Multi-objective optimization of milk powder spray drying system considering environmental impact, economy and product quality

Performance optimization of the milk powder spray drying system is of great significance to the sustainable development of the dairy industry with the growing market demand for milk powder. The present study aims to propose a multi-objective optimization framework for the drying system to improve the environmental performance, economic performance, and product quality of the system. For this purpose, inlet air temperature, feed pump speed, and atomization pressure are taken as the decision variables. A multi-objective optimization model of the system is established to minimize the system's environmental impact and life cycle cost and maximize the quality of milk powder. In order to solve the problem more efficiently, the non-dominated sorting ant colony genetic algorithm is proposed. The artificial neural network is adopted to construct the surrogate model for the life cycle assessment of the system and the Pareto front is obtained. The TOPSIS method is used to make decisions from the Pareto front to obtain the optimal scheme. The deviation index is adopted to evaluate the schemes obtained by different optimization methods. To demonstrate the advantages of the proposed framework, a case study is carried out and the optimal scenario obtained by the framework is compared with two different goal-oriented solutions, including bi-objective optimization that minimizes the environmental impact and life cycle cost of the system, and single-objective optimization that maximizes the quality of milk powder. The results show that the multi-objective optimization scheme can improve the performance of the system more comprehensively compared with dual-objective optimization and single-objective optimization. The optimized system achieves a good trade-off between environmental friendliness, economy, and quality of milk powder at the following conditions: the inlet air temperature of 182.98 °C, the feed pump speed of 80.74 rpm, and the atomization pressure of 180.34 bar. The environmental impact and the life cycle cost of the optimized system are reduced by 9.0% and 10.56%, respectively, compared with the original system, and the quality of milk powder is improved by 4.35%. The performance of the proposed method in the generational distance, spread and inverted generational distance is improved by more than 36.58%, 30.76% and 87.10%, respectively, compared with common algorithms such as NSGA-II, MOEA/D, NSGA-III, SPEA2. The solutions obtained using the proposed approach have the best performance in the three objectives compared with the schemes obtained by the other algorithms. The LCA surrogate model can reduce the solving time of the optimization from 3.5 h to 8.68 s on the premise of meeting the accuracy.