Transformer Warmstart Unit Commitment

---
name: transformer-warmstart-unit-commitment
description: "Multi-Stage Warm-Start Deep Learning Framework for Unit Commitment. Transformer-based architecture for predicting generator commitment schedules with deterministic post-processing for physical feasibility, warm-start strategy for MILP solver, and confidence-based variable fixation. Use for power grid optimization, unit commitment problems, and MILP warm-starting with machine learning."
---

# Transformer Warm-Start Framework for Unit Commitment

Methodology for accelerating Unit Commitment (UC) optimization using transformer-based deep learning with MILP warm-starting, based on arXiv:2604.21891.

## Problem Context

### Unit Commitment (UC) Problem

**Objective**: Schedule generator on/off states to meet electricity demand at minimum cost.

**Mathematical Formulation**:
```
Minimize: Σ_t Σ_g (C_g^on u_g(t) + C_g^var p_g(t))

Subject to:
  Power balance: Σ_g p_g(t) = D(t) ∀t
  Generator limits: u_g(t) P_g^min ≤ p_g(t) ≤ u_g(t) P_g^max ∀g,t
  Ramp limits: |p_g(t) - p_g(t-1)| ≤ R_g ∀g,t
  Min up/down: u_g(t) satisfies min up/down time constraints
  Reserve requirements: Σ_g u_g(t) P_g^max ≥ D(t) + R(t) ∀t
```

**Complexity**: NP-hard, high-dimensional, tightly constrained.

### Challenges

- **Scale**: 72+ hour horizons, hundreds of generators
- **Renewables**: Variable wind/solar integration
- **Storage**: Long-duration energy storage coordination
- **Time limits**: Operators need solutions in minutes

## Proposed Solution: Multi-Stage Pipeline

### Architecture Overview

```
┌─────────────────┐    ┌──────────────────┐    ┌─────────────────┐    ┌─────────────┐
│  Transformer    │ →  │  Post-Processing │ →  │  Warm-Start     │ →  │  MILP       │
│  Predictor      │    │  (Feasibility)   │    │  + Fixation     │    │  Solver     │
└─────────────────┘    └──────────────────┘    └─────────────────┘    └─────────────┘
     (Stage 1)              (Stage 2)              (Stage 3)           (Stage 4)
```

## Stage 1: Transformer-Based Prediction

### Model Architecture

```python
class UCTransformer(nn.Module):
    """
    Transformer for generator commitment prediction
    
    Input: Demand forecast, renewable forecast, generator parameters
    Output: Binary commitment schedule u_g(t) ∈ {0,1}
    """
    
    def __init__(self, n_generators, horizon, d_model=256, n_heads=8):
        super().__init__()
        
        # Encoder: Process input features
        self.input_encoder = nn.Linear(input_dim, d_model)
        
        # Temporal attention across horizon
        self.temporal_attn = nn.TransformerEncoder(
            nn.TransformerEncoderLayer(d_model, n_heads),
            num_layers=6
        )
        
        # Generator-specific attention
        self.generator_attn = nn.MultiheadAttention(d_model, n_heads)
        
        # Decoder: Predict commitments
        self.commitment_head = nn.Sequential(
            nn.Linear(d_model, d_model // 2),
            nn.ReLU(),
            nn.Linear(d_model // 2, 1),
            nn.Sigmoid()  # Probability of commitment
        )
    
    def forward(self, demand, renewable, gen_params):
        # Encode inputs
        x = self.input_encoder(torch.cat([demand, renewable, gen_params], dim=-1))
        
        # Temporal attention
        x = self.temporal_attn(x)
        
        # Predict commitments
        probs = self.commitment_head(x)
        
        return probs  # Shape: (batch, n_generators, horizon)
```

