International Journal of Engineering Business
and Social Science
Vol. 1 No. 06, July-Augusts 2023, pages: 524-543
e-ISSN: 2980-4108, p-ISSN: 2980-4272
https://ijebss.ph/index.php/ijebss
524
Multi-Objective Performance Steady State Optimization Complete
Membrane-Based Liquid Desiccant Dehumidifier System
Devin Adiriwanto S
1
, Arnas Lubis
2
1,2
Universitas Indonesia
Email: devin[email protected]
Keywords
Abstract
Steady State, Complete
Membrane, Liquid
Desiccant, Dehumidifier
System
This study focuses on the multi-objective performance steady state optimization of a
complete membrane-based liquid desiccant dehumidifier system. The system is designed
to efficiently remove moisture from the air using liquid desiccant technology. The
objective of the optimization is to simultaneously maximize the dehumidification
performance, minimize energy consumption, and optimize the system's operational
parameters. A steady state model of the membrane-based liquid desiccant dehumidifier
system is developed, and a multi-objective genetic algorithm is applied to explore the
optimal solution space. The results demonstrate the trade-offs between dehumidification
performance and energy consumption, providing insights into the performance and
efficiency of the system. The proposed optimization approach offers a valuable tool for
designing and improving the performance of membrane-based liquid desiccant
dehumidifier systems in various applications.
© 2023 by the authors. Submitted
for possible open access publication
under the terms and conditions of the Creative Commons Attribution (CC BY SA)
license (https://creativecommons.org/licenses/by-sa/4.0/).
1. Introduction
Infiltration, ventilation, and occupants all contribute to the air conditioning load of a space structure. When
building heating, ventilation, and air conditioning systems for a building, thermal comfort, energy savings, and indoor
air quality are key considerations. Thermal comfort varies based on what is done. Heating ventilation air conditioning
(HVAC) systems typically must maintain an interior air temperature of 18-26°C and a relative humidity level of 40-
70% to provide comfortable thermal conditions for occupants In fact, 20-40% of the energy consumption of HVAC
systems is in air dehumidification. From the existing system, there are various problems such as weak ability to handle
latent heat loads, and fungal and bacterial growth. Liquid Desiccant has recently received great attention for its good
ability to remove latent heat and moisture loads. However, Liquid Desiccant droplets can be carried into a conditioned
space so as an alternative, a semi-permeable membrane is used to avoid carry-over problems. Bai et. al experimentally
and numerically found that the main parameters that determine the performance of the dehumidifier are NTU and mass
flow rate (m) and they interact with each other (Shirazi et al., 2018). Dehumidification performance is evaluated by
the parameters of sensible effectiveness, latent effectiveness, and moisture flux rate. In this report, an analysis will be
carried out on simulation-based multi-objective optimization with Effectiveness and Moisture Flux rate as conflicting
objective functions. By combining the two programs Design Expert and MATLAB, a multi-objective optimization
model for this case is formulated, thus a set of Optimal Pareto solutions can be determined (Grossman, 2002).
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This paper aims to present comprehensive data and analysis for designing and operating liquid desiccant
dehumidifier systems in the real world. Another thing is to do multi-objective system optimization and study the
optimization results between Design Expert, MATLAB with Design Expert equation, and MATLAB with ANN
equation (Bai et al., 2020).
• All components in this system are well isolated
• Liquid desiccant and airflow in a dehumidifier are considered laminar flow
• All thermodynamic processes operate at steady-state conditions
System Description
Scheme of Liquid Desiccant Dehumidifier System.
The liquid desiccant dehumidifier system mainly consists of a dehumidifier, regenerator, three heat
exchangers, two solution tanks, one chilled water supply unit, and one hot water supply unit. The liquid desiccant used
is Lithium chloride (LiCl). The cooled solution in the Heat Exchanger (HX3) flows to the dehumidifier, where the
temperature and humidity ratio is reduced by the strong solution so that the solution becomes diluted. The air from the
room is used as regenerating air in the regenerator where moist and hot air will be discharged out. Heat Exchanger
(HX1) is used for heat recovery, the dilute solution is further heated with hot water in the Heat Exchanger (HX2) before
flowing into the regenerator (Yuliani & Zainul, 2018). Airflow is regulated by 2 variable speed fans and calculated
with Testo Thermos anemometer with a range of 0-10m/s with accuracy The flow of the solution is driven by 2 15W
magnetic centrifugal pumps. The flow rate
of the solution through the dehumidifier and regenerator is adjusted
by the flow meter with a range of 1-15 L/min and the accuracy of the
Solution Concentration
viewed from the density sing Brannan Hydrometer with solution and
water temperature was calculated using
type K Thermocouple with a range of 0-1100 C and accuracy Air Humidity was calculated with Sensiron Evaluation
KIT with a range of 0-100% and accuracy
(Cheng et al., 2012)
Gambar 1 Skema Liquid Desicccant Dehumidifier System [1]
2. Materials and Methods
Working Flow Chart
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The process undertaken to complete this study can be seen in the flow chart below.
Data Retrieval
Import Data in Design
Expert
ANN in MATLAB
MATLAB optimization
using the Design Expert
equation
Generate function
Data Analysis
Optimization using
Design Expert
Generating Pareto
Front
Numerical and Graphic
Solutions
MATLAB optimization
using ANN function
Generating Pareto
Front
Paper Finalization
Figure 2. Research flowchart
Topsis
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Data Retrieval
The experimental data used in this study is taken from tables contained in reference journals and can be seen
in table 1. (Abdel-Salam et al., 2016)
Table 1 Experiment data
Response Surface Methodology Modelling
The response plot is generated from experimental data. Where there are 3 factors as input, namely NTU
dehumidifier, NTU regenerator, mass solution. And 2 responses as output, namely latent effectiveness (latent) and
Moisture Flux Rate. Where the goal of optimization is to get the maximum possible latent value and the maximum
possible moisture flux rate value. The statistically significant model p-value (p < 0.05) was developed using ANOVA,
Design Expert software (Al-Abidi et al., 2013). For the results of the response analysis from Design Expert can be
seen in the table below.
