Design and optimization of multidimensional control strategy based on optimization algorithm and modeling of wastewater treatment process
, et
24 mars 2025
À propos de cet article
Publié en ligne: 24 mars 2025
Reçu: 27 oct. 2024
Accepté: 10 févr. 2025
DOI: https://doi.org/10.2478/amns-2025-0732
Mots clés
© 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.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

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 |
