ClusterRefinement

The ClusterRefinement method is a refinement algorithm, proprietary to FilmOptima. It improves an existing stack by systematically exploring joint variations of multiple layers (“clusters”) and polishing the best candidates with a local optimizer.

The key idea is a two-stage enumeration:

1. First, the algorithm generates all possible combinations of up to #LayersToCluster layer indices from the current stack.
2. For each index combination, the algorithm enumerates all possible permutations of thickness candidates, using discretized thickness values.

Once the “clustered” candidate stacks are generated, they are refined using AdamW.

By jointly perturbing clusters of layers instead of adjusting them individually, ClusterRefinement can escape shallow local minima while still keeping the total number of layers fixed.

Advantages

• Joint layer optimization: Captures multi-layer interactions by modifying clusters instead of single layers.
• Systematic enumeration: Guarantees coverage of all index combinations and discretized thickness assignments.
• Precise local improvement: Nested AdamW ensures each candidate is fully refined.
• No topology change: Layer count stays fixed, ideal when design structure is constrained.
• Highly Parallelizable: Candidate stacks can be evaluated independently.

Limitations

• Combinatorial growth: Number of candidates rises quickly with number of thickness values and the number of layers to cluster.
• Runtime cost: Full enumeration can be computationally expensive.
• Local scope: Broader than single-layer refinement but still not a global optimization method.

In FilmOptima

In FilmOptima, ClusterRefinement belongs to the Refinement category of algorithms.