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: (i) 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; (ii) 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 thousands of elements.

Abstract. We are interested in supporting software evolution caused by changing requirements and/or changes in the operational environment of a software system. For example, users of a system may want new functionality or performance enhancements to cope with growing user population (changing requirements). Alternatively, vendors of a system may want to minimize costs in implementing requirements changes (evolution requirements). We propose to use Constrained Goal Models (CGMs) to represent the requirements of a system, and capture requirements changes in terms of incremental operations on a goal model. Evolution requirements are then represented as optimization goals that minimize implementation costs or customer value. We can then exploit reasoning techniques to derive optimal new specifications for an evolving software system. CGMs offer an expressive language for modelling goals that comes with scalable solvers that can solve hybrid constraint and optimization problems using a combination of Satisfiability Modulo Theories (SMT) and Optimization Modulo Theories (OMT) techniques. We evaluate our proposal by modeling and reasoning with a goal model for the meeting scheduling examplar.

We are interested in supporting software evolution caused by changing requirements and/or changes in the operational environment of a software system. For example, users of a system may want new functionality or performance enhancements to cope with growing user population (changing requirements). Alternatively, vendors of a system may want to minimize costs in implementing requirements changes (evolution requirements). We propose to use Constrained Goal Models (CGMs) to represent the requirements of a system, and capture requirements changes in terms of incremental operations on a goal model. Evolution requirements are then represented as optimization goals that minimize implementation costs or customer value. We then exploit reasoning techniques to derive optimal new specifications for an evolving software system. CGMs offer an expressive language for modelling goals that comes with scalable solvers that solve hybrid constraint and optimization problems using a combination of Satisfiability Modulo Theories (SMT) and Optimization Modulo Theories (OMT) techniques. We evaluate our proposal by modeling and reasoning with a goal model for a standard exemplar used in Requirement Engineering. Fig. 1. A CGM M1, with a realization µ1 minimizing lexicographically: the difference Penalty-Reward, workTime, and cost.