We propose a procedure to rank the most interesting solutions from high-throughput materials design studies. Such a tool is becoming indispensable due to the growing size of computational screening studies and the large number of criteria involved in realistic materials design. As a proof of principle, the binary tungsten alloys are screened for both large-weight and high-impact materials, as well as for fusion reactor applications. Moreover, the concept is generally applicable to any design problem where multiple competing criteria have to be optimized. DOI: 10.1103/PhysRevLett.111.075501 PACS numbers: 81.05.Zx, 07.05.Kf, 28.52.Fa, 62.20.Àx In recent years, materials design has benefitted considerably from computational searches [1]. The increase in computing power has allowed the screening of large numbers of hypothetical compounds for several well-defined design criteria. However, interpreting the output from such investigations is not a trivial task, especially when multiple objectives are optimized simultaneously. The field of multicriteria decision making [2,3] proposes the use of the so-called Pareto set to drastically reduce the number of materials under consideration. Multicriteria decision making notes that in the case of competing requirements, a single ''best'' solution does not exist. Instead, a number of solutions can be shown to outperform the rest, forming the Pareto set P . Compared to such a Pareto solutionx, none of the alternative x improve all of the decision criteria f ðkÞ simultaneously:Here, we assume the design problem to be described by N normalized, maximizable objective functions f ðkÞ with k ¼ 1; . . . ; N, relating to each Pareto solution a set of coordinates. The assembled Pareto points are therefore also called the Pareto front or skyline, as they outline a hypersurface in N-dimensional space (full black line in Fig. 1). Pareto optimality has already been successfully applied to computational materials design [4,5]. Unfortunately, as the dimensionality of the problem increases, so does the size of the Pareto set P . It then becomes prohibitively time consuming to study every single Pareto compound in more detail. Several post-Pareto analysis methods therefore try to reduce the number of candidates even further [6][7][8], but none of them offer a quantitative ordering. This Letter, on the other hand, proposes a mathematically founded procedure that allows the ranking of the Pareto compounds, thus identifying the most optimal compromises with respect to the design requirements. It is, however, also more generally applicable to any multicriterion design problem, ranging from space technology [9] over urban studies [10] to linguistics [11]. Figure 1 illustrates how a ranking can be based on the tradeoff between two Pareto solutions, using a hypothetical 2D data set. If we consider an arbitrary Pareto point, such as b, its bottom left quadrant (hatched area) contains only suboptimal (dominated) points, while solutions outside this region offer a tradeoff with the properties of b, ...