warmstart-dl-unit-commitment

name	warmstart-dl-unit-commitment
description	Multi-Stage Warm-Start (MSWS) deep learning framework for Unit Commitment optimization. Combines neural network warm-starting with MILP constraints to accelerate power grid scheduling. Use for unit commitment, power system optimization, energy scheduling, and MILP warm-starting.

Multi-Stage Warm-Start Deep Learning Framework for Unit Commitment

This skill provides the Multi-Stage Warm-Start (MSWS) framework for Unit Commitment (UC) optimization, based on the paper "A Multi-Stage Warm-Start Deep Learning Framework for Unit Commitment" (arXiv:2604.21891).

Overview

Unit Commitment (UC) is a high-dimensional, large-scale Mixed-Integer Linear Programming (MILP) problem critical for power grid operations. MSWS progressively refines UC solutions through multiple stages using deep neural networks.

Problem Formulation

Unit Commitment Problem

Objective: Minimize total generation cost while meeting demand

$$ \min \sum_{t=1}^{T} \sum_{i=1}^{N} \left[ C_i(P_{i,t}) + S_i u_{i,t} \right] $$

Variables:

• $P_{i,t}$: Power output of generator $i$ at time $t$ (continuous)
• $u_{i,t} \in {0,1}$: Commitment status (binary)
• $v_{i,t} \in {0,1}$: Start-up indicator (binary)

Constraints:

• Power balance: $\sum_i P_{i,t} = D_t$ (demand)
• Generation limits: $P_{i}^{min} \leq P_{i,t} \leq P_{i}^{max}$
• Ramp rates: $|P_{i,t} - P_{i,t-1}| \leq R_i$
• Minimum up/down times: $u_{i,t}$ consecutive constraints

MSWS Framework Architecture

Stage 1: Load Forecasting

• Input: Historical load patterns, weather, economic indicators
• Output: 24-hour ahead demand prediction $D_{1:T}$
• Model: Temporal Fusion Transformer or LSTM

Stage 2: Binary Variable Prediction

• Input: Load forecast, generator parameters, market prices
• Output: Binary commitment decisions $\hat{u}_{i,t} \in [0,1]$
• Model: Multi-task neural network with constraint-aware loss

Stage 3: Continuous Variable Refinement

• Input: Binary predictions, relaxed UC
• Output: Power outputs $\hat{P}_{i,t}$
• Model: Graph Neural Network capturing grid topology

Stage 4: Feasibility Restoration

• Input: Continuous predictions
• Output: Feasible UC solution via constraint propagation
• Method: Projection onto feasible space

Core Innovation

Constraint-Aware Training

Standard loss function:

loss = MSE(predictions, ground_truth)

MSWS constraint-aware loss:

loss = MSE(predictions, ground_truth) 
     + λ₁ * power_balance_violation 
     + λ₂ * ramp_constraint_violation
     + λ₃ * min_updown_violation

Multi-Stage Refinement

Stage 1: Load Prediction
    ↓
Stage 2: Binary Decision (u) - 95% feasibility
    ↓
Stage 3: Power Output (P) - Economic dispatch
    ↓
Stage 4: Feasibility Fix - 100% feasibility
    ↓
MILP Warm-Start - 60% faster solve

Implementation

Neural Network Architecture

import torch
import torch.nn as nn

class UCWarmStartNetwork(nn.Module):
    def __init__(self, n_generators, n_timesteps):
        super().__init__()
        
        # Encoder
        self.encoder = nn.Sequential(
            nn.Linear(n_timesteps * features, 256),
            nn.ReLU(),
            nn.Dropout(0.2),
            nn.Linear(256, 128),
            nn.ReLU()
        )
        
        # Binary prediction head (with sigmoid)
        self.binary_head = nn.Sequential(
            nn.Linear(128, n_generators * n_timesteps),
            nn.Sigmoid()
        )
        
        # Continuous prediction head
        self.continuous_head = nn.Sequential(
            nn.Linear(128 + n_generators * n_timesteps, 256),
            nn.ReLU(),
            nn.Linear(256, n_generators * n_timesteps)
        )
    
    def forward(self, x):
        encoded = self.encoder(x)
        u_logits = self.binary_head(encoded)
        u_binary = (u_logits > 0.5).float()
        
        # Concatenate for continuous prediction
        combined = torch.cat([encoded, u_logits], dim=-1)
        p_continuous = self.continuous_head(combined)
        
        return u_logits, p_continuous

Constraint-Aware Loss

def constraint_aware_loss(predictions, targets, constraints):
    u_pred, p_pred = predictions
    u_true, p_true = targets
    
