Multi-objective optimization for greenhouse light environment using Gaussian mixture model and an improved NSGA-II algorithm

Research on the optimization and control of greenhouse light environment is of great significance to improve the production efficiency and economic benefits of greenhouse crop. The optimization of greenhouse light environment should not only meet the requirements of crop photosynthesis, but also reduce the energy consumption cost during light supplement. Therefore, in this paper, a multi-objective optimization model of greenhouse light environment was first established, which was aimed at maximizing the photosynthetic rate of crop and minimizing the energy consumption cost. Then, there were errors between the outputs of photosynthetic rate model and the actual values, which led to that the optimization results based on the photosynthetic rate model were not the actual optimal values, so Gaussian mixture model (GMM) was used to describe the error characteristics of photosynthetic rate model. The error compensation of photosynthetic rate model was realized, and it was introduced into the optimization objective, thus forming a multi-objective optimization model of greenhouse light environment after error compensation. In addition, an improved NSGA-II algorithm based on average distance clustering (ADCNSGA-II) was proposed to solve the multi-objective optimization model. The algorithm divided the whole population into several small populations by using average distance, and then selected, crossed, and mutated small populations. This operation could effectively maintain the diversity of Pareto optimal solution set, and further improve the convergence of algorithm. Finally, taking tomato in a solar greenhouse of the experimental base of Shenyang Agricultural University in Northeast China as the research crop, the established model and the proposed optimal regulation method were verified through simulation experiments. The results showed that the RMSE and MAPE of photosynthetic rate model based on error compensation were 0.7641 and 2.6413 respectively, and the CC of the model was 0.9803, indicating that the model has good prediction performance. Moreover, ADCNSGA-II algorithm was used to solve the multi-objective optimization model after error compensation, and the results were compared with those obtained by solving the optimization model before error compensation. The optimization results obtained by solving the optimization model after error compensation were closer to the actual values, which further proved the reliability of the proposed optimal regulation method.