Models for Evolutionary Algorithms and Their Applications in System
Identification and Control Optimization
Rasmus K. Ursem
In recent years, optimization algorithms have received increasing attention by the research community as well as the industry. In the area of evolutionary computation (EC), inspiration for optimization algorithms originates in Darwin's ideas of evolution and survival of the fittest. Such algorithms simulate an evolutionary process where the goal is to evolve solutions by means of crossover, mutation, and selection based on their quality (fitness) with respect to the optimization problem at hand. Evolutionary algorithms (EAs) are highly relevant for industrial applications, because they are capable of handling problems with non-linear constraints, multiple objectives, and dynamic components -- properties that frequently appear in real-world problems.
This thesis presents research in three fundamental areas of EC; fitness function design, methods for parameter control, and techniques for multimodal optimization. In addition to general investigations in these areas, I introduce a number of algorithms and demonstrate their potential on real-world problems in system identification and control. Furthermore, I investigate dynamic optimization problems in the context of the three fundamental areas as well as control, which is a field where real-world dynamic problems appear.
Regarding fitness function design, smoothness of the fitness landscape is of primary concern, because a too rugged landscape may disrupt the search and lead to premature convergence at local optima. Rugged fitness landscapes typically arise from imprecisions in the fitness calculation or low relatedness between neighboring solutions in the search space. The imprecision problem was investigated on the Runge-Kutta-Fehlberg numerical integrator in the context of non-linear differential equations. Regarding the relatedness problem for the search space of arithmetic functions, Thiemo Krink and I suggested the smooth operator genetic programming algorithm. This approach improves the smoothness of fitness function by allowing a gradual change between traditional operators such as multiplication and division.
In the area of parameter control, I investigated the so-called self-adaptation technique on dynamic problems. In self-adaptation, the genome of the individual contains the parameters that are used to modify the individual. Self-adaptation was developed for static problems; however, the parameter control approach requires a significant number of generations before superior parameters are evolved. In my study, I experimented with two artificial dynamic problems and showed that the technique fails on even rather simple time-varying problems. In a different study on static problems, Thiemo Krink and I suggested the terrain-based patchwork model, which is a fundamentally new approach to parameter control based on agents moving in a spatial grid world.
For multimodal optimization problems, algorithms are typically designed with two objectives in mind. First, the algorithm shall find the global optimum and avoid stagnation at local optima. Additionally, the algorithm shall preferably find several candidate solutions, and thereby allow a final human decision among the found solutions. For this objective, I created the multinational EA that employs a self-organizing population structure grouping the individuals into a number of subpopulations located in different parts of the search space. In a related study, I investigated the robustness of the widely used sharing technique. Surprisingly, I found that this algorithm is extremely sensitive to the range of fitness values. In a third investigation, I introduced the diversity-guided EA, which uses a population diversity measure to guide the search. The potential of this algorithm was demonstrated on parameter identification of two induction motor models, which are used in the pumps produced by the Danish pump manufacturer Grundfos.
The field of dynamic optimization has received significant attention since 1990. However, most research performed in an EC-context has focused on artificial dynamic problems. In a fundamental study, Thiemo Krink, Mikkel T. Jensen, Zbigniew Michalewicz, and I investigated artificial dynamic problems and found no clear connection (if any) to real-world dynamic problems. In conclusion, a large part of this research field's foundation, i.e., the test problems, is highly questionable. In continuation of this, Thiemo Krink, Bogdan Filipic, and I investigated online control problems, which have the special property that the search changes the problem. In this context, we examined how to utilize the available computation time in the best way between updates of the control signals. For an EA, the available time can be a trade-off between population size and number of generations. From our experiments, we concluded that the best approach was to have a small population and many generations, which essentially turns the problem into a series of related static problems. To our surprise, the control problem could easily be solved when optimized like this. To further examine this, we compared the EA with a particle swarm and a local search approach, which we developed for dynamic optimization in general. The three algorithms had matching performance when properly tuned. An interesting result from this investigation was that different step-sizes in the local search algorithm induced different control strategies, i.e., the search strategy lead to the emergence of alternative paths of the moving optima in the dynamic landscape. This observation is captured in the novel concept of optima in time, which we introduced as a temporal version of the usual optima the in search space.