The set-based concept approach is suggested as a means to simultaneously explore different design spaces at both the conceptual and the particular design levels. The proposed technique employs dynamic relaxation of concept-based Paretooptimality. Two types of exploration problems are defined. The first type aims to reveal the approximated concepts' fronts, within a relaxation zone, whereas the second type is about which of the concepts' front intersect with that zone. A unique benchmarking approach and measures are employed to test the suggested algorithm with respect to the aforementioned types of problems. The numerical study shows that the algorithm can cope with various numerical difficulties in a simultaneous way. The use of exploration tools, such as proposed here, is expected to enhance the understanding of conceptual design spaces by both experienced and novice designers.