Convergence/Progression Control

The optimization algorithm uses a new function called “convergence based progression control” from version 2025.1 forward to decide how many iterations on which resolution level are needed for each optimization run. The solver automatically adjusts the resolution of the design space during the optimization run. Prior to this release the resolution change was done by static schedule with predefined iteration numbers for each resolution level. With the new function there is a detection based on the change of mass and the change of the “unified failure indicator” (UFI) to determine if the optimization should progress further by changing the resolution and coming closer to the set up constraints.

Metrics:

For the convergence detection different metrics are used to determine a convergence for the current phase and therefore the change to the next one.

Mass: the mass metric operates on the voxel-based mass m(i) of the design candidate in iteration I. For a given iteration I, it computes the mean mass change over the previous k iterations. The default for k is 3.

UFI: The unified failure indicator metric is a measure for the uniform convergence of the UFI CDF (Cumulative Distribution Function) over a window of at most k recent iterations. In general, a metric to detect the target achievement of the optimization. The default for k is 5. First the regarded iterations’ UFI CDF are normalized to a uniform range and bucket count. From these buckets B(i,j) (Iteration I, bucket index ) two means are computed and the final metric U(I) is computed as the maximum absolute difference between the two:

Convergence detection:

The convergence and therefore change of the phase is determined and triggered when the metrics are close enough to a set convergence value (ConvMass M(I), ConvUFI U(I)) for a defined number of iterations.

Adjustments

With the Advanced User Settings the default values for the convergence detection can be adjusted as well as a switch back to the former static schedule.