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# Optimization Strategy — Hydrotech Beam DoE & Landscape Mapping
**Study:** `01_doe_landscape`
**Project:** Hydrotech Beam Structural Optimization
**Author:** ⚡ Optimizer Agent
**Date:** 2025-02-09
**Status:** DRAFT — Awaiting review
**References:** [BREAKDOWN.md](../../BREAKDOWN.md), [DECISIONS.md](../../DECISIONS.md), [CONTEXT.md](../../CONTEXT.md)
---
## 1. Problem Formulation
### 1.1 Objective
$$\min_{x} \quad f(x) = \text{mass}(x) \quad [\text{kg}]$$
Single-objective minimization of total beam mass. This aligns with DEC-HB-001 (approved by Tech Lead, pending CEO confirmation).
### 1.2 Constraints
| ID | Constraint | Operator | Limit | Units | Source |
|----|-----------|----------|-------|-------|--------|
| g₁ | Tip displacement | ≤ | 10.0 | mm | NX Nastran SOL 101 — displacement sensor at beam tip |
| g₂ | Max von Mises stress | ≤ | 130.0 | MPa | NX Nastran SOL 101 — max elemental nodal VM stress |
Both are **hard constraints** — no trade-off or relaxation without CEO approval.
### 1.3 Design Variables
| ID | NX Expression | Type | Lower | Upper | Baseline | Units | Notes |
|----|---------------|------|-------|-------|----------|-------|-------|
| DV1 | `beam_half_core_thickness` | Continuous | 10 | 40 | 20 | mm | Core half-thickness; stiffness scales ~quadratically via sandwich effect |
| DV2 | `beam_face_thickness` | Continuous | 10 | 40 | 20 | mm | Face sheet thickness; primary bending stiffness contributor |
| DV3 | `holes_diameter` | Continuous | 150 | 450 | 300 | mm | Lightening hole diameter; mass ∝ d² reduction |
| DV4 | `hole_count` | **Integer** | 5 | 15 | 10 | — | Number of lightening holes; 11 discrete levels |
**Total design space:** 3 continuous × 1 integer (11 levels) = effectively 3D continuous × 11 slices.
### 1.4 Integer Handling
Per DEC-HB-003, `hole_count` is treated as a **true integer** throughout:
- **Phase 1 (LHS):** Generate continuous LHS, round DV4 to nearest integer. Use stratified integer sampling to ensure coverage across all 11 levels.
- **Phase 2 (TPE):** Optuna `IntDistribution(5, 15)` — native integer support, no rounding hacks.
- **NX rebuild:** The model requires integer hole count. Non-integer values will cause geometry failures.
### 1.5 Baseline Assessment
| Metric | Baseline Value | Constraint | Status |
|--------|---------------|------------|--------|
| Mass | ~974 kg | (minimize) | Overbuilt — room to reduce |
| Tip displacement | ~22 mm | ≤ 10 mm | ❌ **FAILS** by 120% |
| VM stress | (unknown) | ≤ 130 MPa | ⚠️ Assumed OK but unconfirmed |
> ⚠️ **Critical:** The baseline design **violates** the displacement constraint (22 mm vs 10 mm limit). The optimizer must first find the feasible region before it can meaningfully minimize mass. This shapes the entire strategy.
