Design exploration consists in browsing the design space and through the incremental generation of diverse design candidates increases creativity and diversity. When integrated into the early stages of the structural design process, the task is expected to facilitate designers to balance loosely defined criteria with well-defined constraints like static equilibrium. Addressing the lack of tools to support designers during such crucial process, the authors developed a new parametric, policy-based workflow for exploring equilibrium representations: (-) that incrementally grows and transforms bar networks within specified geometric domains; (-) that maintains their static equilibrium at every intermediate transformation step; (-) that is based on parametric, equilibrium-aware policies, controlled by a choice of four low- or high-level rules; (-) and that is not constrained to precedent typologies or recursing topology patterns (e.g. triangles). In this paper, the exploratory power of the presented workflow is augmented by coupling it with interactive genetic algorithms. Its capacity to unveil unprecedented, unexpected, but statically valid, structural forms is illustrated through a case study.