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

Figure 6(d) in "On the Extension of the DIRECT Algorithm to Multiple Objectives" by A. Lovison and K. Miettinen