Models for Evolutionary Algorithms and Their Applications in System Identification and Control Optimization

Abstract In recent years, optimization algorithms have received increasing attention by theresearch community as well as the industry. In the area of evolutionary compu-tation (EC), inspiration for optimization algorithms originates in Darwin’s ideasof evolution and survival of the fittest. Such algorithms simulate an evolutionaryprocess where the goal is to evolve solutions by means of crossover, mutation, andselection based on their quality (fitness) with respect to the optimization problemat hand. Evolutionary algorithms (EAs) are highly relevant for industrial applica-tions, because they are capable of handling problems with non-linear constraints,multiple objectives, and dynamic components – properties that frequently appearin real-world problems.This thesis presents research in three fundamental areas of EC; fitness functiondesign, methods for parameter control, and techniques for multimodal optimiza-tion. In addition to general investigations in these areas, I introduce a numberof algorithms and demonstrate their potential on real-world problems in systemidentification and control. Furthermore, I investigate dynamic optimization prob-lems in the context of the three fundamental areas as well as control, which is afield where real-world dynamic problems appear.Regarding fitness function design, smoothness of the fitness landscape is of pri-mary concern, because a too rugged landscape may disrupt the search and lead topremature convergence at local optima. Rugged fitness landscapes typically arisefrom imprecisions in the fitness calculation or low relatedness between neighboringsolutions in the search space. The imprecision problem was investigated on theRunge-Kutta-Fehlberg numerical integrator in the context of non-linear differentialequations. Regarding the relatedness problem for the search space of arithmeticfunctions, Thiemo Krink and I suggested the smooth operator genetic program-ming algorithm. This approach improves the smoothness of fitness function byallowing a gradual change between traditional operators such as multiplicationand division.In the area of parameter control, I investigated the so-called self-adaptationtechnique on dynamic problems. In self-adaptation, the genome of the individualcontains the parameters that are used to modify the individual. Self-adaptationwas developed for static problems; however, the parameter control approach re-quires a significant number of generations before superior parameters are evolved.In my study, I experimented with two artificial dynamic problems and showedthat the technique fails on even rather simple time-varying problems. In a dif-ferent study on static problems, Thiemo Krink and I suggested the terrain-basedpatchwork model, which is a fundamentally new approach to parameter controlbased on agents moving in a spatial grid world.For multimodal optimization problems, algorithms are typically designed withtwo objectives in mind. First, the algorithm shall find the global optimum andavoid stagnation at local optima. Additionally, the algorithm shall preferably findseveral candidate solutions, and thereby allow a final human decision among thefound solutions. For this objective, I created the multinational EA that employs