The transition towards renewable energy requires long-term energy system planning, which depends on solving constrained optimization (CO) problems. These CO problems are becoming increasingly complex, particularly due to the variability introduced by renewable energy sources. Tra
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The transition towards renewable energy requires long-term energy system planning, which depends on solving constrained optimization (CO) problems. These CO problems are becoming increasingly complex, particularly due to the variability introduced by renewable energy sources. Traditional optimization methods struggle to scale with this growing model complexity. In contrast, machine learning approaches allow faster solution computation, but offer only approximate solutions with no guarantees on solution quality, thereby limiting reliability and interpretability in planning applications.
This research addresses these limitations by exploring the use of neural networks to predict feasible solution pairs for the primal and dual formulations of the CO problem, enabling approximate solutions accompanied by bounds on suboptimality. Self-supervised primal-dual learning (PDL) is adapted and extended to produce paired feasible solutions for both the primal and dual formulations of an economic dispatch problem. Feasibility in the primal network is enforced through differentiable repair and completion layers, including novel domain-specific extensions that adjust supply-demand balancing priorities, which were found to be essential for predictive accuracy. This then exposes a structural limitation of PDL: while repair and completion layers are essential for primal learning, they prevent the learning of meaningful dual predictions. To address this, the dual network is trained using a modified loss function that directly optimizes the dual problem, enabling the use of a completion layer adopted from the literature to ensure dual feasibility. An additional novel classification-based layer that incorporates prior knowledge on the dual variables further improves the dual prediction quality when applied to the economic dispatch problem. Finally, the trained networks are integrated into Benders decomposition, a technique that breaks CO problems into easier, independent problems. This enables a hybrid approach: approximate solutions with bounds on suboptimality can be obtained swiftly, whereas exact solving remains available if necessary, retaining all theoretical convergence and optimality guarantees and potentially reducing computational time.
The proposed framework is evaluated on a generation expansion planning problem, where the economic dispatch subproblems are solved iteratively using the trained networks. The results demonstrate a theoretically grounded and empirically validated proof of concept for producing solutions with quality guarantees using learning-based methods, which is generally applicable to any problem compatible with Benders decomposition where the resulting subproblem admits a conic formulation. However, the results do not show conclusive speed-ups due to a mismatch between the training data and the data encountered during Benders iterations. By demonstrating how neural networks can be used to generate approximate, feasible solutions accompanied by theoretical guarantees on solution quality, this research contributes to the advancement of scalable and reliable constrained optimization methods for energy systems.