---
## 2. Algorithm Selection
### 2.1 Tech Lead's Recommendation
DEC-HB-002 proposes a two-phase strategy:
- **Phase 1:** Latin Hypercube Sampling (LHS) — 40–50 trials
- **Phase 2:** TPE via Optuna — 60–100 trials
### 2.2 My Assessment: **CONFIRMED with refinements**
The two-phase approach is the right call. Here's why, and what I'd adjust:
#### Why LHS → TPE is correct for this problem
| Factor | Implication | Algorithm Fit |
|--------|------------|---------------|
| 4 design variables (low-dim) | All methods work; sample efficiency less critical | Any |
| 1 integer variable | Need native mixed-type support | TPE ✓, CMA-ES ≈ (rounding) |
| Infeasible baseline | Must map feasibility BEFORE optimizing | LHS first ✓ |
| Expected significant interactions (DV1×DV2, DV3×DV4) | Need space-filling to detect interactions | LHS ✓ |
| Potentially narrow feasible region | Risk of missing it with random search | LHS gives systematic coverage ✓ |
| NX-in-the-loop (medium cost) | ~100-200 trials is budget-appropriate | TPE efficient enough ✓ |
#### What I'd modify
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
- Purpose: Landscape mapping, feasibility identification, sensitivity analysis
Phase 2: TPE Optimization
- Trials: 60-100 (adaptive, see convergence criteria)
- Sampler: Optuna TPEsampler
- n_startup_trials: 0 (warm-started from Phase 1 best)
- Constraint handling: Optuna constraint interface with Deb's rules
- Purpose: Converge to minimum-mass feasible design
Total budget: 111-151 evaluations
```
---
## 3. Constraint Handling
### 3.1 The Challenge
The baseline FAILS the displacement constraint by 120% (22 mm vs 10 mm). This means:
- A significant portion of the design space may be infeasible
- Random sampling may return few or zero feasible points
- The optimizer must navigate toward feasibility AND optimality simultaneously
### 3.2 Approach: Deb's Feasibility Rules (Constraint Domination)
For ranking solutions during optimization, use **Deb's feasibility rules** (Deb 2000):
1. **Feasible vs feasible** → compare by objective (lower mass wins)
2. **Feasible vs infeasible** → feasible always wins
3. **Infeasible vs infeasible** → lower total constraint violation wins
This is implemented via Optuna's constraint interface:
```python
def constraints(trial):
"""Return constraint violations (negative = feasible, positive = infeasible)."""
disp = trial.user_attrs["tip_displacement"]
stress = trial.user_attrs["max_von_mises"]
return [
disp - 10.0, # ≤ 0 means displacement ≤ 10 mm
stress - 130.0, # ≤ 0 means stress ≤ 130 MPa
]
```
### 3.3 Why NOT Penalty Functions
| Method | Pros | Cons | Verdict |
|--------|------|------|---------|
| **Deb's rules** (selected) | No tuning params; feasible always beats infeasible; explores infeasible region for learning | Requires custom Optuna integration | ✅ Best for this case |
| **Quadratic penalty** | Simple to implement | Penalty weight requires tuning; wrong weight → optimizer ignores constraint OR over-penalizes | ❌ Fragile |
| **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.
---
## 4. Search Space Analysis
### 4.1 Bound Reasonableness
| Variable | Range | Span | Concern |
|----------|-------|------|---------|
| DV1: half_core_thickness | 10–40 mm | 4× range | Reasonable. Lower bound = thin core, upper = thick. Stiffness-mass trade-off |
| DV2: face_thickness | 10–40 mm | 4× range | Reasonable. 10 mm face is already substantial for steel |
| DV3: holes_diameter | 150–450 mm | 3× range | ⚠️ **Needs geometric check** — see §4.2 |
