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Differential evolution algorithm with self-adaptive strategy and control parameters for P-xylene oxidation process optimization

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Abstract

Considering that the model of the \(p\)-Xylene (PX) oxidation reaction process is a hybrid and highly nonlinear model, a differential evolution algorithm with self-adaptive mutation strategy and control parameters (SSCPDE) was proposed to optimize the operating conditions. In SSCPDE, each individual has its own control parameters and mutation strategies that can be self-adaptively adjusted to different evolution phases and various optimization problems. SSCPDE was compared with 6 state-of-the-art DE variants by 38 different types of benchmark functions. Simulation results show that the average performance of SSCPDE is better than the six famous self-adaptive DE algorithms. Finally, the SSCPDE algorithm was used to optimize the five main operating conditions of the PX oxidation reaction process. Optimization results indicate that the production cost, loss of acetic acid and PX combustion of the PX oxidation reaction process are greatly reduced and that SSCPDE performs better than JADE, EPSDE, SaDE, and the optimizer of Aspen Plus and similar to jDE and CoDE.

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Acknowledgments

The authors gratefully acknowledge the support from the following foundations: 973 project of China (2013CB733600), National Natural Science Foundation of China (21176073) and the Fundamental Research Funds for the Central Universities. Meanwhile, the authors would like to thank Dr. Zhang, Dr. Brest, Dr. Mallipeddi, Dr. Wang, and Dr. Suganthan for providing the source codes of JADE, jDE, EPSDE, CoDE, and SaDE, respectively, and Dr. Xi Chen, who is a professor of Zhejiang University and very kind to freely provide the MAP interface toolbox for us.

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, P.O. BOX 293, MeiLong Road NO. 130, Shanghai , 200237, People’s Republic of China

    Qinqin Fan & Xuefeng Yan

Authors
  1. Qinqin Fan
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  2. Xuefeng Yan
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Correspondence to Xuefeng Yan.

Additional information

Communicated by V. Loia.

Appendix

Appendix

10 a.m. on the July 16, 2009

Operating conditions of reactor (D1-301)

HAC (%wt)

Pressure (MPag)

Drainage flowrate (T/h)

H2O (%wt)

  

73.75

1.41

58

6.95

  

10 a.m. on the July 16, 2009

Operation conditions of the first crystallizer (D1-401)

  

Temperature (\(^{\circ }\)C)

Level (%)

Total volume (m\(^{3}\))

Pressure (MPag)

  

187.26

57.72

135

1.1

  

10 a.m. on the July 16, 2009

Operation conditions of the first heater (E1-304)

Operation conditions of the second heater (E1-305)

  

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

  

158

1.43

136

1.42

  

5 a.m. on the July 8, 2009

Operating conditions of reactor (D1-301)

HAC (%wt)

Pressure (MPag)

Drainage flowrate (T/h)

H2O (%wt)

  

73.48

1.425

58

6.08

  

5 a.m. on the July 8, 2009

Operation conditions of the first crystallizer (D1-401)

  

Temperature (\(^{\circ }\)C)

Level (%)

Total volume (m\(^{3}\))

Pressure (MPag)

  

187.12

60.74

135

1.1

  

5 a.m. on the July 8, 2009

Operation conditions of the first heater (E1-304)

Operation conditions of the second heater (E1-305)

  

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

  

157

1.43

137

1.42

  

10 a.m. on the July 16, 2009

Operating conditions of reactor (D1-301)

Yield

Content of PX (%wt)

Mixed feed (T/h)

Inlet flowrate of air (T/h)

Total reactor volume (m\(^{3}\))

Flowrate of wastegas (kmol/h)

CTA (kg/h)

15.5

200.88

147.12

501

4392.56

45642.55

Operation conditions of the second crystallizer (D1-402)

Operation conditions of the third crystallizer (D1-403)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Total volume (m\(^{3}\))

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Total volume (m\(^{3}\))

156.1

0.27

135

92.05

\(-0.56\)

155

10 a.m. on the July 16, 2009

Operation conditions of the third heater (E1-306)

Operation conditions of the fourth heater (E1-307)

  

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

  

80

1.42

24

1.41

  

5 a.m. on the July 8, 2009

Operating conditions of reactor (D1-301)

Yield

Content of PX (%wt)

Mixed feed (T/h)

Inlet flowrate of air (T/h)

Total reactor volume (m\(^{3}\))

Flowrate of wastegas (kmol/h)

CTA (kg/h)

15.5

201.06

147.25

501

4446.65

46249.56

5 a.m. on the July 8, 2009

Operation conditions of the second crystallizer (D1-402)

Operation conditions of the third crystallizer (D1-403)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Total volume (m\(^{3}\))

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Total volume (m\(^{3}\))

156.4

0.28

135

92.19

\(-0.55\)

155

5 a.m. on the July 8, 2009

Operation conditions of the third heater (E1-306)

Operation conditions of the fourth heater (E1-307)

  

Temperature (\(^{\circ }\)C)

Pressure (MPag)

Temperature (\(^{\circ }\)C)

Pressure (MPag)

  

81

1.42

23

1.41

  

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Fan, Q., Yan, X. Differential evolution algorithm with self-adaptive strategy and control parameters for P-xylene oxidation process optimization. Soft Comput 19, 1363–1391 (2015). https://doi.org/10.1007/s00500-014-1349-y

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