Fitness Noise and Localization Errors of the Optimum in General Quadratic Fitness Models

Evolutionary algorithms are generally believed to perform well in the presence of noise. Thus, they are often used for optimization in noisy environments. It comes as a surprise that hardly more than a handful of studies has dealt with the question of just how well they are doing and what can be done to improve their performance. The present paper presents empirical results regarding the behavior of genetic algorithms and evolution strategies in the presence of fitness noise for a range of objective functions. Bounds for the mean residual location error and the stationary fitness error for optimization of general quadratic fitness models with evolution strategies are derived and compared with measurements.

[1]  H.-G. Beyer,et al.  Mutate large, but inherit small ! On the analysis of rescaled mutations in (1, λ)-ES with noisy fitness data , 1998 .

[2]  Hans-Georg Beyer,et al.  Towards a Theory of 'Evolution Strategies': Results for (1, +λ)-Strategies on (Nearly) Arbitrary Fitness Functions , 1994, PPSN.

[3]  Thomas Bäck,et al.  Evolution Strategies on Noisy Functions: How to Improve Convergence Properties , 1994, PPSN.

[4]  H. Beyer Evolutionary algorithms in noisy environments : theoretical issues and guidelines for practice , 2000 .

[5]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Some Asymptotical Results from the (1,+ )-Theory , 1993, Evolutionary Computation.

[6]  Peter Stagge,et al.  Averaging Efficiently in the Presence of Noise , 1998, PPSN.

[7]  Hans-Georg Beyer Mutate Large, But Inherit Small! On the Analysis of Rescaled Mutations in 1-lambda-ES with Noisy Fitness Data , 1998, PPSN.

[8]  I. Mazin,et al.  Theory , 1934 .

[9]  David E. Goldberg,et al.  Genetic Algorithms, Selection Schemes, and the Varying Effects of Noise , 1996, Evolutionary Computation.

[10]  Volker Nissen,et al.  Optimization with Noisy Function Evaluations , 1998, PPSN.

[11]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: On the Benefits of Sex the (/, ) Theory , 1995, Evolutionary Computation.

[12]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[13]  In Schoenauer,et al.  Parallel Problem Solving from Nature , 1990, Lecture Notes in Computer Science.