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Application-specific multiprocessor systems-on-chip (MPSoCs) are usually designed by using a platform-based approach, where a wide range of customizable parameters can be tuned to find the best tradeoff in terms of the selected figures of merit (such as energy, delay, and area). This optimization phase is called design space exploration (DSE), and it usually consists of a multiobjective optimization problem with multiple constraints. So far, several heuristic techniques have been proposed to address the DSE problem for MPSoC, but they are not efficient enough for managing the application-specific constraints and for identifying the Pareto front. In this paper, an efficient DSE methodology for application-specific MPSoC is proposed. The methodology is efficient in the sense that it is capable of finding a set of good candidate architecture configurations by minimizing the number of simulations to be executed. The methodology combines the design of experiments (DoEs) and response surface modeling (RSM) techniques for managing system-level constraints. First, the DoE phase generates an initial plan of experiments used to create a coarse view of the target design space to be explored by simulations. Then, a set of RSM techniques is used to refine the simulation-based exploration by exploiting the application-specific constraints to identify the maximum number of feasible solutions. To trade off the accuracy and efficiency of the proposed techniques, a set of experimental results for the customization of a symmetric shared-memory on-chip multiprocessor with actual workloads has been reported in this paper.