The development of large-scale multi- and many-core platforms and the rising complexity of embedded applications have led to a significant increase in the number of implementation possibilities for a single application. Furthermore, rising demands on safe, energy-efficient, or real-time capable application execution make the problem of determining feasible implementations that are optimal with respect to such design objectives even more of a challenge. State-of-the-art Design Space Exploration (DSE) techniques for this problem demonstrably suffer from the vast and sparse search spaces posed by modern embedded systems, emphasizing the need for novel design methodologies in this field. Based on the idea of reducing problem complexity by a suitable decomposition of the system specification—in particular, by a reduction of target architecture or task mapping options—the work at hand proposes a portfolio of dynamic decomposition mechanisms that automatically decompose any system specification based on a short pre-exploration of the complete system. We present a two-phase approach consisting of (a) a set of novel data extraction and representation techniques combined with (b) a selection of filtering operations that automatically extract a decomposed system specification based on information gathered during pre-exploration. In particular, we employ heat map data structures and threshold as well as graph-partitioning filters to reduce problem complexity. The proposed decomposition procedure can seamlessly be integrated in any DSE flow, constituting a flexible extension for existing DSE approaches. Furthermore, it improves existing static decomposition techniques and other heuristics relying on information about the problem instance, since systems with irregular architectural topology or distribution of resource types can now be decomposed based on an automatic, problem-independent pre-exploration phase. We illustrate the efficiency of the proposed decomposition portfolio applied to state-of-the-art DSEs for many-core systems as well as networked embedded systems from the automotive domain. Experimental results show significant increases in optimization quality of up to 87% within constant DSE time compared to existing approaches.