Optimal Adaptations over Multi-Dimensional Adaptation Spaces with a Spice of Control Theory

(Self-)Adaptive software systems monitor the status of their requirements and adapt when some of these requirements are failing. The baseline for much of the research on adaptive software systems is the concept of a feedback loop mechanism that monitors the performance of a system relative to its requirements, determines root causes when there is failure, selects an adaptation, and carries it out. The degree of adaptivity of a software system critically depends on the space of possible adaptations supported (and implemented) by the system. The larger the space, the more adaptations a system is capable of. This thesis tackles the following questions: (a) How can we define multi-dimensional adaptation spaces that subsume proposals for requirements- and architecture-based adaptation spaces? (b) Given one of more failures, how can we select an optimal adaptation with respect to one or more objective functions? To answer the first question, we propose a design process for three-dimensional adaptation spaces, named the Three-Peaks Process, that iteratively elicits control and environmental parameters from requirements, architectures and behaviours for the system-to-be. For the second question, we propose three adaptation mechanisms. The first mechanism is founded on the assumption that only qualitative information is available about the impact of changes of the system's control parameters on its goals. The absence of quantitative information is mitigated by a new class of requirements, namely Adaptation Requirements, that impose constraints on the adaptation process itself and dictate policies about how conflicts among failing requirements must be handled. The second mechanism assumes that there is quantitative information about the impact of changes of control parameters on the system’s goals and that the problem of finding an adaptation is formulated as a constrained multi-objective optimization problem. The mechanism measures the degree of failure of each requirement and selects an adaptation that minimizes it along with other objective functions, such as cost. Optimal solutions are derived exploiting OMT/SMT (Optimization Modulo Theories/Satisfiability Modulo Theories) solvers. The third mechanism operates under the assumption that the environment changes dynamically over time and the chosen adaptation has to take into account such changes. Towards this direction, we apply Model Predictive Control, a well-developed theory with myriads of successful applications in Control Theory. In our work, we rely on state-of-the-art system identification techniques to derive the dynamic relationship between requirements and possible adaptations and then propose the use of a controller that exploits this relationship to optimize the satisfaction of requirements relative to a cost-function. This adaptation mechanism can guarantee a certain level of requirements satisfaction over time, by dynamically composing adaptation strategies when necessary. Finally, each piece of our work is evaluated through experimentation using variations of the Meeting-Scheduler exemplar