Visualizations of problem landscapes
Plots
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| Dimension |
| Function |
| Instance |
| Visualization type |
Plot explanations
Level sets
These plots show level sets corresponding to some selected function values f on a 2-D view of the search space that contains the optimal solution and is approximated by a grid. For dimensions larger than 2, the level sets of pairs of variables are organized into a matrix. To improve visibility, only five variables are included in the matrix in the larger dimensions (D \geq 10), corresponding to x_1, x_2, x_{\lfloor D/2 \rfloor}, x_{D-1} and x_D, where D is the search space dimension.
Normalized rank heatmap
The normalized rank heatmap shows, instead of absolute function values f, their normalized rank with 0 corresponding to the best rank and 1 to the worst one on a 2-D view of the search space that contains the optimal solution and is approximated by a grid. In addition to color-coded ranks, the plots include level sets in gray hues. For dimensions larger than 2, the heatmaps of pairs of variables are organized into a matrix. To improve visibility, only five variables are included in the matrix in the larger dimensions (D \geq 10), corresponding to x_1, x_2, x_{\lfloor D/2 \rfloor}, x_{D-1} and x_D, where D is the search space dimension.
Surface plot
The surface plot shows the function values f on a 3-D view of the search space and is available only for 2-D problems. To improve visibility, the z-axis is inverted, so that the global optimum is at the top of the plot.
Search space cuts
The plots with search space cuts show the function value f along various lines in the search space that go through the global optimum \mathbf{x}_\mathrm{opt}. The colored lines change the value of only one variable x_i at a time keeping the rest fixed to \mathbf{x}_\mathrm{opt}. The gray line represents the line that goes through \mathbf{x}_\mathrm{opt} in the direction of the all-ones vector (i.e., in the diagonal direction). To improve visibility, only five colored lines are shown in the larger dimensions (D \geq 10), corresponding to x_1, x_2, x_{\lfloor D/2 \rfloor}, x_{D-1} and x_D, where D is the search space dimension. The plots are shown in three variants:
- lin-lin: both axes are linear,
- lin-log: the x-axis is linear, the y-axis shows the difference between f and the optimal value f_\mathrm{opt} on a logarithmic scale,
- log-log: both axes are logarithmic, the x-axis shows the absolute difference to \mathbf{x}_\mathrm{opt} (positive directions presented as x_i and negative as -x_i), the y-axis shows the difference between f and f_\mathrm{opt}.