Multi-Object Reasoning with Constrained Goal Models

TL;DR

This paper introduces Constrained Goal Models (CGMs), an extended goal modeling language that incorporates preferences, numerical attributes, and optimization, supported by automated reasoning tools to handle complex, large-scale real-world problems.

Contribution

It formalizes CGMs with explicit goal refinement, preferences, and numerical attributes, and develops automated reasoning functionalities implemented in the CGM-Tool using OptiMathSAT.

Findings

Scales well for goal models with thousands of elements

Automates generation of goal refinements under constraints

Supports optimization of multiple objectives

Abstract

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.