Fitness Distance Correlation And Problem Difficulty For Genetic Programming

This work is a first step in the attempt to verify whether (and in which cases) fitness distance correlation can be a good tool for classifying problems on the basis of their difficulty for genetic programming. By analogy with the studies that have already been done on genetic algorithms, we define some notions of distance between genotypes. Then we choose one of these distances to calculate the fitness distance correlation coefficient and we use it to study the difficulty of some problems. First, we do this for a syntactically limited language. Then we extend the study to standard genetic programming. For the functions used here i.e., traps and royal trees, the results confirm that fitness distance correlation is a good predictor of genetic programming difficulty.

[1]  Erik D. Goodman,et al.  The royal tree problem, a benchmark for single and multiple population genetic programming , 1996 .

[2]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[3]  John R. Koza,et al.  Genetic programming (videotape): the movie , 1992 .

[4]  Philippe Collard,et al.  Genetic Heuristic for Search Space Exploration , 1999, IJCAI.

[5]  Victor J. Rayward-Smith,et al.  Fitness Distance Correlation and Ridge Functions , 1998, PPSN.

[6]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[7]  Lee Altenberg,et al.  Fitness Distance Correlation Analysis: An Instructive Counterexample , 1997, ICGA.

[8]  Bernard Manderick,et al.  The Genetic Algorithm and the Structure of the Fitness Landscape , 1991, ICGA.

[9]  Wolfgang Banzhaf,et al.  Genetic Programming: An Introduction , 1997 .

[10]  M. Clergue,et al.  Misleading functions designed from alternation , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[11]  Kalyanmoy Deb,et al.  Analyzing Deception in Trap Functions , 1992, FOGA.

[12]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[13]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[14]  Vidroha Debroy,et al.  Genetic Programming , 1998, Lecture Notes in Computer Science.

[15]  K. Kinnear.  Fitness landscapes and difficulty in genetic programming , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[16]  Philippe Collard,et al.  Fitness Distance Correlation, as statistical measure of Genetic Algorithm difficulty, revisited , 1998, ECAI.