> ⚠️ **Critical:** The baseline design likely **violates** the displacement constraint (~22 mm vs 10 mm limit). Baseline re-run pending — CEO running SOL 101 in parallel. The optimizer must first find the feasible region before it can meaningfully minimize mass. This shapes the entire strategy.
>
> **Introspection note (2026-02-10):** Mass expression is `p173` (body_property147.mass, kg). DV baselines are NOT round numbers (face=21.504mm, core=25.162mm). NX expression `beam_lenght` has a typo (no 'h'). `hole_count` links to `Pattern_p7` in the NX pattern feature.
1.**Phase 1 budget: 50 trials (not 40).** With 4 variables, we want at least 10× the dimensionality for a reliable DoE. 50 trials also divides cleanly for stratified integer sampling (≈4-5 trials per hole_count level).
2.**Enqueue baseline as Trial 0.** LAC critical lesson: CMA-ES doesn't evaluate x0 first. While we're using LHS (not CMA-ES), the same principle applies — **always evaluate the baseline explicitly** so we have a verified anchor point. This also validates the extractor pipeline before burning 50 trials.
3.**Phase 2 budget: 80 trials (flexible 60-100).** Start with 60, apply convergence criteria (Section 6), extend to 100 if still improving.
4.**Seed Phase 2 from Phase 1 data.** Use Optuna's `enqueue_trial()` to warm-start TPE with the best feasible point(s) from the DoE. This avoids the TPE startup penalty (first `n_startup_trials` are random).
#### Algorithms NOT selected (and why)
| Algorithm | Why Not |
|-----------|---------|
| **CMA-ES** | Good option, but integer rounding is a hack; doesn't evaluate x0 first (LAC lesson); TPE is equally good at 4D |
| **NSGA-II** | Overkill for single-objective; population size wastes budget |
| **Surrogate + L-BFGS** | **LAC CRITICAL: Gradient descent on surrogates finds fake optima.** V5 mirror study: L-BFGS was 22% WORSE than pure TPE (WS=325 vs WS=290). V6 confirmed simple TPE beats complex surrogate methods. Do not use. |
| **SOL 200 (Nastran native)** | No integer support for hole_count; gradient-based so may miss global optimum; more NX setup effort. Keep as backup (Tech Lead's suggestion). |
| **Nelder-Mead** | No integer support; poor exploration; would miss the feasible region |
### 2.3 Final Algorithm Configuration
```
Phase 1: LHS DoE
- Trials: 50 (+ 1 baseline = 51 total)
- Sampling: Maximin LHS, DV4 rounded to nearest integer
| **Deb's rules** (selected) | No tuning params; feasible always beats infeasible; explores infeasible region for learning | Requires custom Optuna integration | ✅ Best for this case |
| **Adaptive penalty** | Self-tuning | Complex implementation; may oscillate | ❌ Over-engineered for 4 DVs |
| **Death penalty** (reject infeasible) | Simplest | With infeasible baseline, may reject 80%+ of trials → wasted budget | ❌ Dangerous |
### 3.4 Phase 1 (DoE) Constraint Handling
During the DoE phase, **record all results without filtering.** Every trial runs, every result is stored. Infeasible points are valuable for:
- Mapping the feasibility boundary
- Training the TPE model in Phase 2
- Understanding which variables drive constraint violation
### 3.5 Constraint Margin Buffer
Consider a 5% inner margin during optimization to account for numerical noise:
- Displacement target for optimizer: ≤ 9.5 mm (vs hard limit 10.0 mm)
- Stress target for optimizer: ≤ 123.5 MPa (vs hard limit 130.0 MPa)
The hard limits remain 10 mm / 130 MPa for final validation. The buffer prevents the optimizer from converging to designs that are right on the boundary and may flip infeasible under mesh variation.
**Critical concern:** At extreme DV3 × DV4 combinations, holes may overlap or leave insufficient ligament (material between holes).
#### Overlap condition
If the beam web has usable length `L_web` and `n` holes of diameter `d` are equally spaced:
```
Spacing between hole centers = L_web / (n + 1)
Ligament between holes = spacing - d = L_web/(n+1) - d
```
For **no overlap**, we need: `L_web/(n+1) - d > 0`, i.e., `d < L_web/(n+1)`
#### Worst case: n=15 holes, d=450 mm
```
Required: L_web > (n+1) × d = 16 × 450 = 7200 mm = 7.2 m
```
If the beam is shorter than ~7.2 m, this combination is **geometrically infeasible**.
