【正文】 ol t is the soluble solids concentration in the fruit Vta t is the titratable acidity in fruits Vff t is the fruit firmness Vfs t is fruit size and wssol wta wff and wfs are weighting parameters In tomato fruits soluble solids titratable acidity fruit firmness and size may be related to Xta t and XEC t decision variables using the following linear approach [Dorais et al 2020] and [Sonneveld and van der Burg 1991] 15 Y t ab X t g X t where Y t is the variable to be calculated soluble solids titratable acidity fruit firmness or size X t is the related decision variable XEC t for VSSol t Vta t Vfs t and Xta t for Vff t a is a constant increment coefficient in Y t b is the increment coefficient in Y t per unit of increment in X t and g X t is a piecewise function representing a threshold of X t over which there is an increment in Y t 23 imization of wateruse efficiency The explicit inclusion of this objective in the optimization problem has an environmentrelated purpose In semiarid climates such as Mediterranean ones water is a very scarce and expensive resource mainly during some seasons of the year Some authors maintain that the productivity in such regions is determined by the available water and the water efficiency use Hsiao Xu 2020 Thus an adequate management of water is required With the explicit inclusion of this objective the grower can select a solution from the Pareto front providing the desired water consumption during the growing cycle This objective tries to use the water quantities adequate to the crop growth in close relationship to the supplied concentration of nutrient solution In this paper wateruse efficiency is considered like the biomass efficiency defined as the relationship between the fresh fruit matter production and the water supplied 24 Multiobjective optimization problem All the variables presented in these objectives are functions of the air temperature Xta andor the EC XEC XFFP t Fsf t Wsw t Vta t VSSol t Vfs t Vff t as well as of measurable disturbances such as PAR radiation or CO2 concentration That is the objective functions can be expressed as for i 123 where is a vector of the inside air temperature along the optimization interval is a vector of the EC along the optimization interval and Θ is a vector of the measurable disturbances that have to be predicted along the optimization horizon The solution to the MO optimization problem provides both diurnal and nocturnal setpoint trajectories of EC and inside air temperature for the rest of the control horizon Constant diurnal and nocturnal setpoints are defined and steady state models of greenhouse climate and tomato crop summarized in EqsAlthough several techniques have been evaluated to solve the MO optimization problem Liu et al 2020 in this case a goal attainment algorithm has been used sequential quadratic programing SQPbased Priorities for each objective are determined by using weights that are sequentially modified in each iteration The constraints are defined by imum and minimum values of temperature and EC obtained from experts knowledge that indicate optimal growing temperatures for tomato and by analyzing local data from historical series The resulting constraints are changing throughout time with a yearly pattern designed on the basis of the last twenty years collected data 3 Multilevel hierarchical control architecture The dynamics involved in the greenhouse production process present different time scales as described above namely internal greenhouse climate fast crop dynamics ie transpiration photosynthesis and respiration and slow crop development ie crop growth and fruit changes Hence a multilayer hierarchical control architecture has been proposed and used 31 Crop growth control layer Taking into account the longterm objectives market prices harvesting dates and required quality and the longterm predictions of the growth state using the modified Tomgro model Ram237。rezArias et al 2020 for the estimation of yield and profits the optimization is performed to calculate the setpoint trajectories of the inside greenhouse temperature and the EC along the considered control horizon typically 65 days for a short season 260 decision variables or 120 days for a long season 480 decision variables Models for irrigation have also been developed for control and optimization purposes The longterm weather prediction which is logically one of the elements with a higher degree of uncertainty and is performed using a software tool that accesses the weather predictions given by the Spanish National Institute of Meteorology for the next eight days forward generates patterns based on several indexes clarity imum mean and minimum temperatures and solar radiation and searches within a local historical database for a cl