| DV4: hole_count | 5–15 | 3× range | ⚠️ **Needs geometric check** — see §4.2 |
### 4.2 Geometric Feasibility: Hole Overlap Analysis
**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.
---
## 5. Trial Budget & Compute Estimate
### 5.1 Budget Breakdown
| Phase | Trials | Purpose |
|-------|--------|---------|
| **Trial 0** | 1 | Baseline validation (enqueued) |
| **Phase 1: LHS DoE** | 50 | Landscape mapping, feasibility, sensitivity |
| **Phase 2: TPE** | 60–100 | Directed optimization |
| **Validation** | 3–5 | Confirm optimum, check mesh sensitivity |
| **Total** | **114–156** | |
### 5.2 Compute Time Estimate
| Parameter | Estimate | Notes |
|-----------|----------|-------|
| DOF count | 10K–100K | Steel beam, SOL 101 |
| Single solve time | 30s–3min | Depends on mesh density |
| Model rebuild time | 10–30s | NX parametric update + remesh |
| Total per trial | 1–4 min | Rebuild + solve + extraction |
| Phase 1 (51 trials) | 1–3.5 hrs | |
| Phase 2 (60–100 trials) | 1–7 hrs | |
| **Total compute** | **2–10 hrs** | Likely ~4–5 hrs |
### 5.3 Budget Justification
For 4 design variables, rule-of-thumb budgets:
- **Minimum viable:** 10 × n_vars = 40 trials (DoE only)
- **Standard:** 25 × n_vars = 100 trials (DoE + optimization)
- **Thorough:** 50 × n_vars = 200 trials (with validation)
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) |
| NX solve success rate > 80% | If <80%: investigate failures, fix model, re-run failed trials |
| 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 |
| `algorithm.phase2.type` | `TPE` | Native mixed-integer, sample-efficient, LAC-proven |
| `hole_count.type` | `integer` | DEC-HB-003: true integer, no rounding |
| `constraint_handling` | `deb_feasibility_rules` | Best for infeasible baseline |
| `baseline_trial` | `enqueued` | LAC lesson: always validate baseline first |
| `penalty_config.method` | `deb_rules` | No penalty weight tuning needed |
### 8.2 Extractor Requirements
| ID | Type | Output | Source | Notes |
|----|------|--------|--------|-------|
| `ext_001` | `expression` | `mass` | NX expression `p173` | Direct read from NX |
| `ext_002` | `displacement` | `tip_displacement` | SOL 101 result sensor or .op2 parse | ⚠️ Need sensor setup or node ID |
| `ext_003` | `stress` | `max_von_mises` | SOL 101 elemental nodal | kPa → MPa conversion needed |
### 8.3 Open Items for Spec Finalization
Before this spec can be promoted from `_draft` to production:
1. **Beam web length** — Required to validate DV3 × DV4 geometric feasibility
2. **Displacement extraction method** — Sensor in .sim, or node ID for .op2 parsing?
3. **Stress extraction scope** — Whole model max, or specific element group?
4. **NX expression names confirmed** — Verify `p173` is mass, confirm displacement/stress expression names
5. **Solver runtime benchmark** — Time one SOL 101 run to refine compute estimates
6. **Corner test results** — Validate model rebuilds at all 16 bound corners
---
## 9. Execution Plan Summary
```
┌─────────────────────────────────────────────────────────────────┐
│ HYDROTECH BEAM OPTIMIZATION │
│ Study: 01_doe_landscape │
├─────────────────────────────────────────────────────────────────┤
│ │
│ PRE-FLIGHT (before any trials) │
│ ├── Validate baseline: run Trial 0, verify mass/disp/stress │
│ ├── Corner tests: 16 extreme combinations, check NX rebuilds │
│ ├── Mesh convergence: 3 density levels at baseline │
│ └── Confirm extractors: mass, displacement, stress pipelines │
│ │
│ PHASE 1: DoE LANDSCAPE (51 trials) │
│ ├── Trial 0: Baseline (enqueued) │
│ ├── Trials 1-50: LHS with integer rounding for hole_count │
│ ├── Analysis: sensitivity, interaction, feasibility mapping │
│ └── GATE: ≥5 feasible? NX success >80%? Proceed/escalate │
│ │
│ PHASE 2: TPE OPTIMIZATION (60-100 trials) │
│ ├── Warm-start from best Phase 1 feasible point(s) │
│ ├── Deb's feasibility rules for constraint handling │
│ ├── Convergence check every 20 trials │
│ └── Hard stop at 100 trials │
│ │
│ VALIDATION (3-5 trials) │
│ ├── Re-run best design to confirm repeatability │
│ ├── Perturb ±5% on each variable to check sensitivity │
│ └── Document final design with full NX results │
│ │
│ TOTAL: 114-156 NX evaluations | ~4-5 hours compute │
│ │
└─────────────────────────────────────────────────────────────────┘
```
---
## 10. LAC Lessons Incorporated
| LAC Lesson | Source | How Applied |
|------------|--------|-------------|
| CMA-ES doesn't evaluate x0 first | Mirror V7 failure | Baseline enqueued as Trial 0 for both phases |
| Surrogate + L-BFGS = fake optima | Mirror V5 failure | No surrogates in this study; direct FEA only |
| Never kill NX processes directly | Dec 2025 incident | Timeout-based error handling; NXSessionManager only |
| Copy working studies, never rewrite | Mirror V5 failure | Phase 2 created by copying Phase 1 |
| pyNastran stress in kPa | Support arm success | Extractor divides by 1000 for MPa |
| CAD constraints can limit bounds | Mirror V13 (rib_thickness) | Pre-flight corner tests before DoE |
| Always include README.md | Repeated failures (Dec 2025, Jan 2026) | README.md created with study |
| Simple beats complex (TPE > surrogate) | Mirror V6 vs V5 | TPE selected over surrogate-based methods |
---
*⚡ Optimizer — The algorithm is the strategy.*

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# Study: 01_doe_landscape — Hydrotech Beam
> See [../../README.md](../../README.md) for project overview.