    # Standard MSE
    mse_loss = F.mse_loss(u_pred, u_true) + F.mse_loss(p_pred, p_true)
    
    # Constraint violations
    violation = 0
    
    # Power balance: sum(P) = D
    power_balance = torch.abs(p_pred.sum(dim=1) - constraints['demand'])
    violation += power_balance.mean()
    
    # Generation limits
    limit_violation = torch.relu(p_pred - constraints['p_max']).sum()
    limit_violation += torch.relu(constraints['p_min'] - p_pred).sum()
    violation += limit_violation
    
    # Ramp constraints
    ramp = torch.abs(p_pred[:, 1:] - p_pred[:, :-1])
    ramp_violation = torch.relu(ramp - constraints['ramp_rate']).sum()
    violation += ramp_violation
    
    return mse_loss + λ * violation

Warm-Start Integration

from pulp import LpProblem, LpVariable, LpMinimize, lpSum, LpBinary, LpContinuous
import gurobipy as gp

def warm_start_uc(problem, neural_predictions):
    """
    Use neural network predictions to warm-start MILP solver
    """
    u_pred, p_pred = neural_predictions
    
    # Create MILP model
    model = gp.Model("UC_WarmStart")
    
    # Variables with warm-start values
    u = {}
    p = {}
    
    for i in range(n_generators):
        for t in range(n_timesteps):
            # Binary with warm-start
            u[i,t] = model.addVar(
                vtype=gp.GRB.BINARY,
                name=f"u_{i}_{t}",
                Start=u_pred[i,t].item()  # Warm-start
            )
            
            # Continuous with warm-start
            p[i,t] = model.addVar(
                vtype=gp.GRB.CONTINUOUS,
                lb=p_min[i], ub=p_max[i],
                name=f"p_{i}_{t}",
                Start=p_pred[i,t].item()  # Warm-start
            )
    
    # Solve with warm-start
    model.optimize()
    
    return model

Performance Metrics

Metric	Cold-Start MILP	MSWS	Improvement
Feasibility Rate	~80%	95%	+15%
Solve Time	100%	40%	60% ↓
Optimality Gap	0%	<1%	~1%
Scalability	Limited	1000+ units	✓

Applications

• Day-ahead scheduling: 24-hour UC for power markets
• Real-time dispatch: Intra-hour adjustments
• Renewable integration: Handling stochastic solar/wind
• Microgrid management: Distributed energy resources
• Demand response: Price-responsive load management

Key Advantages

1. Preserves optimality: Solutions within 1% of optimal
2. Maintains feasibility: 95% feasibility rate
3. Scalable: Handles 1000+ generators
4. Interpretable: Each stage has clear purpose
5. Integrable: Works with existing MILP solvers

Training Data Requirements

• Historical UC solutions: 10,000+ solved instances
• Generator parameters: Costs, limits, ramp rates
• Load profiles: Hourly demand patterns
• Market data: Prices, renewable forecasts

Deployment Pipeline

Data Collection
    ↓
Feature Engineering (load patterns, weather)
    ↓
Neural Network Training (multi-stage)
    ↓
Constraint-Aware Fine-Tuning
    ↓
Validation on Test Scenarios
    ↓
MILP Integration (Gurobi/CPLEX)
    ↓
Production Deployment

Comparison with Alternatives

Method	Speed	Feasibility	Optimality	Scalability
Cold-Start MILP	Slow	✓	Optimal	Limited
Pure Neural	Fast	✗	~	✓
Reinforcement Learning	Medium	~	Suboptimal	✓
MSWS	Fast	✓	Near-optimal	✓

References

• Za'ter, M.E., Van Boven, A., Hodge, B.M., et al. (2026). "A Multi-Stage Warm-Start Deep Learning Framework for Unit Commitment." arXiv:2604.21891.
• Padhy, N.P. (2004). "Unit commitment - a bibliographical survey." IEEE Trans. Power Systems.
• Rong, H., et al. (2020). "Fast Unit Commitment using Neural Networks." IEEE Trans. Smart Grid.

Tools and Libraries

• PyTorch/TensorFlow: Neural network training
• Gurobi/CPLEX: MILP solving
• PyPSA: Power system modeling
• Pandapower: Grid analysis

Example Workflow

User: "We need to optimize the unit commitment for a grid with 500 generators 
        over 24 hours, considering renewable uncertainty."

Agent: Using MSWS framework:
1. Train/load neural network on historical UC data
2. Predict binary commitment decisions (Stage 2)
3. Refine power outputs (Stage 3)
4. Warm-start MILP solver with predictions
5. Solve to near-optimality in 40% of cold-start time

Expected: 95% feasibility, 60% time reduction, <1% optimality gap