Figure 1.
Comparisons of different exploration directions at a Pareto optimal solution ${\color{Red} \mathbf{x}^*}$.
The analytic Pareto set (the cylindrical surface) of ZDT2-variant, the gradients ${\color{NavyBlue} \nabla f_1(\mathbf{x}^*)}$ and ${\color{OliveGreen} \nabla f_2(\mathbf{x}^*)}$, and our directions ${\color{BurntOrange} \{\mathbf{v}_i\}}$.
A top-down view to show ours are almost tangent to the Pareto set.
Plots of $\mathbf{f}(\mathbf{x}^*+s\mathbf{d})$ where $s\in[-0.1,0.1]$ and $\mathbf{d}$ is ${\color{NavyBlue} \nabla f_1(\mathbf{x}^*)}$, ${\color{OliveGreen} \nabla f_2(\mathbf{x}^*)}$, and our directions ${\color{BurntOrange} \{\mathbf{v}_i\}}$.