【正文】 n problem a greenhouse crop production model is required in order to estimate the inner climate behavior and the crop growth through the different steps of the algorithm and relate the different function objectives to the decision variables The dynamic behavior of the microclimate inside the greenhouse is a bination of physical processes involving energy transfer radiation and heat and mass balance water vapor fluxes and CO2 concentration On the other hand the crop growth and yield mainly depend among other conditions such as irrigation and fertilizers on the inside temperature of the greenhouse the PAR radiation and the CO2 concentration Thus both climate conditions and crop growth influence each other and their dynamic behavior can be characterized by different time scales Hence the crop growth in response to the environment can be described by two dynamic models represented by two systems of differential equations with a time scale associated to their dynamics which can be represented by where Xcl Xcl t is an n1dimensional vector of greenhouse climate state variables mainly the inside air temperature and humidity CO2 concentration PAR radiation soil surface temperature cover temperature and plant temperature Xgr Xgr t is an n2dimensional vector of crop growth state variables mainly number of nodes on the main stem leaf area index LAI or surface of leaves by soil area total dry matter which represents all the plant constituents– root stem leaves flower and fruit– excluding water fruit dry matter being the biomass of the fruits excluding water and mature fruit dry matter or mature fruit biomass accumulation U U t is an mdimensional vector of input variables natural vents and heating system in this work D D t is an odimensional vector of disturbances outside temperature and humidity wind speed and direction outside radiation and rain V V t is a qdimensional vector of system variables related to transpiration condensation and other processes C is an rdimensional vector of system constants t is the time Xcli and Xgri are the known states at the initial time ti fcl fcl t is a nonlinear function based on mass and heat transfer balances and fgr fgr t is a nonlinear function based on the basic physiological processes of the plants For the Mediterranean area the authors have developed linear and nonlinear models using physical laws These models are too plex to be detailed here but the main growth model equations will be described in the following sections where the problem objectives and the final MO optimization problem are explained These equations will be used to show how the different objectives cost functions are expressed as functions of the decision variables of the optimization problem present and future temperature and EC setpoints 21 imization of profits Profits are calculated as the difference between the ine from the selling of the fresh fruits and the costs associated to their production where Vpr t is the selling price of the production estimated from the market XFFP t is the fresh fruit production obtained from the crop growth model Vcos t are the costs incurred by heating electricity fertilizers and water t is the time ti is the initial time of crop cycle and th is the latest harvesting time both selected by the grower Notice that in practice the tomato crop has multiple harvest during the growing season For that reason th represents the latest harvesting time in Eq An alternative is to consider the next harvesting time tn in the cost function and restarting the optimization process again once the previous harvest has been produced Both alternatives are valid for multiple harvest The ine depends on the price of tomato fruits kg1??g1 the harvesting dates and on the yield in fresh weight per surface unit kg m2 The price policy requires market models or historical data this being a very difficult prediction problem The following subsections describe how the fresh fruit production XFFP t and the process costs Vcos t can be estimated and related with the decision variables 22 imization of quality Although imizing the profits can be understood as the main objective from the growers point of view this cannot always be used as the only one The growers usually belong to cooperatives or agrarian societies that facilitate the introduction of the horticultural products into the market These associations fix the policies on quality products based on the different market requirements and thus the growers must adapt their production process to those policies in order to reach some minimum quality levels Food quality embraces both sensory attributes that are readily perceived by the human senses and hidden attributes such as healthiness and nutrition Shewfelt 1999 In fruits and vegetables the sensory properties are det