## Purpose
Map the design space of the Hydrotech sandwich I-beam to identify feasible regions, characterize variable sensitivities, and converge on a minimum-mass design that satisfies displacement and stress constraints.
## Quick Facts
| Item | Value |
|------|-------|
| **Objective** | Minimize mass (kg) |
| **Constraints** | Tip displacement ≤ 10 mm, Von Mises stress ≤ 130 MPa |
| **Design variables** | 4 (3 continuous + 1 integer) |
| **Algorithm** | Phase 1: LHS DoE (50 trials) → Phase 2: TPE (60-100 trials) |
| **Total budget** | 114–156 NX evaluations |
| **Estimated compute** | ~4–5 hours |
| **Status** | DRAFT — Awaiting pre-flight checks and review |
## Design Variables
| ID | Name | Range | Type | Baseline |
|----|------|-------|------|----------|
| DV1 | `beam_half_core_thickness` | 10–40 mm | Continuous | 20 mm |
| DV2 | `beam_face_thickness` | 10–40 mm | Continuous | 20 mm |
| DV3 | `holes_diameter` | 150–450 mm | Continuous | 300 mm |
| DV4 | `hole_count` | 5–15 | Integer | 10 |
## Baseline Performance
| Metric | Value | Constraint | Status |
|--------|-------|------------|--------|
| Mass | ~974 kg | minimize | Overbuilt |
| Tip displacement | ~22 mm | ≤ 10 mm | ❌ FAILS |
| VM stress | unknown | ≤ 130 MPa | ⚠️ TBD |
## Key Decisions
- **Single-objective** formulation (DEC-HB-001)
- **Two-phase** algorithm: LHS → TPE (DEC-HB-002)
- **True integer** handling for hole_count (DEC-HB-003)
- **Deb's feasibility rules** for constraint handling (infeasible baseline)
- **Baseline enqueued** as Trial 0 (LAC lesson)
## Files
| File | Description |
|------|-------------|
| `OPTIMIZATION_STRATEGY.md` | Full strategy document (problem formulation, algorithm selection, risk mitigation) |
| `atomizer_spec_draft.json` | AtomizerSpec configuration skeleton (DRAFT — open items must be resolved) |
| `README.md` | This file |
## Open Items Before Execution
1. Beam web length needed (geometric feasibility of hole patterns)
2. Displacement extraction method (sensor vs .op2 node parsing)
3. Stress extraction scope (whole model vs element group)
4. Baseline stress measurement
5. SOL 101 runtime benchmark
6. Corner test validation (16 bound combinations)
## References
- [BREAKDOWN.md](../../BREAKDOWN.md) — Tech Lead's technical analysis
- [DECISIONS.md](../../DECISIONS.md) — Decision log
- [CONTEXT.md](../../CONTEXT.md) — Project context
---
*Created by ⚡ Optimizer Agent | 2026-02-09*

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{
"meta": {
"version": "2.0",
"created": "2026-02-09T12:00:00Z",
"modified": "2026-02-09T12:00:00Z",
"created_by": "optimizer-agent",
"modified_by": "optimizer-agent",
"study_name": "01_doe_landscape",
"description": "Hydrotech Beam — DoE landscape mapping + TPE optimization. Minimize mass subject to displacement and stress constraints.",
"tags": ["hydrotech-beam", "doe", "landscape", "tpe", "single-objective"]
},
"model": {
"sim": {
"path": "models/Beam_sim1.sim",
"solver": "nastran"
},
"part": "models/Beam.prt",
"fem": "models/Beam_fem1.fem",
"idealized": "models/Beam_fem1_i.prt"
},
"design_variables": [
{
"id": "dv_001",
"name": "beam_half_core_thickness",
"expression_name": "beam_half_core_thickness",
"type": "continuous",
"bounds": {
"min": 10,
"max": 40
},
"baseline": 20,
"units": "mm",
"enabled": true,
"description": "Core half-thickness. Stiffness scales ~quadratically via sandwich effect (lever arm). Also adds core mass linearly."
