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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

  1. Biggs, N. L., 1993, Algebraic Graph Theory, Cambridge University Press, Cambridge.Google Scholar
  2. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Box, G. E. P. and Jenkins, G. M., 1970, Time Series Analysis, Forecasting and Control, Holden Day, San Francisco.zbMATHGoogle Scholar
  4. Corne, D. A., Dorigo, M. and Glover, F., eds, 1999, New Methods in Optimization, McGraw-Hill, London.Google Scholar
  5. Dawkins, R. (1996) Climbing Mount Improbable, Viking, London.Google Scholar
  6. Dobzhansky, T., 1951, Genetics and the Origin of Species. Columbia University Press, New York.Google Scholar
  7. Eigen, M., 1993, Viral quasispecies, Sci. Am. 269:32–39.CrossRefGoogle Scholar
  8. Eigen, M., McCaskill, J. and Schuster, P., 1989, The molecular quasi-species, Adv. Chem. Phys. 75:149–263.CrossRefGoogle Scholar
  9. Eldredge, N. and Cracraft, J., 1980, Phylogenetic Patterns and the Evolutionary Process, Columbia University Press, New York.Google Scholar
  10. 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
  11. 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
  12. 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
  13. Futuyma, D. J., 1998, Evolutionary Biology, Sinauer Associates, Sunderland, MA.Google Scholar
  14. Godsil, C. D., 1993, Algebraic Combinatorics, Chapman and Hall, London.zbMATHGoogle Scholar
  15. Grover, L. K., 1992, Local search and the local structure of N P-complete problems, Oper. Res. Lett. 12:235–243.zbMATHCrossRefMathSciNetGoogle Scholar
  16. Haldane, J. B. S., 1931, A mathematical theory of natural selection, Part VI: Metastable populations, Proc. Camb. Phil. Soc. 27:137–142.zbMATHCrossRefGoogle Scholar
  17. Hordijk W., 1996, A measure of landscapes, Evol. Comput. 4:335–360.Google Scholar
  18. 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.CrossRefGoogle Scholar
  19. Jones, T. C, 1995, Evolutionary Algorithms, Fitness Landscapes and Search, Doctoral dissertation, University of New Mexico, Albuquerque, NM.Google Scholar
  20. Kauffman, S., 1993, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford.Google Scholar
  21. 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
  22. Lin, S., 1965, Computer solutions of the traveling salesman problem, Bell Syst. Tech. J. 44:2245–2269.zbMATHGoogle Scholar
  23. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  24. 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.CrossRefGoogle Scholar
  25. 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
  26. Reeves, C. R. and Yamada, T., 1998, Genetic algorithms, path relinking and the flowshop sequencing problem, Evol. Comput., 6:45–60.Google Scholar
  27. Reeves, C. R., 1999, Landscapes, operators and heuristic search. Ann. Oper. Res. 86:473–490.zbMATHCrossRefMathSciNetGoogle Scholar
  28. 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
  29. 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
  30. 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
  31. Reeves, C. R. and Rowe, J. E., 2002, Genetic Algorithms—Principles and Perspectives, Kluwer, Norwell, MA.Google Scholar
  32. Reeves, C. R. and Eremeev, A. V, 2004, Statistical analysis of local search landscapes, J. Oper. Res. Soc. 55:687–693.zbMATHCrossRefGoogle Scholar
  33. Reeves, C. R., 2004, Partitioning landscapes. Available online at http://www.dagstuhl.de/04081/Talks/Google Scholar
  34. 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
  35. Reidys, C. M. and Stadler, P. F., 2002, Combinatorial landscapes, SIAM Rev. 44:3–54.zbMATHCrossRefMathSciNetGoogle Scholar
  36. Ridley, M., 1993, Evolution, Blackwell, Oxford.Google Scholar
  37. Simpson, G. G., 1953, The Major Features of Evolution, Columbia University Press, New York.Google Scholar
  38. 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
  39. Stadler, P. F. and Wagner, G. P., 1998, Algebraic theory of recombination spaces, Evol. Comput. 5:241–275.Google Scholar
  40. Waterman, M. S., 1995, Introduction to Computational Biology, Chapman and Hall, London.zbMATHGoogle Scholar
  41. 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.CrossRefMathSciNetGoogle Scholar
  42. Weinberger, E. D., 1990, Correlated and uncorrelated landscapes and how to tell the difference, Biol. Cybernet. 63:325–336.zbMATHCrossRefGoogle Scholar
  43. 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
  44. Wright, S., 1967, Surfaces of selective value, Proc. Natl Acad. Sci. USA 102:81–84.Google Scholar
  45. Wright, S., 1988, Surfaces of selective value revisited, Am. Nat., 131:115–123.CrossRefGoogle Scholar
  46. 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.CrossRefGoogle Scholar
  47. Zweig, G., 1995, An effective tour construction and improvement procedure for the traveling salesman problem, Oper. Res. 43:1049–1057.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2005

Authors and Affiliations

  • Colin R. Reeves
    • 1
  1. 1.School of Mathematical and Information SciencesCoventry UniversityUK

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