas in Optimization, pages 331–339. McGraw-Hill, 1999.
S. Chanas and P. Kobylanski. A new heuristic algorithm solving the linear ordering problem. Computational Optimization and Applications, 6:191–205, 1996.
T. Christof and G. Reinelt. Low-dimensional linear ordering polytopes. Technical report, University of Heidelberg, Germany, 1997.
R. K. Congram. Polynomially Searchable Exponential Neighbourhoods for Sequencing Problems in Combinatorial Optimisation. PhD thesis, University of Southampton, Faculty of Mathematical Studies, UK, 2000.
M. Grötschel, M. Jünger, and G. Reinelt. A cutting plane algorithm for the linear ordering problem. Operations Research, 32(6):1195–1220, 1984.
M. Grötschel, M. Jünger, and G. Reinelt. Optimal triangulation of large real world input-output matrices. Statistische Hefte, 25:261–295, 1984.
H.H. Hoos and T. Stützle. Evaluating Las Vegas algorithms-pitfalls and remedies. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), pages 238–245. Morgan Kaufmann, San Francisco, 1998.
T. Jones and S. Forrest. Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In L.J. Eshelman, editor, Proc. of the 6th International Conference on Genetic Algorithms, pages 184–192. Morgan Kaufman, San Francisco, 1995.
D. E. Knuth. The Stanford GraphBase: A Platform for Combinatorial Computing. Addison Wesley, NewYork, 1993.
M. Laguna, R. Martí, and V. Campos. Intensification and diversification with elite tabu search solutions for the linear ordering problem. Computers and Operation Research, 26:1217–1230, 1999.
H. R. Lourenço, O. Martin, and T. Stützle. Iterated local search. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics, volume 57 of International Series in Operations Research & Management Science, pages 321–353. Kluwer Academic Publishers, Norwell, MA, 2002.
P. Merz and B. Freisleben. Fitness landscapes and memetic algorithm design. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization, pages 245–260. McGraw-Hill, London, 1999.
J. E. Mitchell and B. Borchers. Solving linear ordering problems with a combined interior point/simplex cutting plane algorithm. In H. L. Frenk et al., editor, High Performance Optimization, pages 349–366. Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
C. R. Reeves. Landscapes, operators and heuristic search. Annals of Operational Research, 86:473–490, 1999.
P. Stadler. Towards a theory of landscapes. In R. Lopéz-Peña, R. Capovilla, R. García-Pelayo, H. Waelbroeck, and F. Zertuche, editors, Complex Systems and Binary Networks, volume 461, pages 77–163, Berlin, NewYork, 1995. Springer Verlag.
P. Stadler. Landscapes and their correlation functions. J. of Math. Chemistry, 20:1–45, 1996.
Standard Performance Evaluation Corporation. SPEC CPU95 and CPU2000 Benchmarks. http://www.spec.org/, November 2002.
E. D. Weinberger. Correlated and uncorrelated fitness landscapes and howto tell the difference. Biological Cybernetics, 63:325–336, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schiavinotto, T., Stützle, T. (2003). Search Space Analysis of the Linear Ordering Problem. In: Cagnoni, S., et al. Applications of Evolutionary Computing. EvoWorkshops 2003. Lecture Notes in Computer Science, vol 2611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36605-9_30
Download citation
DOI: https://doi.org/10.1007/3-540-36605-9_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00976-4
Online ISBN: 978-3-540-36605-8
eBook Packages: Springer Book Archive