Recent work has proposed two-phase joint analytical and simulation-based design space exploration (JAS-DSE) approaches. In such approaches, a first analytical phase relies on static performance estimation and either on exhaustive or heuristic search, to perform a very fast filtering of the design space. Then, a second phase obtains the Pareto solutions after an exhaustive simulation of the solutions found as compliant by the analytical phase. However, the capability of such approaches to find solutions close to the actual Pareto set at a reasonable time cost is compromised by current system complexities. This limitation is due to the fact that such approaches do not support an heuristic exploration on the simulation-based phase. It is not straightforward because in the second phase the heuristic is constrained to consider only the custom set of solutions found in the first phase. This set is in general unconnected and irregularly distributed, which prevents the application of existing heuristics. This paper provides as a solution a novel search heuristic called ARS (Adaptive Random Sampling). The ARS strategy enables the application of heuristic search in the two phases of the JAS-DSE flow, by enabling the application of heuristic in the second phase, regardless the type of performance estimation done at each phase. Moreover, it enables the definition of N-phase DSE flows. The paper shows on an experiment focused on predictable multi-core systems how this enhanced JAS-DSE is capable to find more efficient solutions and to tune the trade-off between exploration time and accuracy in finding actual Pareto solutions.