Boyung Jürgens | Searcharxiv

arXiv2026

Surrogate-based prioritization of sub-problems for Benders decomposition in energy planning

Benders decomposition solves optimization problems by separating the first-stage master problem from one or more second-stage sub-problems. While the standard Benders decomposition solves all sub-problems in each iteration, solving only selected sub-problems still guarantees convergence and can reduce solution time, but raises the question of how to select. In this work, we introduce surrogate-based prioritization of sub-problems. The method leverages surrogates to estimate the sub-problems' objectives, assess the current error of the cutting-plane estimator, and then prioritize the sub-problem with the largest error. We implement surrogate-based prioritization within sequential and asynchronous Benders decomposition. Both these algorithms also leverage the surrogate to trigger convergence checks and implement regularization. Benchmarks for an energy planning problem with a few large sub-problems show that the applied prioritization strategy works. The reduction in solution time correlates with the surrogate's accuracy. In our case, geometric interpolation-based surrogates are more accurate than machine learning methods. As a result, prioritization consistently and significantly outperforms the standard algorithm in sequential Benders decomposition. The speed-up increases with the number of scenarios, reaching 33\% with four scenarios and 55% with ten scenarios. In the case of asynchronous parallelization, the impact on performance is less clear, and the average speed-up from prioritization is 19%.

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arXiv2024

Decision-Based vs. Distribution-Driven Clustering for Stochastic Energy System Design Optimization

Stochastic programming is widely used for energy system design optimization under uncertainty but can exponentially increase the computational complexity with the number of scenarios. Common scenario reduction techniques, like moments-matching or distribution-driven clustering, pre-select representative scenarios based on input parameters. In contrast, decision-based clustering groups scenarios by similarity in resulting model decisions. Decision-based clustering has shown potential in network design and fleet planning. However, its potential in energy system design remains unexplored. In our work, we examine the effectiveness of decision-based clustering in energy system design using a four-step method: 1) Determine the optimal design for each scenario; 2) Aggregate and normalize installed capacities as features reflecting optimal decisions; 3) Use these features for k-medoids clustering to identify representative scenarios; 4) Utilize these scenarios to optimize cost in stochastic programming. We apply our method to a real-world industrial energy system modeled as a mixed-integer linear program. We incorporate uncertainty by scaling time series with representative factors. We generate 500 single-year scenarios via Monte Carlo sampling, which we reduce using decision-based clustering. For benchmarking, we conduct distribution-driven k-medoids clustering based on the representative factors. In our case studies, both clustering methods yield designs with similar cost efficiency, although decision-based clustering requires substantially more computational resources. To our knowledge, this is the first application of decision-based clustering on energy system design optimization. Future research should investigate the conditions under which decision-based clustering yields more cost-efficient designs compared to distribution-driven clustering.

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