#### Minimum ligament width
For structural integrity and mesh quality, a minimum ligament of ~20-30 mm is advisable:
```
Minimum ligament constraint: L_web/(n+1) - d ≥ 30 mm
```
> ⚠️ **ACTION REQUIRED:** We need to know the beam web length to validate bounds. If beam length < 7.2 m, either reduce max hole_count, reduce max hole_diameter, or add a geometric feasibility pre-check that skips NX evaluation for impossible geometries.
### 4.3 Hole-to-Web-Height Ratio
The hole diameter must also fit within the web height. If web height = 2 × half_core_thickness + 2 × face_thickness (approximate):
```
At minimum DV1=10, DV2=10: web_height ≈ 2×10 + 2×10 = 40 mm → max hole = 40 mm
```
But holes_diameter goes up to 450 mm — this suggests the web height is substantially larger than what the parametric cross-section variables alone define, OR the holes are in a different part of the geometry (e.g., a wider flange region or a tall web independent of core/face dimensions).
> ⚠️ **ACTION REQUIRED:** Clarify the geometric relationship between DV1/DV2 and the web where holes are placed. The holes may be in a different structural member than the sandwich faces.
### 4.4 Expected Feasible Region
Based on the physics (Tech Lead's analysis §1.2 and §1.3):
| To reduce displacement (currently 22→10 mm) | Effect on mass |
| ↑ DV1 (thicker core) | ↑ mass (but stiffness scales ~d², mass scales ~d) → **efficient** |
| ↑ DV2 (thicker face) | ↑ mass (direct) |
| ↓ DV3 (smaller holes) | ↑ mass (more web material) |
| ↓ DV4 (fewer holes) | ↑ mass (more web material) |
**Prediction:** The feasible region (displacement ≤ 10 mm) likely requires:
- DV1 in upper range (25-40 mm) — the sandwich effect is the most mass-efficient stiffness lever
- DV2 moderate (15-30 mm) — thicker faces help stiffness but cost mass directly
- DV3 and DV4 constrained by stress — large/many holes save mass but increase stress
The optimizer should find a "sweet spot" where core thickness provides stiffness, and holes are sized to save mass without violating stress limits.
### 4.5 Estimated Design Space Volume
- DV1: 30 mm span (continuous)
- DV2: 30 mm span (continuous)
- DV3: 300 mm span (continuous)
- DV4: 11 integer levels
Total configurations: effectively infinite (3 continuous), but the integer dimension creates 11 "slices" of the space. With 50 DoE trials, we get ~4-5 trials per slice — sufficient for trend identification.
Our budget of 114–156 falls in the **standard-to-thorough** range. Appropriate for a first study where we're mapping an unknown landscape with an infeasible baseline.
---
## 6. Convergence Criteria
### 6.1 Phase 1 (DoE) — No Convergence Criteria
The DoE runs all 50 planned trials. It's not iterative — it's a one-shot space-filling design. Stop conditions:
- All 50 trials complete (or fail with documented errors)
- **Early abort:** If >80% of trials fail to solve (NX crashes), stop and investigate
### 6.2 Phase 2 (TPE) — Convergence Criteria
| Criterion | Threshold | Action |
|-----------|-----------|--------|
| **Improvement stall** | Best feasible objective unchanged for 20 consecutive trials | Consider stopping |
| **Relative improvement** | < 1% improvement over last 20 trials | Consider stopping |
| **Budget exhausted** | 100 trials completed in Phase 2 | Hard stop |
| **Perfect convergence** | Multiple trials within 0.5% of each other from different regions | Confident optimum found |
| **Minimum budget** | Always run at least 60 trials in Phase 2 | Ensures adequate exploration |
### 6.3 Decision Logic
```
After 60 Phase 2 trials:
IF best_feasible improved by >2% in last 20 trials → continue to 80
IF no feasible solution found → STOP, escalate (see §7.1)
ELSE → assess convergence, decide 80 or 100
After 80 Phase 2 trials:
IF still improving >1% per 20 trials → continue to 100
ELSE → STOP, declare converged
After 100 Phase 2 trials:
HARD STOP regardless
```
### 6.4 Phase 1 → Phase 2 Gate
Before starting Phase 2, review DoE results:
| Check | Action if FAIL |
|-------|---------------|
| At least 5 feasible points found | If 0 feasible: expand bounds or relax constraints (escalate to CEO) |
| No systematic NX crashes at bounds | If crashes: tighten bounds away from failure region |
| Sensitivity trends visible | If flat: check extractors, may be reading wrong output |
---
## 7. Risk Mitigation
### 7.1 Risk: Feasible Region is Empty
**Likelihood: Medium** (baseline fails displacement by 120%)
**Detection:** After Phase 1, zero feasible points found.
**Mitigation ladder:**
1.**Check the data** — Are extractors reading correctly? Validate against manual NX check.
