Online Learning-Based Adaptive Hybrid Benders Decomposition for Risk-Averse Optimal Sizing

Abstract

Optimal sizing problem (OSP) under uncertainty is often formulated as two-stage stochastic programming (2SP). However, this formulation typically introduces significant computational and RAM (memory) bottlenecks as the scenario size grows. Benders Decomposition (BD) is a popular approach to tackle this problem, but it suffers from slow convergence to the exact solution. To address this problem, we propose an accelerated online learning-based adaptive hybrid BD algorithm. The proposed method avoids getting stuck in the infeasible region during early iterations by explicitly embedding a carefully selected scenario in the master problem, while online learning based on logistic regression (LR) leverages a light machine learning (ML) algorithm to avoid solving the entire scenario set at every iteration. The OSP is formulated to select a behindthe-meter battery energy storage system in a multi-site energy community with existing renewables. The use case explores an interesting middle-ground between deterministic methods and training-heavy ML models, showcasing the potential of MLassisted decision-making. Numerical results on scenario sets of up to 500 illustrate the effectiveness and scalability of the proposed approach. © IEEE. Accepted manuscript. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.