Approximate seasonal optimization of the greenhouse environment for a multi-state-variable tomato model
1998
Ioslovich, I. | Seginer, I.
A complete optimal solution of a greenhouse environmental-control problem, which involves a multi-state-variable crop, requires prohibitively large computer resources. We describe here a sub-optimal solution method, which is based conceptually on Pontryagin's maximum principle. The simplification is due to an approximate decision making process, while the original model remains unchanged. More specifically, only one or two of the scores of costate variables (namely, shadow prices of state variables) were used to optimize the environmental control decisions. Following ideas first developed in previous studies, the costate variable 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 out for a well-established greenhouse tomato model, TOMGRO. The results showed that the performance criterion could not be much improved by letting the costate vary along the season, nor by adding a second costate for the number of nodes along the stem. The optimal value of the costate was found not to be very sensitive to changes in climate. The local (hourly) optimization utilized soft and hard constraints on the environmental variables, to distinguish, based on growers' experience, between 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 difficult to meet, sometimes requiring simultaneous heating and ventilation.
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