Design of integrated renewable energy and recirculating aquaculture systems under uncertainty: a two-stage stochastic optimisation approach

The intensification of aquaculture, while important for food security, faces significant challenges from its dependence on volatile energy markets and pressure to decarbonise. This paper presents a machine learning (ML)-enhanced two-stage stochastic programming (SP) framework, enhanced by machine learning, for the design of resilient hybrid energy systems for Recirculating Aquaculture Systems. The methodology achieves computational tractability, a key challenge in high-dimensional SP, by integrating a Gaussian Copula to model parameter correlation and utilising ML for strategic uncertainty parameter selection. This ML-driven variable selection offers a scalable alternative to traditional, computationally expensive methods, enabling co-optimisation for two sets of uncertainties: both energy and technology parameters, and market-driven risks such as fish and feed prices. The results show a clear advantage to designing for uncertainty. The stochastic designs outperformed their deterministic counterparts, yielding a 24 % higher average net revenue and a more favourable financial profile, with an 89 % probability of profitability compared to 71 % for deterministic designs. Furthermore, a Conditional Value at Risk (CVaR95%) analysis confirms that the optimised solution exhibits a controlled risk profile and a notable degree of implicit risk aversion, preventing from the flexibility of the two-stage structure. Under stringent CO₂ constraints, the mean cost of the stochastic design was found to be up to 35 % lower than the deterministic equivalent, highlighting the economic value of investing in system flexibility. The final model, comprising over 234,000 constraints, was solved in a tractable timeframe of 20 min, confirming the overall computational tractability achieved by the ML-enhanced framework. This superior economic performance is achieved by making strategic investments in energy autonomy, which not only hedges against high electricity prices but also provides a crucial financial buffer against periods of low salmon market prices. The framework provides a practical tool for stakeholders to evaluate and de-risk investments, offering data-driven pathways for aligning economic viability with decarbonisation goals in this important food production sector.