Search Space Analysis of the Linear Ordering Problem
- 873 Downloads
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.
KeywordsLocal Search Global Optimum Local Search Algorithm Matrix Entry Scatter Search
Unable to display preview. Download preview PDF.
- 1.O. Becker. Das Helmstädtersche Reihenfolgeproblem-die Effizienz verschiedener Näherungsverfahren. In Computer uses in the Social Science,Wien, January 1967.Google Scholar
- 2.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.Google Scholar
- 4.T. Christof and G. Reinelt. Low-dimensional linear ordering polytopes. Technical report, University of Heidelberg, Germany, 1997.Google Scholar
- 5.R. K. Congram. Polynomially Searchable Exponential Neighbourhoods for Sequencing Problems in Combinatorial Optimisation. PhD thesis, University of Southampton, Faculty of Mathematical Studies, UK, 2000.Google Scholar
- 8.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.Google Scholar
- 9.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.Google Scholar
- 10.D. E. Knuth. The Stanford GraphBase: A Platform for Combinatorial Computing. Addison Wesley, NewYork, 1993.Google Scholar
- 12.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.Google Scholar
- 13.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.Google Scholar
- 14.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.Google Scholar
- 16.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.Google Scholar
- 18.Standard Performance Evaluation Corporation. SPEC CPU95 and CPU2000 Benchmarks. http://www.spec.org/, November 2002.