Abstract
There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called “Elementary Landscapes” and they have a number of special mathematical properties. The term “Quasi-elementary landscapes” is introduced to describe landscapes that are “almost” elementary; in quasi-elementary landscapes there exists some efficiently computed “correction” that captures those parts of the neighborhood structure that deviate from the normal structure found in elementary landscapes. The “shift” operator, as well as the “3-opt” operator for the Traveling Salesman Problem landscapes induce quasi-elementary landscapes. A local search neighborhood for the Maximal Clique problem is also quasi-elementary. Finally, we show that landscapes which are a superposition of elementary landscapes can be quasi-elementary in structure.
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
Chicano, F., Whitley, D., Alba, E.: A methodology to find the elementary landscape decomposition of combinatorial optimization problems. Evolutionary Computation (2011)
Chicano, F., Whitley, D., Alba, E., Luna, F.: Elementary landscape decomposition of the frequency assignment problem. Theoretical Computer Science 412(43), 6002–6019 (2011)
Chicano, F., Alba, E.: Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization. Journal of Heuristics xx, xx–xx (2011), doi:10.1007/s10732-011-9170-6
Grover, L.K.: Local search and the local structure of NP-complete problems. Operations Research Letters 12, 235–243 (1992)
Katayama, K., Hamamoto, A., Harihisa, H.: An effective local search for the maximum clique problem. Information Processing Letters 95(5), 503–511 (2005)
Kauffman, S., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology 128, 11–45 (1987)
Stadler, P.F.: Toward a theory of landscapes. In: Lopéz-Peña, R., Capovilla, R., García-Pelayo, R., Waelbroeck, H., Zertruche, F. (eds.) Complex Systems and Binary Networks, pp. 77–163. Springer (1995)
Stattenberger, G., Dankesreiter, M., Baumgartner, F., Schneider, J.J.: On the neighborhodd structure of the traveling salesman problem generated by local search moves. Journal of Statistical Physics 129, 623–648 (2007)
Sutton, A., Whitley, D., Howe, A.: Computing the moments of k-bounded pseudo-boolean functions over hamming spheres of arbitrary radius in polynomial time. Theoretical Computer Science (2011), doi:10.1016/j.tcs.2011.02.006
Sutton, A.M., Howe, A.E., Whitley, L.D.: A Theoretical Analysis of the k-Satisfiability Search Space. In: Stützle, T., Birattari, M., Hoos, H.H. (eds.) SLS 2009. LNCS, vol. 5752, pp. 46–60. Springer, Heidelberg (2009)
Whitley, D.: Quasi-elementary landscapes. In: Multi-Interdisciplinary Scheduling: Theory and Applications, MISTA (2011)
Whitley, D., Chicano, F., Alba, E., Luna, F.: Elementary landscapes of frequency assignment problems. In: GECCO 2010, pp. 1409–1416. ACM Press (2010)
Whitley, D., Sutton, A.M.: Partial neighborhoods of elementary landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference, Montreal, Canada, pp. 381–388 (July 2009)
Whitley, L.D., Sutton, A.M., Howe, A.E.: Understanding elementary landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference, Atlanta, GA, pp. 585–592 (July 2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Whitley, D., Chicano, F. (2012). Quasi-elementary Landscapes and Superpositions of Elementary Landscapes. In: Hamadi, Y., Schoenauer, M. (eds) Learning and Intelligent Optimization. LION 2012. Lecture Notes in Computer Science, vol 7219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34413-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-34413-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34412-1
Online ISBN: 978-3-642-34413-8
eBook Packages: Computer ScienceComputer Science (R0)