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This paper presents a methodology for design space exploration (DSE) in high-level synthesis (HLS), based on a multi-objective genetic algorithm. Since all high-level synthesis sub-tasks are notoriously NP-complete and interdependent and the design objectives are in conflict for nature, most of the already proposed approaches are not efficient in the exploration of this design space and not effective in the identification of different trade-offs. For these reasons, evolutionary algorithms can be considered as good candidates to tackle such difficult explorations. Therefore, we will compare our proposed approach, using different solution encoding, with a publicly available HLS framework and we will show that this approach is able to obtain better optimization results, with respect to the design objectives (latency and area have been considered for optimization), in most of situations and our proposed encoding better approaches the situations when multi-modal functional units (e.g. Arithmetic Logic Units) could be used in the final design solutions.