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Search Methodologies pp 587–610Cite as

Fitness Landscapes

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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.

Keywords

  • Local Search
  • Travel Salesman Problem
  • Combinatorial Optimization Problem
  • Neighborhood Structure
  • Fitness Landscape

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • Biggs, N. L., 1993, Algebraic Graph Theory, Cambridge University Press, Cambridge.

    Google Scholar 

  • 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.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • Box, G. E. P. and Jenkins, G. M., 1970, Time Series Analysis, Forecasting and Control, Holden Day, San Francisco.

    MATH  Google Scholar 

  • Corne, D. A., Dorigo, M. and Glover, F., eds, 1999, New Methods in Optimization, McGraw-Hill, London.

    Google Scholar 

  • Dawkins, R. (1996) Climbing Mount Improbable, Viking, London.

    Google Scholar 

  • Dobzhansky, T., 1951, Genetics and the Origin of Species. Columbia University Press, New York.

    Google Scholar 

  • Eigen, M., 1993, Viral quasispecies, Sci. Am. 269:32–39.

    CrossRef  Google Scholar 

  • Eigen, M., McCaskill, J. and Schuster, P., 1989, The molecular quasi-species, Adv. Chem. Phys. 75:149–263.

    CrossRef  Google Scholar 

  • Eldredge, N. and Cracraft, J., 1980, Phylogenetic Patterns and the Evolutionary Process, Columbia University Press, New York.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Flamm, C, Hofacker, I. L., Stadler, P. F. and Wolfinger, M. T., 2002, Barrier trees of degenerate landscapes, Z. Phys. Chem. 216:155–173.

    Google Scholar 

  • Futuyma, D. J., 1998, Evolutionary Biology, Sinauer Associates, Sunderland, MA.

    Google Scholar 

  • Godsil, C. D., 1993, Algebraic Combinatorics, Chapman and Hall, London.

    MATH  Google Scholar 

  • Grover, L. K., 1992, Local search and the local structure of N P-complete problems, Oper. Res. Lett. 12:235–243.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • Haldane, J. B. S., 1931, A mathematical theory of natural selection, Part VI: Metastable populations, Proc. Camb. Phil. Soc. 27:137–142.

    MATH  CrossRef  Google Scholar 

  • Hordijk W., 1996, A measure of landscapes, Evol. Comput. 4:335–360.

    Google Scholar 

  • 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.

    CrossRef  Google Scholar 

  • Jones, T. C, 1995, Evolutionary Algorithms, Fitness Landscapes and Search, Doctoral dissertation, University of New Mexico, Albuquerque, NM.

    Google Scholar 

  • Kauffman, S., 1993, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford.

    Google Scholar 

  • 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.

    Google Scholar 

  • Lin, S., 1965, Computer solutions of the traveling salesman problem, Bell Syst. Tech. J. 44:2245–2269.

    MATH  Google Scholar 

  • 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.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • 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.

    CrossRef  Google Scholar 

  • 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.

    Google Scholar 

  • Reeves, C. R. and Yamada, T., 1998, Genetic algorithms, path relinking and the flowshop sequencing problem, Evol. Comput., 6:45–60.

    Google Scholar 

  • Reeves, C. R., 1999, Landscapes, operators and heuristic search. Ann. Oper. Res. 86:473–490.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Reeves, C. R. and Rowe, J. E., 2002, Genetic Algorithms—Principles and Perspectives, Kluwer, Norwell, MA.

    Google Scholar 

  • Reeves, C. R. and Eremeev, A. V, 2004, Statistical analysis of local search landscapes, J. Oper. Res. Soc. 55:687–693.

    MATH  CrossRef  Google Scholar 

  • Reeves, C. R., 2004, Partitioning landscapes. Available online at http://www.dagstuhl.de/04081/Talks/

    Google Scholar 

  • 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.

    Google Scholar 

  • Reidys, C. M. and Stadler, P. F., 2002, Combinatorial landscapes, SIAM Rev. 44:3–54.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • Ridley, M., 1993, Evolution, Blackwell, Oxford.

    Google Scholar 

  • Simpson, G. G., 1953, The Major Features of Evolution, Columbia University Press, New York.

    Google Scholar 

  • 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.

    Google Scholar 

  • Stadler, P. F. and Wagner, G. P., 1998, Algebraic theory of recombination spaces, Evol. Comput. 5:241–275.

    Google Scholar 

  • Waterman, M. S., 1995, Introduction to Computational Biology, Chapman and Hall, London.

    MATH  Google Scholar 

  • 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.

    CrossRef  MathSciNet  Google Scholar 

  • Weinberger, E. D., 1990, Correlated and uncorrelated landscapes and how to tell the difference, Biol. Cybernet. 63:325–336.

    MATH  CrossRef  Google Scholar 

  • 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.

    Google Scholar 

  • Wright, S., 1967, Surfaces of selective value, Proc. Natl Acad. Sci. USA 102:81–84.

    Google Scholar 

  • Wright, S., 1988, Surfaces of selective value revisited, Am. Nat., 131:115–123.

    CrossRef  Google Scholar 

  • 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.

    CrossRef  Google Scholar 

  • Zweig, G., 1995, An effective tour construction and improvement procedure for the traveling salesman problem, Oper. Res. 43:1049–1057.

    MATH  MathSciNet  CrossRef  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematical and Information Sciences, Coventry University, UK

    Colin R. Reeves

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  1. Colin R. Reeves
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Editor information

Editors and Affiliations

  1. University of Nottingham, UK

    Edmund K. Burke & Graham Kendall & 

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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

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