This paper presents a novel approach to support the selection of conceptual solutions to multi-objective problems. The proposed method involves a comparison between concepts, based on the performances of sets of solutions that represent them. The set-based comparison of concepts is consistent with the so-called Toyota set-based concurrent engineering process. Such an approach discourages early exploitation of solutions and promotes extended exploration of the design space by means of sets of solutions. Both optimality and variability of concepts are considered, and their measures are devised to pose the selection problem as an auxiliary multi-objective problem. The auxiliary objectives are to maximise optimality and to maximise the variability. This highlights the inherent multi-objectivity of concept selection and supports decision-making under the possible contradictory nature of optimality and variability of concepts. Both academic and engineering problems are used to demonstrate the approach and to expose the inherent subjectivity of the measures, which are dependent on the selection of a window of interest by the decision-makers.