High-performance many-core processors have complex computing architectures with many design parameters related to different levels (CPU macro/micro-architecture, interconnect, memory, specific accelerators, etc.). Design Space Exploration (DSE) is key to tackle the challenges related to the design of such processors, especially in the early stages. This work introduces A-DECA, a highly modular DSE approach for automating the exploration of design parameters. A-DECA combines simulators, models, and exploration strategies to derive relevant objective estimations while preserving a reasonable execution time. Thus, it provides a full methodology enabling the exploration of the design space in an easy-to-use, automatic, and effective way. A-DECA is evaluated in the context of next-generation HPC processors with various applications. We combine simulation tools and analytical formulations to assess PPA (Performance, Power, and Area). Based on an efficient implementation of a multi-objective genetic algorithm for the exploration strategy, current results show a great reduction of design space optimization by around 30% compared to the initial population. A-DECA optimizes the objectives and automatically returns a set of configurations with different characteristics allowing the architect to choose the best design according to the application context.