Optimization and optimal control of plant growth: application of GreenLab model for decision aid in agriculture

The objective of the thesis is to improve plant yield through optimization and optimal control based on the GreenLab plant growth model. Therefore, the thesis proposed a methodology for investigation of plant yield improvement, whose characteristics are that (1) investigations are all based on the functional-structural plant growth model GreenLab and (2) heuristic optimization algorithm and optimal control techniques are applied to the plant growth model in order to improve plant yield. By applying optimization techniques on different species of plants (crops or trees) and for different kinds of optimization problems, common characteristics that a plant with high yield should possess were obtained. The optimal results in the thesis revealed the source-sink dynamics during the plant growth. The optimization results can be considered as references to guide breeding for ideotype and to improve cultivation modes. The optimization application of GreenLab could thus be possibly used to the agricultural decision support system. To achieve the aims of the thesis, the thesis investigated the effects of endogenous factors and exogenous environmental factors of plant growth on plant yield separately. First, given environmental conditions, the thesis investigated endogenous factors, and then the thesis did optimal control on exogenous environmental factors given plant genotype. Therefore, the problems investigated in the thesis consist of general optimization problems and optimal control problems. The main contributions of the thesis include following issues: According to the species of plants, single optimization problems, multi-objective optimization problems and optimization problems with constraints with respect to plant endogenous factors were formulated and investigated, in order to find the ideotype of plants with high plant yield. A population based algorithm is more suitable for the optimization problems in this thesis. Due to its better performance compared with other heuristic optimization algorithms, all optimization problems were solved by a population-based, heuristic optimization algorithm, namely Particle Swarm Optimization (PSO). Optimal control on the pruning strategy was formulated and investigated in the thesis. As GreenLab can be considered as discrete dynamic system and the objective function of the optimal control problem is analytical, the gradient based method, which is based on the variational approach and Lagrange theory, was used to solve the optimal control problem. Moreover, the optimal solutions were compared with the ones found by PSO, in order to validate the PSO method. The insect population dynamics was modeled mathematically, which was compatible with the plant model GreenLab in terms of spatial and temporal scales, to study the effect of biotic factors on plant growth. The interaction among plants, pests and auxiliaries was implemented, and the ecosystem model, which involves the three tri-trophic components, was thus developed in the thesis. The tri-trophic ecosystem model can simulate the insect population dynamics and the plant growth with consideration of the interaction of insects. Moreover, the tri-trophic ecosystem model considered the partition of individuals in the insect population among plant organs, which is not taken into account in the previous works. A global sensitivity analysis method Morris method was used to analyze the most important parameters and the least influential parameters to model outputs of interest. Through optimization on pest management techniques, the optimal strategies of the application of the pest management techniques were obtained. Estimation of GreenLab parameters with about 400 sets of observation data of 44 tomato genotypes was done in the thesis, by using a generalized non-linear least square algorithm. Taking the estimated parameter values as parameter space, the GreenLab model parameters were optimized, in order to maximize the fruit yield. Through the analy