Arithmetic Semantics of Feature and Goal Models for Adaptive Cyber-Physical Systems

Many Cyber-Physical Systems (CPSs) today are self-adaptive, in order to handle frequent changes in environmental conditions and requirements. In CPSs, goal-based reasoning is often used to include stakeholder and social concerns in decision making during design and runtime adaptation activities. To better support some of these activities, arithmetic semantics for goal models were proposed to enable the generation of mathematical functions usable by systems. However, goal models often allow invalid combinations of alternatives, which can be prevented by companion feature models. In this paper, to enable the generation of valid and optimal configurations for adaptive CPSs, we propose new arithmetic semantics for feature models that enable their transformations to mathematical functions (in several programming languages) further restricting the ones generated from goal models. The composition of feature and goal functions results in a smaller design space, leading to fewer but valid solutions that can be generated (e.g., through optimization) and used in simulations and running adaptive CPSs with social concerns. Finally, a simulation model in SysML is proposed in this paper to demonstrate the feasibility and usefulness of this composition.