Abstract
One of the most commonly-used metaphors to describe the process of heuristic methods such as local search in solving a combinatorial optimization problem is that of a “fitness landscape”. However, describing exactly what we mean by such a term is not as easy as might be assumed. Indeed, many cases of its usage in both the biological and optimization literature reveal a rather serious lack of understanding.
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
Biggs, N. L., 1993, Algebraic Graph Theory, Cambridge University Press, Cambridge.
Boese, K. D., Kahng, A. B. and Muddu, S., 1994, A new adaptive multi-start technique for combinatorial global optimizations, Oper. Res. Lett. 16:101–113.
Box, G. E. P. and Jenkins, G. M., 1970, Time Series Analysis, Forecasting and Control, Holden Day, San Francisco.
Corne, D. A., Dorigo, M. and Glover, F., eds, 1999, New Methods in Optimization, McGraw-Hill, London.
Dawkins, R. (1996) Climbing Mount Improbable, Viking, London.
Dobzhansky, T., 1951, Genetics and the Origin of Species. Columbia University Press, New York.
Eigen, M., 1993, Viral quasispecies, Sci. Am. 269:32–39.
Eigen, M., McCaskill, J. and Schuster, P., 1989, The molecular quasi-species, Adv. Chem. Phys. 75:149–263.
Eldredge, N. and Cracraft, J., 1980, Phylogenetic Patterns and the Evolutionary Process, Columbia University Press, New York.
Eremeev, A. V. and Reeves, C. R., 2002, Non-parametric estimation of properties of combinatorial landscapes, in: Applications of Evolutionary Computing, Lecture Notes in Computer Science, Vol. 2279, J. Gottlieb and G. Raidl, ed., Springer, Berlin, pp. 31–40.
Eremeev, A. V. and Reeves, C. R., 2003, On confidence intervals for the number of local optima, in: Applications of Evolutionary Computing, Lecture Notes in Computer Science, Vol. 2611, G. Raidl et al., ed., Springer, Berlin, pp. 224–235.
Flamm, C, Hofacker, I. L., Stadler, P. F. and Wolfinger, M. T., 2002, Barrier trees of degenerate landscapes, Z. Phys. Chem. 216:155–173.
Futuyma, D. J., 1998, Evolutionary Biology, Sinauer Associates, Sunderland, MA.
Godsil, C. D., 1993, Algebraic Combinatorics, Chapman and Hall, London.
Grover, L. K., 1992, Local search and the local structure of N P-complete problems, Oper. Res. Lett. 12:235–243.
Haldane, J. B. S., 1931, A mathematical theory of natural selection, Part VI: Metastable populations, Proc. Camb. Phil. Soc. 27:137–142.
Hordijk W., 1996, A measure of landscapes, Evol. Comput. 4:335–360.
Johnson, D. S., 1990, Local optimization and the traveling salesman problem, in: Automata, Languages and Programming, Lecture Notes in Computer Science, Vol. 443, G. Goos and J. Hartmanis, eds, Springer, Berlin, pp. 446–461.
Jones, T. C, 1995, Evolutionary Algorithms, Fitness Landscapes and Search, Doctoral dissertation, University of New Mexico, Albuquerque, NM.
Kauffman, S., 1993, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford.
Levenhagen, J., Bortfeldt, A. and Gehring, H., 2001, Path tracing in genetic algorithms applied to the multiconstrained knapsack problem, in: Applications of Evolutionary Computing, E. J. W. Boers et al., eds, Springer, Berlin, pp. 40–49.
Lin, S., 1965, Computer solutions of the traveling salesman problem, Bell Syst. Tech. J. 44:2245–2269.
Martin, O., Otto, S. W. and Felten, E. W., 1992, Large step Markov chains for the TSP incorporating local search heuristics. Oper. Res. Lett. 11:219–224.
Merz, P. and Freisleben, B., 1998, Memetic algorithms and the fitness landscape of the graph bi-partitioning problem, in: Parallel Problem-Solving from Nature—PPSN V, A. E. Eiben, T. Bäck, M. Schoenauer and H-P. Schwefel, eds, Springer, Berlin, pp. 765–774.
