APPROXIMATE SEASONAL OPTIMIZATION OF THE GREENHOUSE ENVIRONMENT FOR AMULTI-STATE-VARIABLE TOMATO MODEL

A complete optimal solution of a greenhouse environmental-control prob lem, which involves a multi-state-variable crop, requires prohibitivel y large computer resources. We describe here a sub-optimal solution me thod which is based conceptually on Pontryagin's maximum principle. Th e simplification is due to an approximate decision making process, whi le the original model remains unchanged. More specifically, only one o r two of the scores of costate variables (namely, shadow prices of sta te variables) were used to optimize the environmental control decision s. Following ideas first developed in previous studies, the costate va riable for dry matter accumulation was transformed in a way that made it nearly constant throughout the season (vegetative and reproductive stages included). Simulation-optimization computations were carried ou t for a well-established greenhouse tomato model, TOMGRO. The results showed that the performance criterion could not be much improved by le tting the costate vary along the season, nor by adding a second costat e for the number of nodes along the stem. The optimal value of the cos tate was found not to be very sensitive to changes in climate. The loc al (hourly) optimization utilized soft and hard constraints on the env ironmental variables, to distinguish, based on growers' experience, be tween more and less desirable portions of the feasible region. Penalty functions were used to drive the solution, as much as possible, into the more desirable space. The high humidity constraint was the most di fficult to meet, sometimes requiring simultaneous heating and ventilat ion.