Beyond Hypervolume: Dynamic visualization of MOEA runtime

Multi-objective evolutionary algorithms have become an essential tool for decision support in water resources systems. A core challenge we face when applying them to real world problems is that we don’t have analytic solutions to evaluate algorithmic performance, i.e. since we don’t know what solutions are possible before hand, we don’t have a point of reference to assess how well our algorithm is performing. One way we can gain insight into algorithmic performance is by examining runtime dynamics. To aid our understanding of the dynamics of the Borg MOEA, I’ve written a small Python library to read Borg runtime files and build a dynamic dashboard that visualizes algorithmic progress.

The Borg MOEA produces runtime files which track algorithmic parameters and the evolving Pareto approximate set over an optimization run. Often we use these data to calculate performance metrics, which provide information on the relative convergence of an approximation set and the diversity of solutions within it (for background on metrics see Joe’s post here). Commonly, generational distance, epsilon indicator and hypervolume are used to examine quality of the approximation set. An animation of these metrics for the 3 objective DTLZ2 test problem is shown in Figure 1 below.

Figure 1: Runtime metrics for the DTLZ2 test problem. The x-axis is number of function evaluations, the y-axis is the each individual metric

While these metrics provide a helpful picture of general algorithmic performance, they don’t provide insight into how the individual objectives are evolving or Borg’s operator dynamics.

Figure 2 shows a diagnostic dashboard of the same 3 objective DTLZ2 test problem run. I used the Celluloid python package to animate the figures. I like this package because it allows you to fully control each frame of the animation.

Figure 2: DTLZ2 runtime dynamics. The tree objectives are shown in a scatter plot and a parallel axis plot. The third figure plots hypervolume over the optimization run and the bottom figure shows Borg’s operator dynamics. (a higher resolution version of this file can be found here: https://www.dropbox.com/s/0nus5xhwqoqtghk/DTLZ2_runtime.gif?dl=0)

One thing we can learn from this dashboard is that though hypervolume starts to plateau around 3500 NFE, the algorithm is still working to to find solutions that represent an adequately diverse representation of the Pareto front. We can also observe that for this DTLZ2 run, the SPX and SBX operators were dominant. SBX is an operator tailored to problems with independent decision variables, like DTLZ2, so this results make sense.

I’m planning on building off this dashboard to include a broader suite of visualization tools, including pairwise scatter plots and radial plots. The library can be found here: https://github.com/dgoldri25/runtimeDiagnostics

If anyone has suggestions or would like to contribute, I would love to hear from you!