Abstract
It is well-known that evolutionary algorithms succeed in optimizing some functions efficiently and fail for others. Therefore, one would like to classify fitness functions as more or less hard to optimize for evolutionary algorithms. The aim of this paper is to clarify limitations and possibilities for classifications of fitness functions from a theoretical point of view. We distinguish two different types of classifications, descriptive and analytical ones. We shortly discuss three widely known approaches, namely the NK-model, epistasis variance, and fitness distance correlation. Furthermore, we consider another recent measure, bit-wise epistasis. We discuss shortcomings and counter examples for all four measures and use this to motivate a discussion about possibilities and limitations of classifications of fitness functions in a broader context.
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References
L. Altenberg. Fitness distance correlation analysis: an instructive counter-example. In T. Bäck, editor, Proceedings of the 7th International Conference on Genetic Algorithms (ICGA ‘97), pages 57–64. Morgan Kaufmann, San Francisco, 1997.
L. Altenberg. NK fitness landscapes. In Handbook of Evolutionary Computation, page B2.7.2. Oxford University Press, Oxford, 1997.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. McGrawHill, New York, 1990.
Y. Davidor. Epistasis variance: a viewpoint on GA-hardness. In G. J. E. Rawlins, editor, Proceedings of the 1 st Workshop on Foundations of Genetic Algorithms (FOGA), pages 23–35. Morgan Kaufmann, San Francisco, 1991.
S. Droste, Th. Jansen, and I. Wegener. On the analysis of the (1 + 1) evolutionary algorithm. Technical Report CI-21/98, University of Dortmund, SFB 531, Dortmund, Germany, 1998.
S. Droste, T. Jansen, and I. Wegener. On the optimization of unimodal functions with the (1 + 1) evolutionary algorithm. In A. E. Eiben, T. Bäck, M. Schoenauer, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature — PPSN V, volume 1498 of LNCS, pages 47–56. Springer-Verlag, Berlin Heidelberg New York, 1998.
S. Droste, T. Jansen, and I. Wegener. A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs. Evolutionary Computation, 6(2):185–196, 1998.
S. Droste, T. Jansen, and I. Wegener. Perhaps not a free lunch but at least a free appetizer. In W. Banzhaf et al., editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ‘99), pages 833–839. Morgan Kaufmann, San Francisco, 1999.
C. Fonlupt, D. Robilliard, and P. Preux. A bit-wise epistasis measure for binary search spaces. In A. E. Eiben, T. Bäck, M. Schoenauer, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature — PPSN V, volume 1498 of LNCS, pages 47–56. Springer-Verlag, Berlin Heidelberg New York, 1998.
M. R. Garey and D. S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.
J. Gamier, L. Kallel, and M. Schoenauer. Rigorous hitting times for binary mutations. Evolutionary Computation, 7(2):173–203, 1999.
D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA, 1989.
O. Goldreich, S. Goldwasser, and D. Ron. Property testing and its connections to learning and approximation. Journal of the ACM, 45(4):563–750, 1998.
R. B. Heckendorn and D. Whitley. Predicting epistasis from mathematical models. Evolutionary Computation, 7(1):69–101, 1999.
D. S. Johnson, C. H. Papadimitriou, and M. Yannakakis. How easy is local search? Journal of Computer and System Sciences, 37:79–100, 1988.
T. Jones. Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico, Albuquerque, NM, 1995.
T. Jones and S. Forrest. Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In L. J. Eshelman, editor, Proceedings of the 6th International Conference on Genetic Algorithms (ICGA ‘95), pages 184–192. Morgan Kaufmann, San Francisco, 1995.
S. A. Kauffman. The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford, 1993.
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671–680, 1983.
B. Naudts. Measuring GA-hardness. PhD thesis, University of Antwerp, Department of Mathematics and Computer Science, Antwerpen, Belgium, 1998.
B. Naudts and L. Kallel. A Comparison of Predictive Measures of Problem Difficulty in Evolutionary Algorithms. IEEE Transactions on Evolutionary Computing, 4(1):1–15, 2000.
B. Naudts, D. Suys, and A. Verschoren. Epistasis as a basic concept in formal landscape analysis. In T. Bäck, editor, Proceedings of the 7th International Conference on Genetic Algorithms (ICGA ‘97), pages 65–72. Morgan Kaufmann, San Francisco, 1997.
C. H. Papadimitriou, A. A. Schäffer, and M. Yannakakis. On the complexity of local search (extended abstract). In ACM Symposium on Theory of Computing, pages 438–445, 1990.
R. J. Quick, V. J. Rayward-Smith, and G. D. Smith. Fitness distance correlation and ridge functions. In A. E. Eiben, T. Bäck, M. Schoenauer, and H.-P. Schwefel, editors, Parallel Problem Solving From Nature — PPSN V, volume 1498 of LNCS, pages 77–86. Springer-Verlag, Berlin Heidelberg New York, 1998.
G. Rudolph. Convergence Properties of Evolutionary Algorithms. Verlag Dr. Kovač, Hamburg, Germany, 1997.
R. K. Thompson and A. H. Wright. Additively decomposable fitness functions. Technical Report, University of Montana, Computer Science Department, 1996.
E. D. Weinberger. NP completeness of Kauffman’s n-k model, a tuneably rugged fitness landscape. Technical Report SFI-TR-96–02–003, The Sante Fe Institute, Santa Fe, NM, 1996.
D. H. Wolpert and W. G. Macready. No free lunch theorem for optimization. IEEE Transactions on Evolutionary Computation, 1(1):67–82, 1997.
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Jansen, T. (2001). On Classifications of Fitness Functions. In: Kallel, L., Naudts, B., Rogers, A. (eds) Theoretical Aspects of Evolutionary Computing. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04448-3_18
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DOI: https://doi.org/10.1007/978-3-662-04448-3_18
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