Atomizer/studies/simple_beam_optimization/OPTIMIZATION_RESULTS_50TRIALS.md

Simple Beam Optimization - 50 Trials Results

Date: 2025-11-17 Study: simple_beam_optimization Substudy: full_optimization_50trials Total Runtime: ~21 minutes

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Executive Summary

The 50-trial optimization successfully explored the 4D design space but did not find a feasible design that meets the displacement constraint (< 10mm). The best design achieved 11.399 mm displacement, which is 14% over the limit.

Key Findings

• Total Trials: 50
• Feasible Designs: 0 (0%)
• Best Design: Trial 43
  • Displacement: 11.399 mm (1.399 mm over limit)
  • Stress: 70.263 MPa
  • Mass: 1987.556 kg
  • Objective: 702.717

Design Variables (Best Trial 43)

beam_half_core_thickness: 39.836 mm  (upper bound: 40 mm) ✓
beam_face_thickness:      39.976 mm  (upper bound: 40 mm) ✓
holes_diameter:           235.738 mm (mid-range)
hole_count:               11         (mid-range)

Observation: The optimizer pushed beam thickness to the maximum allowed values, suggesting that the constraint might not be achievable within the current design variable bounds.

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Detailed Analysis

Performance Statistics

Metric	Minimum	Maximum	Range
Displacement (mm)	11.399	37.075	25.676
Stress (MPa)	70.263	418.652	348.389
Mass (kg)	645.90	1987.56	1341.66

Constraint Violation Analysis

• Minimum Violation: 1.399 mm (Trial 43) - Closest to meeting constraint
• Maximum Violation: 27.075 mm (Trial 1)
• Average Violation: 5.135 mm across all 50 trials

Top 5 Trials (Closest to Feasibility)

Trial	Displacement (mm)	Violation (mm)	Stress (MPa)	Mass (kg)	Objective
43	11.399	1.399	70.263	1987.56	842.59
49	11.578	1.578	73.339	1974.84	857.25
42	11.614	1.614	71.674	1951.52	852.44
47	11.643	1.643	73.596	1966.00	860.82
32	11.682	1.682	71.887	1930.16	852.06

Pattern: All top designs cluster around 11.4-11.7 mm displacement with masses near 2000 kg, suggesting this is the practical limit for the current design space.

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Physical Interpretation

Why No Feasible Design Was Found

1. Beam Thickness Maxed Out: Both beam_half_core_thickness (39.836mm) and beam_face_thickness (39.976mm) are at or very near the upper bound (40mm), indicating that thicker beams are needed to meet the constraint.

2. Moderate Hole Configuration: hole_count=11 and holes_diameter=235.738mm suggest a balance between:

   • Weight reduction (more/larger holes)
   • Stiffness maintenance (fewer/smaller holes)

3. Trade-off Tension: The multi-objective formulation (minimize displacement, stress, AND mass) creates competing goals:

   • Reducing displacement requires thicker beams → increases mass
   • Reducing mass requires thinner beams → increases displacement

Engineering Insights

The best design (Trial 43) achieved:

• Low stress: 70.263 MPa (well within typical aluminum limits ~200-300 MPa)
• High stiffness: Displacement only 14% over limit
• Heavy: 1987.56 kg (high mass due to thick beams)

This suggests the design is structurally sound but overweight for the displacement target.

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Recommendations

Option 1: Relax Displacement Constraint (Quick Win)

Change displacement limit from 10mm to 12.5mm (10% margin above best achieved).

Why: Trial 43 is very close (11.399mm). A slightly relaxed constraint would immediately yield 5+ feasible designs.

Implementation:

// In beam_optimization_config.json
"constraints": [
  {
    "name": "displacement_limit",
    "type": "less_than",
    "value": 12.5,  // Changed from 10.0
    "units": "mm"
  }
]

Expected Outcome: Feasible designs with good mass/stiffness trade-off.

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Option 2: Expand Design Variable Ranges (Engineering Solution)

Allow thicker beams to meet the original constraint.

Why: The optimizer is already at the upper bounds, indicating it needs more thickness to achieve <10mm displacement.

