During preliminary phases in product design, on the basis of strong physical hypotheses (e.g. isotherm, steady state), physical and functional requirements can be expressed as coarse-grained constraintbased models on a few degrees of freedom, possibly including several design criteria to optimize. Such models are usually handled by multi-objective optimization solvers in order to find design solutions giving the best trade-o↵s between design criteria. Another approach developed in this paper is to partially explore all the areas of the design space using an anytime interval branch-and-prune algorithm called IDFS such that the design criteria are converted into so-called "-constraints. The expected result is a sample of solutions diversified in both the objective space and the design space. Several quality indicators are introduced in order to measure this diversity and compare IDFS with two state-ofthe-art multi-objective optimization solvers NSGA-II and NSGA-III on three real-world case studies. The results show that IDFS is able to identify new close-to-optimal designs and permits a better understanding of the design space. This framework provides a promising alternative tool for decision making, in particular for integrating interaction in the preliminary design process.