Difficulty of Unimodal and Multimodal Landscapes in Genetic Programming

This paper presents an original study of fitness distance correlation as a measure of problem difficulty in genetic programming. A new definition of distance, called structural distance, is used and suitable mutation operators for the program space are defined. The difficulty is studied for a number of problems, including, for the first time in GP, multimodal ones, both for the new hand-tailored mutation operators and standard crossover. Results are in agreement with empirical observations, thus confirming that fitness distance correlation can be considered a reasonable index of difficulty for genetic programming, at least for the set of problems studied here.

[1]  John R. Koza,et al.  Genetic programming 1997 : proceedings of the Second Annual Conference, July 13-16, 1997, Stanford University , 1997 .

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

[3]  Nikolay I. Nikolaev,et al.  Fitness Landscapes and Inductive Genetic Programming , 1997, ICANNGA.

[4]  N. Hopper,et al.  Analysis of genetic diversity through population history , 1999 .

[5]  Leonardo Vanneschi,et al.  Fitness Distance Correlation in Structural Mutation Genetic Programming , 2003, EuroGP.

[6]  Edwin D. de Jong,et al.  Reducing bloat and promoting diversity using multi-objective methods , 2001 .

[7]  Peter J. Angeline,et al.  The Royal Tree Problem, a Benchmark for Single and Multiple Population Genetic Programming , 1996 .

[8]  Kalyanmoy Deb,et al.  Multimodal Deceptive Functions , 1993, Complex Syst..

[9]  Una-May O'Reilly,et al.  An analysis of genetic programming , 1995 .

[10]  P. Ross,et al.  An adverse interaction between crossover and restricted tree depth in genetic programming , 1996 .

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

[12]  W. Langdon.  An Analysis of the MAX Problem in Genetic Programming , 1997 .

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

[14]  Leonardo Vanneschi,et al.  Fitness Distance Correlation And Problem Difficulty For Genetic Programming , 2002, GECCO.

[15]  Anikó Ekárt,et al.  Maintaining the Diversity of Genetic Programs , 2002, EuroGP.

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

[17]  Una-May O’Reilly.  Using a distance metric on genetic programs to understand genetic operators , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.