Finding the Broad Gini in the Bottle: Optimizing Equity, Efficiency, and Resilience in Grid Restoration

Beibei Liu, Junchi Yan

Keywords: non-convex optimization, Mixed-Integer Linear Program (MILP), stochastic programming, uncertainty quantification (UQ), power grid restoration, societal considerations

TL;DR: Integrating a Hidden Markov Model (HMM), a game-theoretic model, and Conditional Value-at-Risk (CVaR) into a Mixed-Integer Linear Program (MILP) improves power grid restoration resilience by 22% and fairness by 32%.

Abstract:

Restoring a damaged power grid requires balancing efficiency, resilience to tail events, and equitable service under deep uncertainty. We **diagnose** a structural “Alignment Trap” where standard linear scalarizations of these objectives cause optimization to collapse into degenerate “zero-restoration” solutions.

We address this by establishing a **foundational framework for safe learning**, integrating (i) a physics-grounded mixed-integer **Oracle that generates high-fidelity expert demonstrations**, (ii) a CVaR-based formulation that **restores informative gradients**, and (iii) a fast policy surrogate distilled from optimal plans to **prove the learnability of the restoration manifold**.

To evaluate societal trade-offs, we introduce **Broad Gini**, a composite metric capturing efficiency, resilience, and equity. Across diverse topologies, our method prevents collapse, improving N-1 resilience by **23.3% (IEEE-145)** and reducing inequity by **96% (IEEE-30)**. **Rather than proposing a singular control algorithm**, this work establishes a rigorous, verifiable benchmark that **unlocks the solution space** for safety-critical reinforcement learning agents, bridging the gap between operations research and scalable AI.

Primary Area: optimization

Submission Number: 24028