Clustering-enhanced adaptive Benders decomposition for energy systems planning optimization

Abstract: High-resolution energy system capacity expansion models (CEMs) for energy transition planning often result in large-scale mixed-integer linear programming (MILP) formulations. Benders decomposition (BD) offers a scalable solution approach by iteratively solving a master problem (MP) for investment decisions and multiple subproblems (SPs) for operational decisions. However, accumulated Benders cuts generated by the SPs can make MP solution a major computational bottleneck. Incomplete SP parallelization can also introduce further bottlenecks when SPs exceed available CPUs. We develop clustering-enhanced BD methods to address these challenges, by using clustering to group similar SPs for: a) aggregated Benders cut construction and b) identification of representative SPs to be solved most frequently. For grouped-cuts, we examine two adaptive formulations based on dual variables and a fixed-grouping formulation based on exogenous time-series inputs. We evaluate these methods in an electricity-sector CEM across varying system sizes, temporal SP lengths, inter-SP coupling strengths represented by CO2 policy, computational resources, and stochastic settings. Relative to a benchmark regularized multi-cut formulation, adaptive grouped cuts outperform fixed grouping and provide substantial benefits under weak inter-temporal coupling. The largest gains occur in larger systems with shorter SP horizons, where the MP accounts for a greater share of runtime. Their effectiveness declines under strong inter-temporal coupling, such as annual CO2 emissions limits, where the benchmark multi-cut performs best. The representative-SP method outperforms the benchmark under limited parallelization when SP solution dominates runtime. Overall, the preferred BD strategy depends on inter-SP coupling strength and whether computational burden lies in the MP or the SPs.