Statistical Exploratory Analysis of Genetic Algorithms

Abstract

ara MacNish was instrumental in this part of my academic career. I respect Cara as an individual of significant intellect and I humbly offer Cara my profound thanks and appreciation. I should like to also thank Kaipillil Vijayan for the honour of allowing me to complete a PhD thesis under his supervision. I thank Kaipillil Vijayan also for his personal support and assistance. I could not have completed this doctorate without the collaboration of Berwin Turlach to whom I also owe my profound thanks and appreciation. During this doctorate I contracted a life-threatening illness which left sustained problems with my health. However, with the support of an exceptional team of health professionals I have been able to complete the present work. Thus, my many thanks go to

Efficient relevance estimation and value calibration of evolutionary algorithm parameters

“…In order to study the design layer, we need to define an EA for the algorithm layer and some specific objective functions for the application layer. For both purposes we rely on [2], which applies rigorous statistical exploratory analysis to study the effect of calibrating the mutation and crossover operators in a simple GA of highly variable performance. The EA here is a generational GA with 22 bits per variable, Gray coding, probabilistic rank-based selection, single point crossover and bit flip mutation.…”

“…The EA here is a generational GA with 22 bits per variable, Gray coding, probabilistic rank-based selection, single point crossover and bit flip mutation. In addition to the two parameters calibrated in [2], mutation p m ∈ [0, 1] and crossover p c ∈ [0, 1], we also calibrate the population size of n ∈ [10,200] chromosomes, a total of 3 parameters.…”

“…F is calculated from the negative 2 number of generations that are needed to solve the function, times the population size. I.e., when a GA needs 100 generations of 100 individuals 2 we want to maximize performance or 200 generations of 50 individuals, we will say that it has a performance index F of -10,000. A test function is considered solved as soon as one individual of the population encodes a value that is within certain bounds of the best feasible solution.…”

“…A classical example of this approach is Analysis of Variance (ANOVA), which provides a clear set of rules how to optimally combine a number of carefully chosen parameter values, how to calculate the number of replications needed to decide whether one combination of values has a significantly better response than another, and how to infer parameter interaction. An exhaustive overview of how to apply ANOVA to EA calibration is given in [2].…”

“…Fifth, and maybe most important, it is difficult to infer from a small number of measurements in a multi-dimensional search space, reliable as they might be, important measures of robustness like sensitivity to small changes and the size of value ranges for which a certain EA performance can be achieved. This last problem has been clearly recognized since [3], but, as [2] points out, it is difficult to fit anything more sophisticated than a cubic curve to the response curve of an EA.…”