},
{
"id": "dv_002",
"name": "beam_face_thickness",
"expression_name": "beam_face_thickness",
"type": "continuous",
"bounds": {
"min": 10,
"max": 40
},
"baseline": 20,
"units": "mm",
"enabled": true,
"description": "Face sheet thickness. Primary bending stiffness contributor AND primary mass contributor. Key trade-off variable."
},
{
"id": "dv_003",
"name": "holes_diameter",
"expression_name": "holes_diameter",
"type": "continuous",
"bounds": {
"min": 150,
"max": 450
},
"baseline": 300,
"units": "mm",
"enabled": true,
"description": "Lightening hole diameter. Mass reduction scales with d². Stress concentration scales with hole size. Geometric feasibility depends on beam web length."
},
{
"id": "dv_004",
"name": "hole_count",
"expression_name": "hole_count",
"type": "integer",
"bounds": {
"min": 5,
"max": 15
},
"baseline": 10,
"units": "",
"enabled": true,
"description": "Number of lightening holes in the web. Integer variable (11 levels). Interacts strongly with holes_diameter for geometric feasibility."
}
],
"extractors": [
{
"id": "ext_001",
"name": "Mass Extractor",
"type": "expression",
"config": {
"expression_name": "p173",
"description": "Total beam mass from NX expression"
},
"outputs": [
{
"name": "mass",
"metric": "total",
"units": "kg"
}
]
},
{
"id": "ext_002",
"name": "Displacement Extractor",
"type": "displacement",
"config": {
"method": "result_sensor_or_op2",
"component": "magnitude",
"location": "beam_tip",
"description": "Tip displacement magnitude from SOL 101. Preferred: NX result sensor. Fallback: parse .op2 at tip node ID.",
"TODO": "Confirm displacement sensor exists in Beam_sim1.sim OR identify tip node ID"
},
"outputs": [
{
"name": "tip_displacement",
"metric": "max_magnitude",
"units": "mm"
}
]
},
{
"id": "ext_003",
"name": "Stress Extractor",
"type": "stress",
"config": {
"method": "op2_elemental_nodal",
"stress_type": "von_mises",
"scope": "all_elements",
"unit_conversion": "kPa_to_MPa",
"description": "Max von Mises stress (elemental nodal) from SOL 101. pyNastran returns kPa for NX kg-mm-s units — divide by 1000 for MPa.",
"TODO": "Verify element types in model (CQUAD4? CTETRA? CHEXA?) and confirm stress scope"
},
"outputs": [
{
"name": "max_von_mises",
"metric": "max",
"units": "MPa"
}
]
}
],
"objectives": [
{
"id": "obj_001",
"name": "Minimize beam mass",
"direction": "minimize",
"weight": 1.0,
"source": {
"extractor_id": "ext_001",
"output_name": "mass"
},
"units": "kg"
}
],
"constraints": [
{
"id": "con_001",
"name": "Tip displacement limit",
"type": "hard",
"operator": "<=",
"threshold": 10.0,
"source": {
"extractor_id": "ext_002",
"output_name": "tip_displacement"
},
"penalty_config": {
"method": "deb_rules",
"description": "Deb's feasibility rules: feasible always beats infeasible; among infeasible, lower violation wins"
},
"margin_buffer": {
"optimizer_target": 9.5,
"hard_limit": 10.0,
"description": "5% inner margin during optimization to account for numerical noise"
}
},
{
"id": "con_002",
"name": "Von Mises stress limit",
"type": "hard",
"operator": "<=",
"threshold": 130.0,
"source": {
"extractor_id": "ext_003",
"output_name": "max_von_mises"
},
"penalty_config": {
"method": "deb_rules",
