Optimal control of nitrate in lettuce by a hybrid approach: differential evolution and adjustable control weight gradient algorithms

Abstract Since high concentration levels of nitrate in lettuce and other leafy vegetables are undesirable, cultivation of lettuce according to specified governmental regulations is currently an important issue. Therefore, methods are sought in order to produce a lettuce crop that allow maximization of the profits of the grower while at the same time insuring the quality of the crops. Using a two-state dynamic lettuce model that predicts the amount of nitrate at harvest time, an optimal control problem with terminal constraints is formulated. The situation considered may be relevant in a plant factory where a fixed head weight should be reached in fixed time while minimizing light input. First, optimal trajectories of light, CO2 and temperature are calculated using the adjustable control weight (ACW) gradient method. Subsequently, novel, efficient and modified differential evolution (DE) algorithms are used to obtain an approximate solution to the same optimal control problem. While the gradient method yields a more accurate result, the optimum may be local. In order to exploit the salient characteristics of a DE algorithm as a global direct search method, a hybrid-combined approach is proposed. An approximate solution obtained with a DE algorithm is used to initialize the ACW gradient method. Although local minima did not seem to occur in this particular case, the results show the feasibility of this approach.