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Design and optimization of multidimensional control strategy based on optimization algorithm and modeling of wastewater treatment process

You Li

You Li

The Green Building and Low-carbon Technology Academy, Guangxi Mechanical and Electrical Vocational and Technical CollegeNanning, China
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Li, You
, 
Yueying Huang

Yueying Huang

Guangxi Zhuang Autonomous Region Environmental Protection Science Research InstituteNanning, China
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Huang, Yueying
 und 
Baoyue Zhang

Baoyue Zhang

Guangxi Zhuang Autonomous Region Geological and Mineral Testing and Research CenterNanning, China
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Zhang, Baoyue
  
24. März 2025
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Online veröffentlicht: 24. März 2025
Eingereicht: 27. Okt. 2024
Akzeptiert: 10. Feb. 2025
DOI: https://doi.org/10.2478/amns-2025-0732
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© 2025 You Li et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

The Schematic of wastewater treatment process
The Schematic of wastewater treatment process

Figure 2.

Multi-objective optimization control structure of wastewater treatment
Multi-objective optimization control structure of wastewater treatment

Figure 3.

Model results of EC
Model results of EC

Figure 4.

Model results of EQ
Model results of EQ

Figure 5.

Pareto optimal solutions and identify ofpreferred solution
Pareto optimal solutions and identify ofpreferred solution

Figure 6.

Solution of solution and control
Solution of solution and control

Figure 7.

Solution of solution
Solution of solution

Figure 8.

The determination of nitrate and the tracking control
The determination of nitrate and the tracking control

Figure 9.

Nitrous nitrogen tracking control error
Nitrous nitrogen tracking control error

Figure 10.

Variations of KLa with different time
Variations of KLa with different time

Figure 11.

Variations of Qa with different time
Variations of Qa with different time

Figure 12.

Optimized control curves and error plots of SO and SNO in sunny days
Optimized control curves and error plots of SO and SNO in sunny days

RPS pvalues for different optimization algorithms

Function name Index MSIMOSSA MOPSO MODA MOALO MOMVO MSSA
MMF1 Mean 0.0876 0.0816 0.0836 0.1286 0.0969 0.2215
Variance 0.049 0.0463 0.0285 0.0434 0.0328 0.0742
MMF2 Mean 0.0686 0.0359 0.0931 0.1304 0.0726 0.0778
Variance 0.0362 0.0198 0.0338 0.0874 0.0373 0.027
MMF3 Mean 0.0471 0.0689 0.0865 0.0675 0.0512 0.0986
Variance 0.0241 0.0395 0.0365 0.0277 0.045 0.0396
MMF8 Mean 0.1424 1.0264 0.1843 1.4026 1.453 1.8445
Variance 0.0808 0.6093 0.1064 0.7393 0.6186 0.7991
MMF12 Mean 1.0448 1.4048 1.0592 2.0869 2.3115 2.7801
Variance 0.5952 0.8052 0.5926 0.9307 0.7662 1.1146
MMF15 Mean 0.1962 0.4926 0.4136 0.4438 0.6363 0.5434
Variance 0.0927 0.2252 0.185 0.2199 0.2108 0.2218

IGD values of different optimization algorithms

Function name Index MSIMOSSA MOPSO MODA MOALO MOMVO MSSA
MMF1 Mean 0.0077 0.0098 0.008 0.0108 0.0081 0.0221
Variance 0.0044 0.0054 0.0036 0.0044 0.0036 0.0083
MMF2 Mean 0.0062 0.0137 0.0502 0.0166 0.0137 0.0204
Variance 0.0036 0.0073 0.0214 0.0067 0.0086 0.0075
MMF3 Mean 0.0059 0.0125 0.0325 0.0138 0.0068 0.0188
Variance 0.0035 0.0067 0.0116 0.0062 0.0031 0.0071
MMF8 Mean 0.008 0.0117 0.0102 0.0151 0.009 0.0192
Variance 0.0045 0.0063 0.0056 0.007 0.0038 0.0071
MMF12 Mean 0.0758 0.086 0.0927 0.0876 0.0792 0.0874
Variance 0.0378 0.0427 0.046 0.0305 0.0284 0.0311
MMF15 Mean 0.2148 0.1978 0.1939 0.2175 0.2262 0.2517
Variance 0.1013 0.093 0.094 0.0729 0.0757 0.0846

6 ceccec2022 test function parameter information

Function name Target number Functional relation The solution exists
MMF1 2 Nonlinearity No
MMF2 2 Nonlinearity Yes
MMF3 2 Nonlinearity Yes
MMF8 2 Nonlinearity No
MMF12 2 Linearity Yes
MMF15 3 Linearity Yes

Parameter setting of different multi-objective optimization algorithm

Algorithm Parameter setting
MSIMOSSA Q=230,q=450,FADs=0.1,P=0.4
MOEA/D Q=230,q=450,w=0.4
MODA Q=230,q=450,w=0.4~0.8
MOALO Q=230,q=450
MOMV0 Q=230,q=450
MSSA Q=230,q=450
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