From Crop and Energy Data to Optimized Lighting Scheduling: A Surrogate-Based MILP Framework for Vertical Farming

Vertical farming enables high productivity and stable crop production under controlled conditions, but its economic feasibility remains limited by electricity demand for artificial lighting and climate control. This study develops a surrogate-based optimization framework for cost-minimizing lighting management in hydroponic vertical farms. A key contribution is a procedure for converting crop-energy response data into relationships suitable for mathematical programming. The method can be applied to experimental datasets or outputs from validated dynamic models, provided that relevant ranges of control variables, crop stages, and energy responses are represented. The framework is applied to lettuce cultivation in an industrial-scale vertical farm in northern Italy. Synthetic data generated by a verified agri-energy model are used to derive surrogate relationships for fresh biomass growth, leaf area index, and electricity demand for lighting, heating, and cooling. These relationships depend on photosynthetic photon flux density, crop stage, and outdoor temperature. Different temporal aggregation levels are examined to evaluate the trade-off among surrogate accuracy, scheduling flexibility, and computational compactness. The surrogate model reproduced crop and energy trends of the reference model with sufficient accuracy for optimization. Compared with fixed-lighting benchmarks, optimized schedules reduced electric energy consumption by up to 15.9% and electricity cost by up to 17.8%, while achieving the target harvest weight. Results indicate that moderate light intensities combined with flexible photoperiods are more cost-effective than high-intensity lighting under the investigated conditions. The proposed framework offers a tractable and generalizable approach for integrating crop growth, energy demand, and electricity price variability into vertical farming lighting strategies.