# SYS_11: Multi-Objective Support

<!--
PROTOCOL: Multi-Objective Optimization Support
LAYER: System
VERSION: 1.0
STATUS: Active (MANDATORY)
LAST_UPDATED: 2025-12-05
PRIVILEGE: user
LOAD_WITH: []
-->

## Overview

**ALL** optimization engines in Atomizer **MUST** support both single-objective and multi-objective optimization without requiring code changes. This protocol ensures system robustness and prevents runtime failures when handling Pareto optimization.

**Key Requirement**: Code must work with both `study.best_trial` (single) and `study.best_trials` (multi) APIs.

---

## When to Use

| Trigger | Action |
|---------|--------|
| 2+ objectives defined in config | Use NSGA-II sampler |
| "pareto", "multi-objective" mentioned | Load this protocol |
| "tradeoff", "competing goals" | Suggest multi-objective approach |
| "minimize X AND maximize Y" | Configure as multi-objective |

---

## Quick Reference

**Single vs. Multi-Objective API**:

| Operation | Single-Objective | Multi-Objective |
|-----------|-----------------|-----------------|
| Best trial | `study.best_trial` | `study.best_trials[0]` |
| Best params | `study.best_params` | `trial.params` |
| Best value | `study.best_value` | `trial.values` (tuple) |
| Direction | `direction='minimize'` | `directions=['minimize', 'maximize']` |
| Sampler | TPE, CMA-ES, GP | NSGA-II (mandatory) |

---

## The Problem This Solves

Previously, optimization components only supported single-objective. When used with multi-objective studies:

1. Trials run successfully
2. Trials saved to database
3. **CRASH** when compiling results
   - `study.best_trial` raises RuntimeError
   - No tracking files generated
   - Silent failures

**Root Cause**: Optuna has different APIs:

```python
# Single-Objective (works)
study.best_trial    # Returns Trial object
study.best_params   # Returns dict
study.best_value    # Returns float

# Multi-Objective (RAISES RuntimeError)
study.best_trial    # ❌ RuntimeError
study.best_params   # ❌ RuntimeError
study.best_value    # ❌ RuntimeError
study.best_trials   # ✓ Returns LIST of Pareto-optimal trials
```

---

## Solution Pattern

### 1. Always Check Study Type

```python
is_multi_objective = len(study.directions) > 1
```

### 2. Use Conditional Access

```python
if is_multi_objective:
    best_trials = study.best_trials
    if best_trials:
        # Select representative trial (e.g., first Pareto solution)
        representative_trial = best_trials[0]
        best_params = representative_trial.params
        best_value = representative_trial.values  # Tuple
        best_trial_num = representative_trial.number
    else:
        best_params = {}
        best_value = None
        best_trial_num = None
else:
    # Single-objective: safe to use standard API
    best_params = study.best_params
    best_value = study.best_value
    best_trial_num = study.best_trial.number
```

### 3. Return Rich Metadata

Always include in results:

```python
{
    'best_params': best_params,
    'best_value': best_value,  # float or tuple
    'best_trial': best_trial_num,
    'is_multi_objective': is_multi_objective,
    'pareto_front_size': len(study.best_trials) if is_multi_objective else 1,
}
```

---

## Implementation Checklist

When creating or modifying any optimization component:

- [ ] **Study Creation**: Support `directions` parameter
  ```python
  if len(objectives) > 1:
      directions = [obj['type'] for obj in objectives]  # ['minimize', 'maximize']
      study = optuna.create_study(directions=directions, ...)
  else:
      study = optuna.create_study(direction='minimize', ...)
  ```

- [ ] **Result Compilation**: Check `len(study.directions) > 1`
- [ ] **Best Trial Access**: Use conditional logic
- [ ] **Logging**: Print Pareto front size for multi-objective
- [ ] **Reports**: Handle tuple objectives in visualization
- [ ] **Testing**: Test with BOTH single and multi-objective cases

---

## Configuration

**Multi-Objective Config Example**:

```json
{
  "objectives": [
    {
      "name": "stiffness",
      "type": "maximize",
      "description": "Structural stiffness (N/mm)",
      "unit": "N/mm"
    },
    {
      "name": "mass",
      "type": "minimize",
      "description": "Total mass (kg)",
      "unit": "kg"
    }
  ],
  "optimization_settings": {
    "sampler": "NSGAIISampler",
    "n_trials": 50
  }
}
```

