Neural networks for multi-horizon stochastic programming

TL;DR

This paper tackles the computational intractability of multi-horizon stochastic programming for energy-system planning by embedding a neural-network surrogate of the operational recourse directly into MHSP. A feed-forward neural network is trained to approximate expected operational costs and is reformulated as a MILP with ReLU activations to enable joint optimization of investment and operation. Across a UK power-system case study, the surrogate-embedded MHSP achieves high predictive accuracy (R² ≈ 0.99) and substantial speed-ups (up to 34.72x) while maintaining in-sample and out-of-sample robustness. The work demonstrates that surrogate models can generalize well under limited scenarios and offers a scalable pathway for exploring multi-timescale uncertainty in energy planning.

Abstract

This paper proposes a machine-learning-based solution approach for solving multi-horizon stochastic programs. The approach embeds a deep learning neural network into a multi-horizon stochastic program to approximate the recourse operational objective function. The proposed approach is demonstrated on a UK power system planning problem with uncertainty at investment and operational timescales. The results show that (1) the surrogate neural network performs well across three different architectures, (2) the proposed approach is up to 34.72 times faster than the direct solution of the monolithic deterministic equivalent counterpart, (3) the surrogate-based solutions yield comparable in-sample stability and improved out-of-sample performance relative to the deterministic equivalent, indicating better generalisation to unseen scenarios. The main contributions of the paper are: (1) we propose a machine-learning-based framework for solving multi-horizon stochastic programs, (2) we introduce a neural network embedding formulation tailored to multi-horizon stochastic programs with continuous first-stage decisions and fixed scenario sets, extending existing surrogate modelling approaches from two-stage to multi-horizon settings, and (3) we provide an extensive computational study on a realistic UK power system planning problem, demonstrating the trade-off between approximation accuracy, computational efficiency, and solution robustness for different neural network architectures and scenario set sizes.

Figures (4)

• Figure 1: Illustration of MHSP with short-term and long-term uncertainty (blue circles: investment nodes, red squares: operational periods, $i:$ index of the investment nodes).
• Figure 2: Long-term scenarios
• Figure 3: In-sample objective stability
• Figure 4: Out-of-sample stability of the surrogate models and the deterministic equivalent