G-ORACLE: A Fast Geometric Method To Explore All Near-Optimal Designs for Energy Systems
Abstract
Modeling to Generate Alternatives (MGA) methods explore the near-optimal solutions of energy system optimization models (ESOMs), i.e., alternative planning pathways whose cost lies within a small predefined slack of the optimum but which can differ substantially in technology composition, regional distribution, and environmental impacts. Among MGA methods, ORACLE uniquely guarantees convergence to the near-optimal set within a targeted tolerance by iteratively refining inner and outer polytope approximations. At each iteration, given a trial point, it solves a problem as hard as the ESOM to find the nearest near-optimal solution to it. However, the trial point is obtained by solving a bilevel problem whose solution time grows rapidly with the number of iterations and eventually dominates the computational cost of the method. To eliminate this bottleneck, we present G-ORACLE, which exploits the fact that an optimal solution of the bilevel problem is always attained at a vertex of the outer approximation. G-ORACLE therefore replaces the bilevel problem with incremental vertex enumeration by the double description method and one convex projection per vertex, while retaining the convergence guarantee of ORACLE. A supporting-hyperplane check further avoids unnecessary recomputation of these projections as the inner approximation grows. We evaluate G-ORACLE on an electricity-only PyPSA-Eur model, exploring the near-optimal space of the installed capacities of six generation and two storage technologies. While ORACLE's bilevel problem exceeds 20 minutes at iteration 64, G-ORACLE performs the trial-point search in at most 14 seconds throughout 240 iterations, leaving the ESOM solves as the only significant computational cost.
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BibTeX
@misc{hajikazemi2026goracle,
title = {{G-ORACLE: A Fast Geometric Method To Explore All Near-Optimal Designs for Energy Systems}},
author = {Sina Hajikazemi and Florian Steinke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32759},
eprint = {2610.32759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32759},
}
RIS
TY - UNPB
TI - G-ORACLE: A Fast Geometric Method To Explore All Near-Optimal Designs for Energy Systems
AU - Sina Hajikazemi
AU - Florian Steinke
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32759
UR - https://arxiv.org/abs/2610.32759
AB - Modeling to Generate Alternatives (MGA) methods explore the near-optimal solutions of energy system optimization models (ESOMs), i.e., alternative planning pathways whose cost lies within a small predefined slack of the optimum but which can differ substantially in technology composition, regional distribution, and environmental impacts. Among MGA methods, ORACLE uniquely guarantees convergence to the near-optimal set within a targeted tolerance by iteratively refining inner and outer polytope approximations. At each iteration, given a trial point, it solves a problem as hard as the ESOM to find the nearest near-optimal solution to it. However, the trial point is obtained by solving a bilevel problem whose solution time grows rapidly with the number of iterations and eventually dominates the computational cost of the method. To eliminate this bottleneck, we present G-ORACLE, which exploits the fact that an optimal solution of the bilevel problem is always attained at a vertex of the outer approximation. G-ORACLE therefore replaces the bilevel problem with incremental vertex enumeration by the double description method and one convex projection per vertex, while retaining the convergence guarantee of ORACLE. A supporting-hyperplane check further avoids unnecessary recomputation of these projections as the inner approximation grows. We evaluate G-ORACLE on an electricity-only PyPSA-Eur model, exploring the near-optimal space of the installed capacities of six generation and two storage technologies. While ORACLE's bilevel problem exceeds 20 minutes at iteration 64, G-ORACLE performs the trial-point search in at most 14 seconds throughout 240 iterations, leaving the ESOM solves as the only significant computational cost.
ER -