### Training

```python
def train_uc_transformer(model, train_loader, epochs=100):
    """
    Train transformer on historical UC solutions
    
    Loss: Binary cross-entropy with optimal solutions as labels
    """
    optimizer = Adam(model.parameters(), lr=1e-4)
    
    for epoch in range(epochs):
        for batch in train_loader:
            demand, renewable, gen_params, optimal_commit = batch
            
            # Forward pass
            pred_probs = model(demand, renewable, gen_params)
            
            # Binary cross-entropy loss
            loss = F.binary_cross_entropy(pred_probs, optimal_commit)
            
            # Backward pass
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
```

## Stage 2: Deterministic Post-Processing

### Problem: Raw Predictions are Infeasible

ML predictions often violate:
- Minimum up/down times
- Physical constraints
- Reserve requirements

### Post-Processing Heuristics

```python
def post_process_commitments(raw_predictions, gen_params):
    """
    Enforce physical feasibility constraints
    
    Returns: Feasible commitment schedule
    """
    schedule = raw_predictions.clone()
    n_gen, horizon = schedule.shape
    
    # Enforce minimum up/down times
    for g in range(n_gen):
        min_up = gen_params[g]['min_up_time']
        min_down = gen_params[g]['min_down_time']
        
        schedule[g] = enforce_min_up_down(schedule[g], min_up, min_down)
    
    # Enforce power balance (greedy repair)
    for t in range(horizon):
        shortage = calculate_shortage(schedule[:, t], demand[t])
        if shortage > 0:
            # Commit additional generators
            schedule[:, t] = commit_additional(schedule[:, t], shortage)
    
    # Minimize excess capacity
    for t in range(horizon):
        excess = calculate_excess(schedule[:, t], demand[t])
        if excess > 0:
            # Decommit generators if possible
            schedule[:, t] = decommit_excess(schedule[:, t], excess)
    
    return schedule
```

### Minimum Up/Down Time Enforcement

```python
def enforce_min_up_down(commitment, min_up, min_down):
    """
    Ensure commitment satisfies minimum up/down constraints
    
    Algorithm:
    1. Identify violations
    2. Extend commitments forward (min_up) or backward (min_down)
    3. Resolve conflicts
    """
    result = commitment.copy()
    
    # Track state transitions
    transitions = np.diff(result, prepend=0, append=0)
    
    # Fix short up periods
    for i, t in enumerate(transitions):
        if t == 1:  # Startup
            # Check if runs long enough
            if i + min_up < len(result) and np.all(result[i:i+min_up] == 0):
                # Extend startup
                result[i:i+min_up] = 1
    
    # Fix short down periods (similar logic)
    
    return result
```

## Stage 3: Confidence-Based Variable Fixation

### Concept

Fix high-confidence predictions to reduce MILP search space.

```python
def confidence_based_fixation(predictions, confidence_threshold=0.9):
    """
    Fix variables with high prediction confidence
    
    Returns:
        fixed_vars: Dictionary of fixed variable values
        free_vars: Set of variables to be optimized
    """
    fixed_vars = {}
    free_vars = set()
    
    for g in range(n_generators):
        for t in range(horizon):
            confidence = max(prediction[g, t], 1 - prediction[g, t])
            
            if confidence > confidence_threshold:
                # Fix this variable
                fixed_vars[(g, t)] = round(prediction[g, t])
            else:
                # Keep variable free for optimization
                free_vars.add((g, t))
    
    return fixed_vars, free_vars
```

### Search Space Reduction

| Threshold | Variables Fixed | Search Space Reduction |
|-----------|-----------------|----------------------|
| 0.95 | ~80% | 10⁵× |
| 0.90 | ~70% | 10³× |
| 0.85 | ~60% | 10²× |

### Warm-Start Strategy

```python
def warm_start_milp(problem, fixed_vars, post_processed_schedule):
    """
    Initialize MILP solver with ML predictions
    
    1. Fix high-confidence variables
    2. Use post-processed schedule as initial solution
    3. Solve reduced MILP
    """
    # Create modified problem with fixed variables
    reduced_problem = fix_variables(problem, fixed_vars)
    
    # Set warm-start solution
    solver.set_initial_solution(post_processed_schedule)
    
    # Solve
    solution = solver.solve(reduced_problem)
    
    return solution
```

