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 \(\color{BurntOrange} \{\mathbf{v}_i\}\).