Advanced tools used in model-based systems engineering (MBSE) frequently represent
their models as graphs. In order to test those tools, the automated generation of
well-formed (or intentionally malformed) graph models is necessitated which is often
carried out by solver-based model generation techniques. In many model generation
scenarios, one needs more refined control over the generated unit tests to focus on
the more relevant models. Type scopes allow to precisely define the required number
of newly generated elements, thus one can avoid the generation of unrealistic and
highly symmetric models having only a single type of elements. In this paper, we propose
a 3-valued scoped partial modeling formalism, which innovatively extends partial graph
models with predicate abstraction and counter abstraction. As a result, well-formedness
constraints and multiplicity requirements can be evaluated in an approximated way
on incomplete (unfinished) models by using advanced graph query engines with numerical
solvers (e.g., IP or LP solvers). Based on the refinement of 3-valued scoped partial
models, we propose an efficient model generation algorithm that generates models that
are both well-formed and satisfy the scope requirements. We show that the proposed
approach scales significantly better than existing SAT-solver techniques or the original
graph solver without multiplicity reasoning. We illustrate our approach in a complex
design-space exploration case study of collaborating satellites introduced by researchers
at NASA JPL.
