Optimization Methods

TFStudio ships a full toolbox of optimizers. This page explains what each one is, when to reach for it, and summarizes the benchmark we ran across every method to set the defaults.

There are two fundamentally different jobs:

Refinement — fixed structure, move only the layer thicknesses to minimize the merit function. Never adds or removes layers.
Synthesis — changes the structure: inserts, removes, splits or merges layers to find a better topology.

All methods minimize exactly the same merit function (the operand set from the Merit Function Editor) and honor the surface mode set in the Design Editor (front_only / back_only / both_independent / symmetric).

Pick the method from the dropdown in the Refinement window. They split into local (follow the merit-function slope down from your current design) and global (search broadly, gradient-free).

Local refiners

Method	What it is	Best for
Sequential QP (SQP) ⭐ default	Bounded Newton step with the layer bounds [MNT/MXT] ∩ [Dmin,Dmax] as hard constraints (box-QP, exact bound satisfaction — no penalty tuning).	The default. Best / tied-best MF across every benchmark case, decisively so on constrained problems (it handles a min-thickness natively). Slower on hard problems — switch to DLS if you want speed first.
Damped Least Squares (DLS)	Levenberg–Marquardt — the classic thin-film least-squares refiner. QR-solved damped step, exact analytic Jacobian.	The fast, robust classic; called after every synthesis step. Pick it when you want speed over the last fraction of MF.
Conjugate Gradient (CG)	Polak–Ribière⁺ gradient-only method (Nocedal & Wright §5.2), exact analytic ∇MF, projected backtracking line search.	Very large stacks and polishing a decent design. Won the 30-layer detuned-HR benchmark; the preferred inner refiner for Needle.
Newton	Second-order. Exact analytic Hessian (JᵀJ + curvature) when scoring a single side; Gauss-Newton (JᵀJ) for full-filter (Both / symmetric).	A quadratic endgame in the fewest iterations — small stacks, near the minimum, when you want the last digits.
Newton-CG	Truncated Newton — matrix-free; solves the Newton step with inner CG using Hessian-vector products (no dense Hessian).	Second-order quality without the cost. Scales to large stacks where dense Newton is too slow (see the 75.9 s → 2.8 s figure below).

Global refiners

Method	What it is	Best for
DLS multi-start	Runs DLS from N randomly-perturbed starts, keeps the best.	Escaping shallow local minima around a known-decent design.
Differential Evolution (DE)	Storn & Price (1997) population search, gradient-free; runs in parallel across your CPU cores.	Poor / unknown starting point, multimodal targets. The strongest global on smooth problems.
Simulated Annealing (SA)	Kirkpatrick (1983) — accepts uphill moves with probability `exp(−ΔMF/T)`, then cools.	Rugged merit surfaces where you need to climb out of deep wells.
Try all — keep best	Runs every method from the same start and keeps the lowest MF (DLS multi-start last, as it’s the slowest).	When you don’t want to choose — let TFStudio pick the winner.

All methods work in all surface modes. Newton / Newton-CG / SQP use the full analytic Hessian for a single side and Gauss-Newton for coupled full-filter evaluation — no silent fallback.

Synthesis methods

These change the number of layers. See each tool’s page for details.

Tool	What it does	Default inner refiner
Needle	Inserts infinitesimal “needle” layers where the P-function says the merit improves, then refines.	CG — keeps the design “loose” so the scan keeps finding improving needles (a heavier refiner over-refines and the loop stops early).
Gradual Evolution	Needle optimization wrapped in an outer loop that forces a needle in (even uphill) to escape local minima.	CG — it does not stall on demanding multi-passband targets the way a least-squares refiner can, and the forced step escapes the minimum it lands in.
Structural Optimizer	Randomly add / remove / split / merge / perturb layers with a simulated-annealing accept.	CG. Best layer-efficiency in the benchmark.

The per-tool inner refiner is selectable; the defaults above are benchmark-confirmed on real designs.

How to choose

Just want the best result?         → SQP   (the default; best across the benchmark)
Want it faster, near-best?         → DLS
Decent design, large stack?        → CG    (or Newton-CG to polish)
Near the minimum, want last digits?→ Newton-CG  (or Newton on small stacks)
Hard min-thickness to respect?     → SQP   (handles bounds natively)
Bad / unknown start, multimodal?   → DE    (or SA on a rugged surface)
Too few layers for the target?     → Synthesis: Needle → GE → Structural
Not sure?                          → Try all — keep best

A reliable full workflow:

Synthesize unconstrained → Refine with your min-thickness on → Design Cleaner → Refine again.

The grand benchmark

To set the defaults and the guidance on this page, we ran every method across a fixed set of representative designs — a broadband anti-reflection coating, a 50/50 beam splitter, a three-line bandpass, a shortpass edge filter, and a demanding multi-passband filter — and measured the final merit function, the run time, and the resulting layer count, both unconstrained and with a realistic minimum-thickness limit.

What it found

SQP is the best overall local refiner — best or tied-best MF in every case, constrained and unconstrained, and decisively ahead on constrained problems because it treats a min-thickness as a hard box constraint (no penalty tuning). It’s now the default Refinement method. It costs more time on hard problems than DLS/Newton-CG, but the quality margin is large.
Newton-CG is the best matrix-free second-order method — it matches Newton / SQP quality without forming a dense Hessian. On the 12-layer bandpass, dense Newton took 75.9 s vs Newton-CG 2.8 s for the same result.
CG wins on very large stacks — it took the 30-layer detuned-HR case.
DE is the strongest global optimizer on smooth problems; on a multimodal BBAR it reached MF 0.019 where plain DLS stuck at 0.089 (it escaped the local minimum).
Synthesis wins raw MF — tools that grow layers (Needle / GE) reach lower merit than any fixed-structure refiner, given enough layers.
Structural Optimizer gives the best layer-efficiency — the lowest MF per layer.
The dMin 1 ↔ 40 trade-off is real and visible — dMin = 1 nm lets synthesis reach a lower MF (more, thinner layers); a manufacturable floor raises MF but yields a buildable stack. Synthesize at dMin = 1, then enforce your real floor in a Refinement + Cleaner pass.
Constraint behavior is tool-specific and deliberate: Needle ignores MNT by design (an MNT penalty would wipe every improving candidate), GE respects MNT, and Structural / Refinement respect it via the penalty.

Speed

Two things make every method faster without changing its results:

Parallel processing — multi-start refinement, Differential Evolution, and synthesis candidate searches spread their work across your CPU cores, so they stay responsive on large designs.
Hardware-accelerated math — the core optical calculation runs through an optimized engine (on by default; Settings → Performance), giving a large speed-up on every optimization.

References

K. Levenberg, Quart. Appl. Math. 2, 164 (1944); D. Marquardt, J. SIAM 11, 431 (1963) — DLS / Levenberg–Marquardt.
J. Nocedal & S. Wright, Numerical Optimization, 2nd ed., §5.2 (CG), Ch. 6–7 (Newton / truncated Newton), Ch. 18 (SQP).
R. Storn & K. Price, J. Global Optim. 11, 341 (1997) — Differential Evolution.
S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983) — Simulated Annealing.
A. V. Tikhonravov et al., Appl. Opt. 35, 5493 (1996) & 46, 6936 (2007) — needle / gradual evolution.
H. A. Macleod, Thin-Film Optical Filters, 5th ed., Ch. 9 & §13 — synthesis & refinement overview.

Refinement methods