Abstract
Feeding management in aquaculture involves complex trade-offs among biological growth, economic efficiency, and environmental sustainability. However, existing modelling approaches typically treat stage-specific feed formulation and continuous feeding strategies as decoupled static problems, failing to capture the dynamic bioenergetic feedback over a full production cycle. To bridge this gap, this study develops a dynamic non-linear programming (NLP) framework that integrates stage-specific diet formulation, bioenergetic growth differential equations, and environmental impacts within a unified multi-objective optimisation model. By formulating assimilable energy as a dynamic function of macronutrients, the framework allows formulation decisions to concurrently drive biomass trajectories, economic profit, and ecological footprints. Using largemouth bass (Micropterus salmoides) as a proof-of-concept case study, the framework's capability was demonstrated through dynamic simulations across three growth stages. A bi-objective evaluation (cost vs. growth) successfully identified Pareto knee-point solutions to avoid sharp marginal cost escalation near physiological limits. Furthermore, tri-objective optimisation (incorporating GWP and freshwater EP) quantitatively revealed non-linear trade-offs, demonstrating that over 70% of environmental burdens can be reduced with a 6.1% profit penalty. Ultimately, this framework provides a quantitative, algorithm-driven decision-support tool for designing precision feeding strategies that balance profitability and environmental sustainability under complex dynamic constraints.
•Dynamic NLP framework couples diet formulation, growth, and ecology.•Assimilable energy bridges economic feed formulation and biological trajectories.•Multi-objective optimisation quantifies trade-offs among profit, GWP, and EP.•Sensitivity analysis assesses robustness against nutritional and market volatility.