Trivial example with Three Points
Potential Pareto Optimality for three hyperintervals on different $\sigma$-levels.
Although for small values of $\alpha_1$ and $\alpha_2$ the virtual lower bound for $F_1$ is dominated by the virtual lower bound for $F_2$, and for large values $F_3$ dominates both $F_1$ and $F_2$, when $alpha_1\ll\alpha_2$, $F_2^A$ is non dominated.
Figure 6(d) in "On the Extension of the DIRECT Algorithm to Multiple Objectives" by A. Lovison and K. Miettinen