Implementation:

// In beam_optimization_config.json
"design_variables": {
  "beam_half_core_thickness": {
    "min": 10.0,
    "max": 60.0,  // Increased from 40.0
    ...
  },
  "beam_face_thickness": {
    "min": 10.0,
    "max": 60.0,  // Increased from 40.0
    ...
  }
}

Trade-off: Heavier beams (mass will increase significantly).

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Option 3: Adjust Objective Weights (Prioritize Stiffness)

Give more weight to displacement reduction.

Current Weights:

• minimize_displacement: 33%
• minimize_stress: 33%
• minimize_mass: 34%

Recommended Weights:

"objectives": [
  {
    "name": "minimize_displacement",
    "weight": 0.50,  // Increased from 0.33
    ...
  },
  {
    "name": "minimize_stress",
    "weight": 0.25,  // Decreased from 0.33
    ...
  },
  {
    "name": "minimize_mass",
    "weight": 0.25   // Decreased from 0.34
    ...
  }
]

Expected Outcome: Optimizer will prioritize meeting displacement constraint even at the cost of higher mass.

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Option 4: Run Refined Optimization in Promising Region

Focus search around the best trial's design space.

Strategy:

1. Use Trial 43 design as baseline

2. Narrow variable ranges around these values:

   • beam_half_core_thickness: 35-40 mm (Trial 43: 39.836)
   • beam_face_thickness: 35-40 mm (Trial 43: 39.976)
   • holes_diameter: 200-270 mm (Trial 43: 235.738)
   • hole_count: 9-13 (Trial 43: 11)

3. Run 30-50 additional trials with tighter bounds

Why: TPE sampler may find feasible designs by exploiting local gradients near Trial 43.

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Option 5: Multi-Stage Optimization (Advanced)

Stage 1: Focus solely on meeting displacement constraint

• Objective: minimize displacement only
• Constraint: displacement < 10mm
• Run 20 trials

Stage 2: Optimize mass while maintaining feasibility

• Use Stage 1 best design as starting point
• Objective: minimize mass
• Constraint: displacement < 10mm
• Run 30 trials

Why: Decoupling objectives can help find feasible designs first, then optimize them.

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Validation of 4D Expression Updates

All 50 trials successfully updated all 4 design variables using the new .exp import system:

• ✅ beam_half_core_thickness: Updated correctly in all trials
• ✅ beam_face_thickness: Updated correctly in all trials
• ✅ holes_diameter: Updated correctly in all trials
• ✅ hole_count: Updated correctly in all trials (previously failing!)

Verification: Mesh element counts varied across trials (e.g., Trial 43: 5665 nodes), confirming that hole_count changes are affecting geometry.

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Next Steps

Immediate Actions

1. Choose a strategy from the 5 options above based on project priorities:

   • Need quick results? → Option 1 (relax constraint)
   • Engineering rigor? → Option 2 (expand bounds)
   • Balanced approach? → Option 3 (adjust weights)

2. Update configuration accordingly

3. Run refined optimization (30-50 trials should suffice)

Long-Term Enhancements

1. Pareto Front Analysis: Since this is multi-objective, generate Pareto front to visualize displacement-mass-stress trade-offs

2. Sensitivity Analysis: Identify which design variables have the most impact on displacement

3. Constraint Reformulation: Instead of hard constraint, use soft penalty with higher weight

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Conclusion

The 50-trial optimization was successful from a technical standpoint:

• All 4 design variables updated correctly (validation of .exp import system)
• Optimization converged to a consistent region (11.4-11.7mm displacement)
• Multiple trials explored the full design space

However, the displacement constraint appears infeasible with the current design variable bounds. The optimizer is telling us: "To meet <10mm displacement, I need thicker beams than you're allowing me to use."

Recommended Action: Start with Option 1 (relax constraint to 12.5mm) to validate the workflow, then decide if achieving <10mm is worth the mass penalty of thicker beams (Options 2-5).

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Files

• Configuration: beam_optimization_config.json
• Best Trial: substudies/full_optimization_50trials/best_trial.json
• Full Log: ../../beam_optimization_50trials.log
• Analysis Script: ../../analyze_beam_results.py
• Summary Data: ../../beam_optimization_summary.json

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Generated: 2025-11-17 Analyst: Claude Code Atomizer Version: Phase 3.2 (NX Expression Import System)