"description": "Deb's feasibility rules: feasible always beats infeasible; among infeasible, lower violation wins"
},
"margin_buffer": {
"optimizer_target": 123.5,
"hard_limit": 130.0,
"description": "5% inner margin during optimization to account for mesh sensitivity"
}
}
],
"optimization": {
"phases": [
{
"id": "phase_1",
"name": "DoE Landscape Mapping",
"algorithm": {
"type": "LHS",
"config": {
"criterion": "maximin",
"integer_handling": "round_nearest_stratified",
"seed": 42
}
},
"budget": {
"max_trials": 50,
"baseline_enqueued": true,
"total_with_baseline": 51
},
"purpose": "Map design space, identify feasible region, assess sensitivities and interactions"
},
{
"id": "phase_2",
"name": "TPE Optimization",
"algorithm": {
"type": "TPE",
"config": {
"sampler": "TPESampler",
"n_startup_trials": 0,
"warm_start_from": "phase_1_best_feasible",
"seed": 42,
"constraint_handling": "deb_feasibility_rules"
}
},
"budget": {
"min_trials": 60,
"max_trials": 100,
"adaptive": true
},
"convergence": {
"stall_window": 20,
"stall_threshold_pct": 1.0,
"min_trials_before_check": 60
},
"purpose": "Directed optimization to converge on minimum-mass feasible design"
}
],
"total_budget": {
"min": 114,
"max": 156,
"estimated_hours": "4-5"
},
"baseline_trial": {
"enqueue": true,
"values": {
"beam_half_core_thickness": 20,
"beam_face_thickness": 20,
"holes_diameter": 300,
"hole_count": 10
},
"expected_results": {
"mass_kg": 974,
"tip_displacement_mm": 22,
"max_von_mises_mpa": "UNKNOWN — must measure"
}
}
},
"error_handling": {
"trial_timeout_seconds": 600,
"on_nx_rebuild_failure": "record_infeasible_max_violation",
"on_solver_failure": "record_infeasible_max_violation",
"on_extraction_failure": "record_infeasible_max_violation",
"max_consecutive_failures": 5,
"max_failure_rate_pct": 30,
"nx_process_management": "NEVER kill NX directly. Use NXSessionManager.close_nx_if_allowed() only."
},
"pre_flight_checks": [
{
"id": "pf_001",
"name": "Baseline validation",
"description": "Run Trial 0 with baseline parameters, verify mass ≈ 974 kg and displacement ≈ 22 mm"
},
{
"id": "pf_002",
"name": "Corner tests",
"description": "Test 16 corner combinations (min/max for each DV). Verify NX rebuilds and solves at all corners."
},
{
"id": "pf_003",
"name": "Mesh convergence",
"description": "Run baseline at 3 mesh densities. Verify stress convergence within 10%."
},
{
"id": "pf_004",
"name": "Extractor validation",
"description": "Confirm mass, displacement, and stress extractors return correct values at baseline."
},
{
"id": "pf_005",
"name": "Geometric feasibility",
"description": "Determine beam web length. Verify max(hole_count) × max(holes_diameter) fits. Add ligament constraint if needed."
}
],
"open_items": [
"Beam web length needed for geometric feasibility validation (holes_diameter × hole_count vs available length)",
"Displacement extraction method: result sensor in .sim or .op2 node ID parsing?",
"Stress extraction scope: whole model or specific element group?",
"Verify NX expression name 'p173' maps to mass",
"Benchmark single SOL 101 runtime to refine compute estimates",
"Confirm baseline stress value (currently unknown)",
"Clarify relationship between core/face thickness DVs and web height where holes are placed"
]
}