## Stage 4: MILP Solver Integration

### Complete Pipeline

```python
def uc_ml_warmstart_pipeline(demand, renewable, gen_params, model, solver):
    """
    Complete multi-stage UC pipeline
    
    Returns: Optimal commitment schedule
    """
    # Stage 1: Transformer prediction
    raw_predictions = model(demand, renewable, gen_params)
    
    # Stage 2: Post-processing for feasibility
    feasible_schedule = post_process_commitments(raw_predictions, gen_params)
    
    # Stage 3: Confidence-based fixation
    fixed_vars, free_vars = confidence_based_fixation(raw_predictions, threshold=0.9)
    
    # Stage 4: Warm-start MILP
    optimal_schedule = warm_start_milp(
        problem=build_uc_problem(demand, renewable, gen_params),
        fixed_vars=fixed_vars,
        post_processed_schedule=feasible_schedule
    )
    
    return optimal_schedule
```

## Performance Results

### Key Metrics

| Metric | Traditional MILP | ML Warm-Start | Improvement |
|--------|-----------------|---------------|-------------|
| Feasibility | 100% | 100% | - |
| Computation Time | 300s | 45s | 6.7× faster |
| Optimality Gap | 0% | <1% | Near-optimal |
| Cost (20% cases) | Baseline | -5% | Better solutions |

### Validation

- **Test System**: Single-bus system with 10-50 generators
- **Horizon**: 72 hours
- **Renewable Integration**: 30% penetration
- **Feasibility**: 100% guarantee via post-processing

## Implementation Considerations

### Data Requirements

```python
# Training data generation
# For each instance:
training_data = {
    'demand_forecast': [...],      # 72-hour demand
    'renewable_forecast': [...],   # Wind/solar forecast
    'generator_params': [...],     # Costs, limits, ramp rates
    'optimal_commitment': [...]    # From exact solver (label)
}
```

### Model Variants

1. **Single-Bus Model** (Current): Aggregated demand/supply
2. **Multi-Bus Model**: Network constraints, transmission limits
3. **Stochastic UC**: Scenario-based uncertainty
4. **Multi-Period**: Rolling horizon implementation

### Deployment

```python
class UCOptimizationService:
    """
    Production service for UC optimization
    """
    
    def __init__(self, model_path, solver_config):
        self.model = load_model(model_path)
        self.solver = configure_solver(solver_config)
    
    def optimize(self, demand_forecast, renewable_forecast, gen_params):
        """
        Real-time UC optimization
        
        Target: < 5 minutes for 72-hour horizon
        """
        start_time = time.time()
        
        # Run pipeline
        schedule = uc_ml_warmstart_pipeline(
            demand_forecast,
            renewable_forecast,
            gen_params,
            self.model,
            self.solver
        )
        
        elapsed = time.time() - start_time
        logger.info(f"UC solved in {elapsed:.1f}s")
        
        return schedule
```

## Extensions and Future Work

### Multi-Objective Optimization

```python
# Beyond cost minimization
objectives = {
    'cost': minimize_operating_cost(),
    'emissions': minimize_emissions(),
    'flexibility': maximize_ramping_capability()
}

# Pareto frontier exploration
solutions = multi_objective_uc(objectives, weights)
```

### Online Learning

```python
# Adapt model to new grid conditions
def online_update(model, new_data):
    """
    Fine-tune model with recent operational data
    """
    model.train(new_data, epochs=5, lr=1e-5)
```

## References

- **Paper**: arXiv:2604.21891 [eess.SY, cs.AI]
- **Authors**: Za'ter, Van Boven, Hodge, Baker
- **Date**: April 2026
- **Application**: Power system optimization, renewable integration

## Related Skills

- `power-systems-optimization`
- `milp-solving`
- `transformer-architectures`
- `warm-start-optimization`