Multi-objective Optimization of Formal Specifications

Even in the domain of safety critical systems, safety and reliability are not the only goals and a developing engineer is faced with the problem to find good compromises wrt. other antagonistic objectives, in particular economic aspects of a system. Thus there does not exist a single optimal design variant of a system but only compromises each "best" in its own rights. With the rising complexity, especially of cyber-physical systems, the process of manually finding best compromises becomes even more difficult. To cope with this problem, we propose a model-based optimization approach which uses quantitative model-based safety analysis. While the general approach is tool-independent, we implement it technically by introducing well defined variation points to a formal system model. These allow enough variability to cover whole families of systems while still being rigorous enough for formal analysis. From the specification of this family of system variants and a set of objective functions, we compute Pareto optimal sets, which represent best compromises. In this paper we present a framework which allows for optimization of arbitrary quantitative goal functions, in particular probabilistic temporal logic properties used for model-based safety analysis. Nevertheless, the approach itself is well applicable to other domains.