Networked systems operating under uncertainty require decision making frameworks capable of balancing nominal efficiency and robustness against correlated risks. In this work, we study a distributionally robust weighted dominating set problem as a system-level model for robust network design, where node selection decisions are affected by uncertainty in costs and their correlation structure. We formulate the problem as a bi-objective optimization model that simultaneously minimizes the expected price and a risk measure derived from mean–covariance ambiguity. Rather than proposing new optimization algorithms, we conduct a systematic, methodological, and computational analysis of classical multiobjective solution approaches within this nonconvex and combinatorial setting. In particular, we compare weighted-sum, lexicographic, and ε-constraint methods, highlighting their ability to reveal different structural properties of the Pareto Frontier. Our numerical results demonstrate that the methods that use scalarization allow us to obtain only partial insights for networked systems where robustness is inherent. However, the ε-constraint method is highly efficient in recovering the full set of Pareto-optimal solutions. Once obtained, the Pareto Frontier exposes non-supported solutions and disruptive changes in its form. Notice that the latter is directly related to different configurations of dominating sets which are induced by the uncertainties. Consequently, these observations allow us to select from different subsets of relevant operating conditions for robust network designs that are significantly different for a decision maker.
Adasme et al. (Thu,) studied this question.