Energy system transition under uncertainty
Planning a transition to a decarbonized energy system presents notable mathematical challenges. These arise from balancing ecological sustainability and economic feasibility while managing uncertainties in energy demand, weather-dependent renewables, and geopolitical price fluctuations. Despite these uncertainties, reliable investment decisions need to be made, requiring optimization models with millions of variables that must be frequently optimized under slight variations. We collaborate with industry partners and solver companies to address these challenges, integrating real-world insights with state-of-the-art solver technology to develop advanced modeling and optimization techniques.
Solution strategies with first-order methods
Efficient solutions require leveraging massively parallel high-performance computing (HPC) and GPU technology. Solving energy-related mixed-integer problems (MIPs) is computationally demanding, including already computationally expensive linear programming (LP) relaxations. At ZIB, we push computational boundaries by integrating decomposition techniques with interiorpoint methods in our solver, PIPS-IPM++, harnessing HPC for high-accuracy LP solutions. For MIPs, first-order methods (FOMs) provide a faster, lower-accuracy alternative by iteratively applying gradient information via matrix products, a process well suited for GPUs. We embed these LP techniques into a heuristic framework called fix-and-propagate (FP), enabling efficient optimization of large-scale energy system models.
Decision support under uncertainty
Long-term energy investments must consider uncertainties that cannot be fully captured by a single optimization outcome. We integrate high-performance LP solvers into robust optimization frameworks to facilitate sensitivity and robustness analyses. Using a modeling-to-generate-alternatives approach, we provide stakeholders with multiple near-optimal solutions, which offer a broad catalog of investment options close to the economically optimal set. Given the large scale and numerical intricacy of energy system models, efficient re-optimization is crucial. Our warm-starting techniques significantly reduce computation time from several hours on parallel machines to just minutes on a single computer, enhancing decision-making efficiency.
Conflicting targets in energy system optimization
When dealing with conflicting targets for large MIPs, computing all Pareto-optimal solutions (that is, such that no objective can be improved without worsening another) is often impossible and not beneficial to the decision-maker. Instead, we focus on generating a representative subset that balances solution diversity with computational efficiency while considering both convex and non-convex regions. For example, when optimizing Berlin’s district heating network, we investigate variants of the classical ε-constraint algorithm for three objectives (f1, f2, f3). Through lexicographic optimization, we restrict the search region projected onto the f2/f3-hyperplane to a rectangular shape defined by including f1-optimal (usually cost-optimal) solutions. Infeasible subregions can be eliminated early by employing the appropriate order of the subproblems. Depending on the generation of the ε-constraints – grid-wise or dynamically – we can either compute well-distributed or clustered solution sets to produce valuable insights for the decision-maker.
Advancing energy-system planning for the Berlin energy system
At ZIB, we enhance large-scale energy-system planning by leveraging HPC, FOMs, and heuristic frameworks. Validated on the Berlin-Brandenburg multi-sectoral energy system design and the Berlin district heating system, our approach integrates robust optimization in decision-support tools, enabling faster re-optimization and providing stakeholders with diverse, near-optimal solutions for more informed decision-making – even in uncertain times.
Nils-Christian Kempke, Niels Lindner, Stephanie Riedmüller, Janina Zittel
