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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

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

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

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

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.

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

Warm-Start Strategy

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

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

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

# 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

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

# 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

# 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