2.**Examine near-feasible** — Find the trial closest to feasibility. How far off? If displacement = 10.5 mm, we're close. If displacement = 18 mm, we have a problem.
3.**Targeted exploration** — Run additional trials at extreme stiffness (max DV1, max DV2, min DV3, min DV4). If even the stiffest/heaviest design fails, the constraint is physically impossible with this geometry.
4.**Constraint relaxation** — Propose to CEO: relax displacement to 12 or 15 mm. Document the mass-displacement Pareto front from DoE data to support the discussion.
5.**Geometric redesign** — If the problem is fundamentally infeasible, the beam geometry needs redesign (out of optimization scope).
### 7.2 Risk: NX Crashes at Parameter Extremes
**Likelihood: Medium** (LAC: rib_thickness had undocumented CAD constraint at 9mm, causing 34% failure rate in V13)
**Detection:** Solver returns no results for certain parameter combinations.
**Mitigation:**
1.**Pre-flight corner tests** — Before Phase 1, manually test the 16 corners of the design space (2⁴ combinations of min/max for each variable). This catches geometric rebuild failures early.
2.**Error-handling in run script** — Every trial must catch exceptions and log:
- NX rebuild failure (geometry Boolean crash)
- Meshing failure (degenerate elements)
- Solver failure (singularity, divergence)
- Extraction failure (missing result)
3.**Infeasible-by-default** — If a trial fails for any reason, record it as infeasible with maximum constraint violation (displacement=9999, stress=9999). This lets Deb's rules naturally steer away from crashing regions.
4.**NEVER kill NX processes directly** — LAC CRITICAL RULE. Use NXSessionManager.close_nx_if_allowed() only. If NX hangs, implement a timeout (e.g., 10 min per trial) and let NX time out gracefully.
### 7.3 Risk: Mesh-Dependent Stress Results
**Likelihood: Medium** (stress at hole edges is mesh-sensitive)
**Mitigation:**
1.**Mesh convergence pre-study** — Run baseline at 3 mesh densities. If stress varies >10%, refine mesh or use stress averaging region.
2.**Consistent mesh controls** — Ensure NX applies the same mesh size/refinement strategy regardless of parameter values. The parametric model should have mesh controls tied to hole geometry.
3.**Stress extraction method** — Use elemental nodal stress (conservative) per LAC success pattern. Note: pyNastran returns stress in kPa for NX kg-mm-s unit system — **divide by 1000 for MPa**.
### 7.4 Risk: Surrogate Temptation
**Mitigation: DON'T DO IT (yet).**
LAC lessons from the M1 Mirror project are unequivocal:
- V5 surrogate + L-BFGS was 22% **worse** than V6 pure TPE
- MLP surrogates have smooth gradients everywhere → L-BFGS descends to fake optima outside training distribution
- No uncertainty quantification = no way to detect out-of-distribution predictions
With only 4 variables and affordable FEA (~2 min/trial), direct FEA evaluation via TPE is both simpler and more reliable. Surrogate methods should only be considered if:
- FEA solve time exceeds 30 minutes per trial, AND
- We have 100+ validated training points, AND
- We use ensemble surrogates with uncertainty quantification (SYS_16 protocol)
### 7.5 Risk: Study Corruption
**Mitigation:** LAC CRITICAL — **Always copy working studies, never rewrite from scratch.**
- Phase 2 study will be created by **copying** the Phase 1 study directory and adding optimization logic
- Never modify `run_optimization.py` in-place for a new phase — copy to a new version
- Git-commit the study directory after each phase completion
---
## 8. AtomizerSpec Draft
See [`atomizer_spec_draft.json`](./atomizer_spec_draft.json) for the full JSON config.
### 8.1 Key Configuration Decisions
| Setting | Value | Rationale |
|---------|-------|-----------|
| `algorithm.phase1.type` | `LHS` | Space-filling DoE for landscape mapping |