Reeves, C. R., 1994, Genetic algorithms and neighbourhood search, in: Evolutionary Computing: AISB Workshop, Leeds, UK, April 1994; Selected Papers, T. C. Fogarty, ed., Springer, Berlin, pp. 115–130.
Reeves, C. R. and Yamada, T., 1998, Genetic algorithms, path relinking and the flowshop sequencing problem, Evol. Comput., 6:45–60.
Reeves, C. R., 1999, Landscapes, operators and heuristic search. Ann. Oper. Res. 86:473–490.
Reeves, C. R. and Yamada, T., 1999, Goal-Oriented Path Tracing Methods, in: New Methods in Optimization, D. A. Corne, M. Dorigo and F. Glover, eds, McGraw-Hill, London.
Reeves, C. R., 2000, Fitness landscapes and evolutionary algorithms, in: Artificial Evolution: 4th Eur. Conf, AE99, Lecture Notes in Computer Science, Vol. 1829, C. Fonlupt, J-K. Hao, E. Lutton, E. Ronald and M. Schoenauer, eds, Springer, Berlin, pp. 3–20.
Reeves, C. R., 2001, Direct statistical estimation of GA landscape features, in: Foundations of Genetic Algorithms 6, W. N. Martin and W. M. Spears, eds, Morgan Kaufmann, San Mateo, CA, pp. 91–107.
Reeves, C. R. and Rowe, J. E., 2002, Genetic Algorithms—Principles and Perspectives, Kluwer, Norwell, MA.
Reeves, C. R. and Eremeev, A. V, 2004, Statistical analysis of local search landscapes, J. Oper. Res. Soc. 55:687–693.
Reeves, C. R., 2004, Partitioning landscapes. Available online at http://www.dagstuhl.de/04081/Talks/
Reeves, C. R. and Aupetit-Bélaidouni, M., 2004, Estimating the number of solutions for SAT problems, in: Parallel Problem-Solving from Nature—PPSN VIII, X. Yao et al., eds, Springer, Berlin, pp. 101–110.
Reidys, C. M. and Stadler, P. F., 2002, Combinatorial landscapes, SIAM Rev. 44:3–54.
Ridley, M., 1993, Evolution, Blackwell, Oxford.
Simpson, G. G., 1953, The Major Features of Evolution, Columbia University Press, New York.
Stadler, P. F., 1995, Towards a Theory of Landscapes, in: Complex Systems and Binary Networks, R. Lopéz-Peña, R. Capovilla, R. García-Pelayo, H. Waelbroeck and F. Zertuche, eds, Springer, Berlin, pp. 77–163.
Stadler, P. F. and Wagner, G. P., 1998, Algebraic theory of recombination spaces, Evol. Comput. 5:241–275.
Waterman, M. S., 1995, Introduction to Computational Biology, Chapman and Hall, London.
Watson, J-P, Barbalescu, L., Whitley, L. D. and Howe, A. E., 2002, Contrasting structured and random permutation flow-shop scheduling problems: Search-space topology and algorithm performance, INFORMS J. Comput. 14:98–123.
Weinberger, E. D., 1990, Correlated and uncorrelated landscapes and how to tell the difference, Biol. Cybernet. 63:325–336.
Wright, S., 1932, The roles of mutation, inbreeding, crossbreeding and selection in evolution, in: Proc. 6th Int. Congress on Genetics, D. Jones, ed., 1:356–366.
Wright, S., 1967, Surfaces of selective value, Proc. Natl Acad. Sci. USA 102:81–84.
Wright, S., 1988, Surfaces of selective value revisited, Am. Nat., 131:115–123.
Yamada, T. and Reeves, C. R., 1998, Solving the C sum permutation flowshop scheduling problem by genetic local search, in: Proc. 1998 Int. Conf. on Evolutionary Computation, IEEE, Piscataway, NJ, pp. 230–234.
Zweig, G., 1995, An effective tour construction and improvement procedure for the traveling salesman problem, Oper. Res. 43:1049–1057.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Reeves, C.R. (2005). Fitness Landscapes. In: Burke, E.K., Kendall, G. (eds) Search Methodologies. Springer, Boston, MA. https://doi.org/10.1007/0-387-28356-0_19
Download citation
DOI: https://doi.org/10.1007/0-387-28356-0_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-23460-1
Online ISBN: 978-0-387-28356-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)