We present a new approach for synthesising Paretooptimal Markov decision process (MDP) policies that satisfy complex combinations of quality-of-service (QoS) software requirements. These policies correspond to optimal designs or configurations of software systems, and are obtained by translating MDP models of these systems into parametric Markov chains, and using multi-objective genetic algorithms to synthesise Pareto-optimal parameter values that define the required MDP policies. We use case studies from the service-based systems and robotic control software domains to show that our MDP policy synthesis approach can handle a wide range of QoS requirement combinations unsupported by current probabilistic model checkers. Moreover, for requirement combinations supported by these model checkers, our approach generates better Pareto-optimal policy sets according to established quality metrics.

Abstract. Self-adaptive systems have the ability to adapt their behavior to dynamic operation conditions. In reaction to changes in the environment, these systems determine the appropriate corrective actions based in part on information about which action will have the best impact on the system. Existing models used to describe the impact of adaptations are either unable to capture the underlying uncertainty and variability of such dynamic environments, or are not compositional and described at a level of abstraction too low to scale in terms of specification effort required for non-trivial systems. In this paper, we address these shortcomings by describing an approach to the specification of impact models based on architectural system descriptions, which at the same time allows us to represent both variability and uncertainty in the outcome of adaptations, hence improving the selection of the best corrective action. The core of our approach is an impact model language equipped with a formal semantics defined in terms of Discrete Time Markov Chains. To validate our approach, we show how employing our language can improve the accuracy of predictions used for decisionmaking in the Rainbow framework for architecture-based self-adaptation.

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