Multi-objective reasoning with constrained goal models

Goal models have been widely used in computer science to represent software requirements, business objectives, and design qualities. Existing goal modelling techniques, however, have shown limitations of expressiveness and/or tractability in coping with complex real-world problems. In this work, we exploit advances in automated reasoning technologies, notably satisfiability and optimization modulo theories (SMT/OMT), and we propose and formalize: (1) an extended modelling language for goals, namely the constrained goal model (CGM), which makes explicit the notion of goal refinement and of domain assumption, allows for expressing preferences between goals and refinements and allows for associating numerical attributes to goals and refinements for defining constraints and optimization goals over multiple objective functions, refinements, and their numerical attributes; (2) a novel set of automated reasoning functionalities over CGMs, allowing for automatically generating suitable refinements of input CGMs, under user-specified assumptions and constraints, that also maximize preferences and optimize given objective functions. We have implemented these modelling and reasoning functionalities in a tool, named CGM-Tool, using the OMT solver OptiMathSAT as automated reasoning backend. Moreover, we have conducted an experimental evaluation on large CGMs to support the claim that our proposal scales well for goal models with 1000s of elements.