Kaipillil Vijayan

Statistical exploratory analysis of genetic algorithms

Genetic algorithms have been extensively used and studied in computer science, yet there is no generally accepted methodology for exploring which parameters significantly affect performance, whether there is any interaction between parameters, and how performance varies with respect to changes in parameters. This paper presents a rigorous yet practical statistical methodology for the exploratory study of genetic and other adaptive algorithms. This methodology addresses the issues of experimental design, blocking, power calculations, and response curve analysis. It details how statistical analysis may assist the investigator along the exploratory pathway. As a demonstration of our methodology, we describe case studies using four well-known test functions. We find that the effect upon performance of crossover is pre-dominantly linear, while the effect of mutation is predominantly quadratic. Higher order effects are noted but contribute less to overall behavior. In the case of crossover, both positive and negative gradients are found suggesting the use of a maximum crossover rate for some problems and its exclusion for others. For mutation, optimal rates appear higher compared with earlier recommendations in the literature, while supporting more recent work. The significance of interaction and the best values for crossover and mutation are problem specific.

Statistical exploratory analysis of genetic algorithms: the influence of gray codes upon the difficulty of a problem

An important issue in genetic algorithms is the relationship between the difficulty of a problem and the choice of encoding Two questions remain unanswered: is their a statistically demonstrable relationship between the difficulty of a problem and the choice of encoding, and, if so, what it the actual mechanism by which this occurs? In this paper we use components of a rigorous statistical methodology to demonstrate that the choice of encoding has a real effect upon the difficulty of a problem Computer animation is then used to illustrate the actual mechanism by which this occurs.

The detrimentality of crossover

The traditional concept of a genetic algorithm (GA) is that of selection, crossover and mutation. However, data from the literature has suggested that the niche for the beneficial effect of crossover upon GA performance may be smaller than has been traditionally held. We explored the class of problems for which crossover is detrimental by performing a statistical analysis of two test problem suites, one comprising linear-separable non-rotated functions and the other comprising the same functions rotated by 45 degrees rendering them not-linear-separable We find that for the difficult rotated functions the crossover operator is detrimental to the performance of the GA. We conjecture that what makes a problem difficult for the GA is complex and involves factors such as the degree of optimization at local minima due to crossover, the bias associated with the mutation operator and the Hamming Distances present in the individual problems due to the encoding. Finally, we test our GA on a practical landscape minimization problem to see if the results obtained match those from the difficult rotated functions. We find that they match and that the features which make certain of the test functions difficult are also present in the real world problem.

Optimal 12 Run Designs

In this paper we consider twelve run designs with four factors each at 2 levels. We present a specific design and show that it is optimal when one wishes to estimate all the main effects and a subset of two factor interactions. The optimality criteria used are D-optimality and a form of E-optimality