NSGAIII based on utopian point improvements and its application in wastewater treatment process

To reduce energy consumption (EC) in the wastewater treatment process (WWTP) for achieving energy conservation and emission reduction, multi-objective evolutionary algorithm (MOEA) applied in WWTP needs to have better convergence and diversity. In this paper, a non-dominated sorting genetic algorithm III based on utopian point improvement (NSGAIII-UP) is proposed, which overcomes the disadvantage that multi-objective evolutionary algorithm based on utopian point decomposition (MOEA/D-UP) cannot handle the multi-segment discontinuous Pareto front (PF) problem well. By comparing the proposed NSGAIII-UP with 8 advanced algorithms by 2 metrics on 22 benchmark functions, the effectiveness of the proposed algorithm in dealing with the complex PF problems is proved. Moreover, a multivariable model predictive controller (MMPC) is used to control the dissolved oxygen and nitrate nitrogen concentrations in WWTP, in which NSGAIII-UP is applied to the upper EC optimization of WWTP. The simulation results show that compared with the closed-loop control, the EC in the WWTP is reduced by 7.395 %, and the lowest EC is achieved compared with the other 8 algorithms. It helps to reduce energy waste in WWTP and promotes ecological sustainability. The source code of NSGAIII-UP is publicly available at https://github.com/sut16/NSGAIII-UP.