**Objective Function Return Format**:

```python
# Single-objective: return float
def objective_single(trial):
    # ... compute ...
    return objective_value  # float

# Multi-objective: return tuple
def objective_multi(trial):
    # ... compute ...
    return (stiffness, mass)  # tuple of floats
```

---

## Semantic Directions

Use semantic direction values - no negative tricks:

```python
# ✅ CORRECT: Semantic directions
objectives = [
    {"name": "stiffness", "type": "maximize"},
    {"name": "mass", "type": "minimize"}
]
# Return: (stiffness, mass) - both positive values

# ❌ WRONG: Negative trick
def objective(trial):
    return (-stiffness, mass)  # Don't negate to fake maximize
```

Optuna handles directions correctly when you specify `directions=['maximize', 'minimize']`.

---

## Testing Protocol

Before marking any optimization component complete:

### Test 1: Single-Objective
```python
# Config with 1 objective
directions = None  # or ['minimize']
# Run optimization
# Verify: completes without errors
```

### Test 2: Multi-Objective
```python
# Config with 2+ objectives
directions = ['minimize', 'minimize']
# Run optimization
# Verify: completes without errors
# Verify: ALL tracking files generated
```

### Test 3: Verify Outputs
- `2_results/study.db` exists
- `2_results/intelligent_optimizer/` has tracking files
- `2_results/optimization_summary.json` exists
- No RuntimeError in logs

---

## NSGA-II Configuration

For multi-objective optimization, use NSGA-II:

```python
import optuna
from optuna.samplers import NSGAIISampler

sampler = NSGAIISampler(
    population_size=50,      # Pareto front population
    mutation_prob=None,      # Auto-computed
    crossover_prob=0.9,      # Recombination rate
    swapping_prob=0.5,       # Gene swapping probability
    seed=42                  # Reproducibility
)

study = optuna.create_study(
    directions=['maximize', 'minimize'],
    sampler=sampler,
    study_name="multi_objective_study",
    storage="sqlite:///study.db"
)
```

---

## Pareto Front Handling

### Accessing Pareto Solutions

```python
if is_multi_objective:
    pareto_trials = study.best_trials
    print(f"Found {len(pareto_trials)} Pareto-optimal solutions")

    for trial in pareto_trials:
        print(f"Trial {trial.number}: {trial.values}")
        print(f"  Params: {trial.params}")
```

### Selecting Representative Solution

```python
# Option 1: First Pareto solution
representative = study.best_trials[0]

# Option 2: Weighted selection
def weighted_selection(trials, weights):
    best_score = float('inf')
    best_trial = None
    for trial in trials:
        score = sum(w * v for w, v in zip(weights, trial.values))
        if score < best_score:
            best_score = score
            best_trial = trial
    return best_trial

# Option 3: Knee point (maximum distance from ideal line)
# Requires more complex computation
```

---

## Troubleshooting

| Symptom | Cause | Solution |
|---------|-------|----------|
| RuntimeError on `best_trial` | Multi-objective study using single API | Use conditional check pattern |
| Empty Pareto front | No feasible solutions | Check constraints, relax if needed |
| Only 1 Pareto solution | Objectives not conflicting | Verify objectives are truly competing |
| NSGA-II with single objective | Wrong config | Use TPE/CMA-ES for single-objective |

---

## Cross-References

- **Depends On**: None (mandatory for all)
- **Used By**: All optimization components
- **Integrates With**:
  - [SYS_10_IMSO](./SYS_10_IMSO.md) (selects NSGA-II for multi-objective)
  - [SYS_13_DASHBOARD_TRACKING](./SYS_13_DASHBOARD_TRACKING.md) (Pareto visualization)
- **See Also**: [OP_04_ANALYZE_RESULTS](../operations/OP_04_ANALYZE_RESULTS.md) for Pareto analysis

---

## Implementation Files

Files that implement this protocol:
- `optimization_engine/intelligent_optimizer.py` - `_compile_results()` method
- `optimization_engine/study_continuation.py` - Result handling
- `optimization_engine/hybrid_study_creator.py` - Study creation

Files requiring this protocol:
- [ ] `optimization_engine/study_continuation.py`
- [ ] `optimization_engine/hybrid_study_creator.py`
- [ ] `optimization_engine/intelligent_setup.py`
- [ ] `optimization_engine/llm_optimization_runner.py`

---

## Version History

| Version | Date | Changes |
|---------|------|---------|
| 1.0 | 2025-11-20 | Initial release, mandatory for all engines |