Cluster analysis of local optima

Cluster analysis is now available as an optional addition to optimization analysis. This powerful new feature lets you identify and analyze plateaus (that is, groups of optimization runs with similar objective function) for multi-start optimizations.

To enable cluster analysis, select the Enable Additional Settings option in the Advanced Settings page of the Run Settings dialog, and enter the following command in the additional settings text area:

OptimizationAnalyzerConfiguration = ClusterAnalysis

When you optimize with cluster analysis enabled, the Cluster Analysis tool calculates the means and standard deviations of the objective functions in the plateaus, and of the degrees of freedom of the model in each plateau. This information is added to the Cluster Analysis section in the optimization analysis JSON report.

The initial version of cluster analysis identifies up to two plateaus. This restriction will be lifted in release 2025.3. You can use the MultiStartSeeds additional run setting to limit the run to seeds that produce plateaus of interest. For instance, use the command MultiStartSeeds = 4, 8, 9, 16 to run seeds 4, 8, 9 and 16.

Contact Support (spiral.support@aveva.com) to receive an Excel workbook where you can load your JSON optimization analysis report to better investigate the differences between plateaus. The workbook presents a summary of the plateaus detected, a worksheet detailing the degrees of freedom for each run seed, statistics for the degrees of freedom within each plateau, and tools to help you identify and analyze areas of the model that might be contributing to local optima.

The following example shows a multi-start solution with two plateaus.

In the Cluster Analysis sheet of the workbook, two sets of columns let you identify degrees of freedom with significant differences between plateaus:

• In the Zero Switch columns the True values identify degrees of freedoms that are on average zero on one plateau and on average non-zero on another.

• In the Plateau Switch columns the True values identify degrees of freedom that on average are different in both plateaus but only vary by a small amount within each plateau.

The following image shows the degrees of freedom with True values for both the Zero Switch and Plateau Switch columns. A splitter output flow and feed volume flow are zero on one plateau and nonzero on the other, which may offer clues as to the model behavior that causes the plateaus. Further analysis is possible by applying different filters on the Type and Switch columns.