Optimal control of sewage treatment process using a dynamic multi-objective particle swarm optimization based on crowding distance

A variety of multi-objective optimization algorithms has been extensively investigated in the past decades to tackle the optimal decision of sewage treatment process. However, achieving the ideal solutions is challenging in the multi-criteria decision-making process from Pareto optimal sets due to the complicated relationships among influencing factors, especially in the case of large decision variables involved in the wastewater treatment process. We thus proposed an improved dynamic multi-objective particle swarm optimization algorithm based on crowding distance (DMOPSO-CD) to obtain global optimal solutions for the balance between energy consump-tion (EC) and effluent quality (EQ) in sewage treatment processes. The algorithm consists of optimization modules and a self-organizing fuzzy neural network, improving the global searching ability of particles, main-taining the diversity of non-inferior solutions, and solving the multi-objective vital issues in the optimization of sewage treatment process. The proposed optimization algorithm was applied to benchmark simulation model No.1, and the optimization results showed that the EC for wastewater treatment in dry, rainy, and storm weather was reduced by 7.87%, 6.28%, and 7.30%, respectively. This methodology outperformed several widely applied algorithms, including the multi-objective cuckoo search, non-dominated sorting genetic algorithm-II, and improving Pareto evolutionary algorithm in terms of EQ and EC, which opens a new window for the optimal decision of sewage treatment.

Automated summary

In the past few decades, a variety of multi-objective optimization algorithms have been extensively studied to solve the optimal decision-making problem in sewage treatment processes. However, it is challenging to achieve ideal solutions due to complicated relationships among influencing factors, especially when dealing with a large number of decision variables in wastewater treatment. Therefore, an improved dynamic multi-objective particle swarm optimization algorithm (DMOPSO-CD) based on crowding distance is proposed to obtain global optimal solutions for the balance between energy consumption (EC) and effluent quality (EQ) in sewage treatment processes. The algorithm includes optimization modules and a self-organizing fuzzy neural network, enhancing the global search ability of particles, maintaining the diversity of non-inferior solutions, and addressing the crucial issues in multi-objective optimization of sewage treatment processes. The optimization results on a benchmark simulation model No.1 showed that the EC for wastewater treatment in dry, rainy, and storm weather was reduced by 7.87%, 6.28%, and 7.30%, respectively. This methodology outperformed several widely applied algorithms, including the multi-objective cuckoo search, non-dominated sorting genetic algorithm-II, and improving Pareto evolutionary algorithm, in terms of EQ and EC, providing a new approach for optimal decision-making in sewage treatment.