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 thickness limits (see below) as hard constraints (box-QP, exact bound satisfaction, no penalty tuning).	The default. Holds a min-thickness as a hard limit, and was far ahead of the other local refiners on the hardest constrained case of the benchmark. No local refiner wins every case, so when SQP stalls, try CG or Try all, keep best.
Damped Least Squares (DLS)	Levenberg–Marquardt, the classic thin-film least-squares refiner. QR-solved damped step, exact analytic Jacobian.	The robust classic; called after every synthesis step. Close to the best without a min-thickness, well behind with one.
Conjugate Gradient (CG)	Polak–Ribière⁺ gradient-only method (Nocedal & Wright §5.2), exact analytic ∇MF, projected backtracking line search.	Polishing a decent design. The best local refiner on the beam splitter and the three-line bandpass of the benchmark, with and without a min-thickness.
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 steps without forming the Hessian. Best of the local refiners on the unconstrained multi-passband case.

Thickness limits. No method has a built-in maximum layer thickness: a layer can grow as thick as the merit function asks, which is what half-wave layers in the infrared and thick cavity spacers need. For an upper limit, add an MXT row in the Merit Function Editor; for a manufacturing floor, an MNT row. SQP holds MNT and MXT as hard limits, so no step leaves them. The other methods carry them as penalty terms in the merit function, which stay at zero while the limit holds. Every method also keeps each layer at or above a minimum thickness: 1 nm in Refinement, the Min thickness setting in the synthesis windows. DLS, Newton and Newton-CG hold a layer on that floor for as long as the merit pushes it thinner and release it as soon as the merit pulls it back, so the step is spent on the layers that can move.

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.
Simulated Annealing (SA)	Kirkpatrick (1983), accepting uphill moves with probability `exp(−ΔMF/T)`, then cooling.	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 and would rather 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, with 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.	Trust-region Newton, which ended lower than CG on most of the benchmark’s cases and grows the stack without collapsing it.
Gradual Evolution	Needle optimization wrapped in an outer loop that forces a needle in (even uphill) to escape local minima.	CG, which 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

One method for most designs?       → SQP   (the default)
No min-thickness, want the classic?→ DLS
Decent design to polish?           → CG    (or Newton-CG)
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

No local refiner wins every case. SQP, the default, treats a min-thickness as a hard box constraint and was far ahead on the hardest constrained case, the multi-passband with a 40 nm floor (MF 0.235 where the others reached 0.51 to 0.56). CG was the best local refiner on the beam splitter and the three-line bandpass, with and without the floor; with it, CG reached MF 0.009 on the beam splitter where SQP stopped at 0.067. DLS, Newton and SQP tied on the shortpass edge.
The global refiners escape local minima: on the broadband AR, DE reached MF 0.012 and DLS multi-start 0.008, where plain DLS stopped at 0.118.
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

Multi-start refinement, Differential Evolution, and synthesis candidate searches spread their work across your CPU cores, so they stay responsive on large designs.

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).