Reverse Engineering of Radical Polymerizations by Multi-Objective Optimization
Abstract
:1. Introduction
2. Reverse Engineering Modeling Approach
2.1. Model Development
2.2. Data Acquisition and Processing
3. Results and Discussion
3.1. Direct Pareto Optimization
3.2. Clustering-Supported Pareto Optimization
4. Conclusions and Outlook
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Variables | Description | Restrictions |
---|---|---|
cm,0 | initial monomer concentration | cm,0(min) ≤ cm,0 ≤ cm,0(max) |
cini,0 | initial initiator concentration | cini,0(min) ≤ cini,0 ≤ cini,0(max) |
t | reaction time | tmin ≤ t ≤ tmax |
r = [cm,0, cini,0, t] | initial recipe |
Objectives | Description |
---|---|
fMSE(r)= | minimal MSE, where MMD(r) is simulated |
fcm(r)= | minimal relative monomer concentration |
ft(r) = t | minimal reaction time (directly from r) |
IDs of the Best Recipe | 1 | 34 | 2 | 46 | 20 | 37 | ||
---|---|---|---|---|---|---|---|---|
wi | Time Focus (A) | wi | Conversion Focus (B) | |||||
cm,0/mol∙L−1 | 2.0 | 2.21 | 2.0 | 2.21 | 2.43 | 2.43 | ||
cini,0/mmol∙L−1 | 20 | 20 | 20 | 8.4 | 16.1 | 20 | ||
time/min | 0.9 | 20 | 40 | 40 | 0.19 | 120 | 80 | 80 |
MSE/×10−3 | 0.05 | 1.63 | 1.37 | 0.08 | 0.01 | 1.72 | 1.58 | 1.81 |
conversion/% | 0.05 | 25.9 | 46.6 | 45.9 | 0.8 | 71.3 | 69.6 | 73.7 |
IDs of the Best Recipe | 35 | 32 | 21 | 43 | 12 | 7 | ||
wi | Equal Weights (C) | wi | MSE Focus (D) | |||||
cm,0/mol∙L−1 | 2.21 | 2.21 | 2.21 | 2.0 | 2.0 | 2.0 | ||
cini,0/mmol∙L−1 | 20.0 | 10.5 | 13.0 | 12.4 | 10.0 | 1.5 | ||
time/min | 1/3 | 60 | 80 | 80 | 0.01 | 180 | 200 | 160 |
MSE/×10−5 | 1/3 | 35 | 31 | 54 | 0.9 | 0.086 | 0.032 | 0.15 |
conversion/% | 1/3 | 61.8 | 60.2 | 64.4 | 0.09 | 48.3 | 48.2 | 48.2 |
Objective Weights | Cand. ID | cm,0/mol∙L−1 | cini,0/mmol∙L−1 | Time/min | MSE/10−3 | Conversion/% |
---|---|---|---|---|---|---|
0 | 2.00 | 20.0 | 20 | 1.63 | 25.9 | |
time focus: (wcm = 0.2, wt = 0.8) | 1 | 2.21 | 20.0 | 40 | 1.37 | 46.6 |
2 | 2.43 | 20.0 | 60 | 1.94 | 62.7 | |
equal weights: (wcm = 0.5, wt = 0.5) | 3 | 2.43 | 20.0 | 80 | 1.81 | 73.7 |
conversion focus: (wcm = 0.8, wt = 0.2) | 4 | 2.43 | 16.1 | 100 | 2.61 | 77.7 |
5 | 2.43 | 6.86 | 160 | 2.79 | 78.3 | |
6 | 2.43 | 5.54 | 180 | 2.83 | 78.5 | |
7 | 2.43 | 2.91 | 260 | 2.98 | 79.0 |
Number of Clusters | 20 | 40 | 60 | |
---|---|---|---|---|
Cand. ID/ | 3 | 2 | 1 | |
property | wi | |||
cm,0/mol∙L−1 | 3.50 | 3.07 | 2.86 | |
cini,0/mmol∙L−1 | 13.0 | 20.0 | 20.0 | |
time/min | 0.5 | 60.0 | 40.0 | 20.0 |
MSE/×10−3 | 3.04 | 0.32 | 0.03 | |
conversion/% | 0.5 | 58.2 | 49.2 | 27.0 |
score (wt = 0.5, wcm = 0.5) | 0.50 | 0.39 | 0.50 | |
score (wMSE = 1/3, wcm = 1/3, wt = 1/3) | 0.67 | 0.30 | 0.33 |
Approach | Direct | Clustering-Supported Approach | ||||
---|---|---|---|---|---|---|
20 Clusters | 40 Clusters | 60 Clusters | 80 Clusters | 100 Clusters | ||
execution time, s | 679 | 56 | 25 | 18 | 14 | 12 |
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Fiosina, J.; Sievers, P.; Kanagaraj, G.; Drache, M.; Beuermann, S. Reverse Engineering of Radical Polymerizations by Multi-Objective Optimization. Polymers 2024, 16, 945. https://doi.org/10.3390/polym16070945
Fiosina J, Sievers P, Kanagaraj G, Drache M, Beuermann S. Reverse Engineering of Radical Polymerizations by Multi-Objective Optimization. Polymers. 2024; 16(7):945. https://doi.org/10.3390/polym16070945
Chicago/Turabian StyleFiosina, Jelena, Philipp Sievers, Gavaskar Kanagaraj, Marco Drache, and Sabine Beuermann. 2024. "Reverse Engineering of Radical Polymerizations by Multi-Objective Optimization" Polymers 16, no. 7: 945. https://doi.org/10.3390/polym16070945