Title: Finding the Broad Gini in the Bottle: Optimizing Equity, Efficiency, and Resilience in Grid Restoration
Primary area: optimization
Keywords: non-convex optimization, Mixed-Integer Linear Program (MILP), stochastic programming, uncertainty quantification (UQ), power grid restoration, societal considerations

Abstract: Post-disaster power grid restoration faces a critical trilemma of maximizing efficiency, ensuring social equity, and maintaining resilience. This challenge is amplified by uncertainties that current methods fail to address holistically, as traditional single-objective approaches yield imbalanced solutions and lack a quantitative framework for navigating these trade-offs.

We propose a two-stage stochastic Mixed-Integer Linear Program (MILP) that uses a Hidden Markov Model (HMM) to generate scenarios, which are then clustered by K-means into a tractable set. The first stage determines grid topology, while the second adapts power dispatch to scenarios. Its objective function balances expected energy restoration (efficiency), a Conditional Value-at-Risk (CVaR) metric for robustness, and the Gini Coefficient for fairness.

Ablation studies on the IEEE 30-bus system demonstrate our model can boost the N-1 reserve ratio by 22\% for resilience with a modest 7\% energy trade-off, or reduce the Gini Coefficient by 32\% for fairness while maintaining high energy output. Our framework provides a powerful quantitative tool for multi-objective decision-making, revealing the unavoidable trade-offs among efficiency, fairness, and resilience.

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%.