Factor 1 Factor 2 Factor 3 Response 1 Response 2
NTU de NTU re m solution e laten m flux rate
(kg/s)
1 4 0.009 0.251 0.0073
1 4 0.012 0.249 0.0068
4 4 0.0056 0.689 0.0049
6 6 0.0037 0.79 0.0038
4 4 0.0224 0.667 0.0046
8 4 0.012 0.833 0.0029
4 4 0.0112 0.718 0.0051
6 6 0.0074 0.831 0.0039
4 8 0.009 0.678 0.0049
4 1 0.009 0.702 0.0049
4 4 0.009 0.698 0.0048
8 4 0.009 0.85 0.0031
4 4 0.012 0.702 0.0046
4 8 0.012 0.676 0.0045
4 4 0.009 0.708 0.0048
4 4 0.012 0.682 0.0046
6 6 0.0148 0.807 0.0034
4 1 0.012 0.699 0.0048
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A. laten
Fit Summary:
Table 2 Fit Summary.
Anova:
Table 3 Anova
Actual Equation:
For A = NTU dehumidifier; B = NTU regenerator; C = m solution.
laten = -0.078686 + 0.251718A + 0.014844B + 9.03603C - 0.003080AB 0.591858AC + 0.248142BC -
0.016520
- 0.000943
- 333.91460
Diagnostic:
Source
Sequential
p-value
Lack of Fit
p-value
Adjusted R² Predicted R²
Linear < 0.0001 0.0140 0.7280 0.5951
2FI 0.9984 0.0105 0.6548 0.2787
Quadratic < 0.0001 0.4651 0.9941 0.9310 Suggested
Cubic 0.6579 0.2320 0.9928 Aliased
Source
Sum of
Squares
df Mean Square F-value p-value
Model 0.4760 9 0.0529 318.56 < 0.0001 significant
A-NTU de 0.1096 1 0.1096 660.42 < 0.0001
B-NTU re 0.0003 1 0.0003 1.81 0.2154
C-m solution 0.0004 1 0.0004 2.25 0.1723
AB 0.0002 1 0.0002 1.45 0.2624
AC 0.0001 1 0.0001 0.3530 0.5689
BC 0.0000 1 0.0000 0.0620 0.8096
A² 0.0903 1 0.0903 543.74 < 0.0001
B² 0.0003 1 0.0003 1.77 0.2198
C² 0.0008 1 0.0008 4.86 0.0585
Residual 0.0013 8 0.0002
Lack of Fit 0.0011 6 0.0002 1.44 0.4651 not significant
Pure Error 0.0002 2 0.0001
Cor Total 0.4773 17
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(a) (b)
(c) (d)
Figure 3. Normal plot (a); residual vs predicted (b); predicted vs actual (c); residual vs A: NTU de (d)
Table 4 Report
Run
Order
Actual
Value
Predicted
Value
Residual Leverage
Internally
Studentized
Residuals
Externally
Studentized
Residuals
Cook's
Distance
Influence
on Fitted
Value
DFFITS
Standard
Order
1 0.2510 0.2464 0.0046 0.688 0.644 0.619 0.092 0.919 1
2 0.7080 0.7008 0.0072 0.181 0.620 0.594 0.008 0.279 2
3 0.8500 0.8441 0.0059 0.689 0.825 0.806 0.151 1.201 3
4 0.2490 0.2536 -0.0046 0.688 -0.644 -0.619 0.092 -0.919 4
5 0.6820 0.7027 -0.0207 0.234 -1.837 -2.261 0.103 -1.250 5
6 0.8330 0.8389 -0.0059 0.689 -0.825 -0.806 0.151 -1.201 6
7 0.7020 0.7006 0.0014 0.688 0.189 0.177 0.008 0.262 7
8 0.6980 0.7008 -0.0028 0.181 -0.238 -0.223 0.001 -0.105 8
9 0.6780 0.6745 0.0035 0.689 0.482 0.458 0.052 0.681 9
10 0.6990 0.7004 -0.0014 0.688 -0.189 -0.177 0.008 -0.262 10
11 0.7020 0.7027 -0.0007 0.234 -0.064 -0.060 0.000 -0.033 11
12 0.6760 0.6795 -0.0035 0.689 -0.482 -0.458 0.052 -0.681 12
13 0.6890 0.6913 -0.0023 0.565 -0.271 -0.254 0.010 -0.290 13
14 0.7180 0.7028 0.0152 0.209 1.327 1.406 0.046 0.722 14
15 0.6670 0.6629 0.0041 0.975 2.011 2.676 16.026⁽¹⁾ 16.843⁽¹⁾ 15
16 0.7900 0.8024 -0.0124 0.697 -1.743 -2.069 0.699 -3.139⁽¹⁾ 16
17 0.8310 0.8144 0.0166 0.388 1.642 1.886 0.171 1.501 17
18 0.8070 0.8112 -0.0042 0.827 -0.783 -0.762 0.293 -1.665 18
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Moisture Flux Rate
Fit Summary:
Table 5 Fit Summary
Anova:
Table 6 Anova
Actual Equation:
For A = NTU dehumidifier; B = NTU regenerator; C = m solution.
= +0.008254 - 0.001037A + 0.000196 B – 0.060048C - 0.000019AB + 0.012569AC –
0.014098BC + 0.000045
+ 0.0000005712
+ 1.42484
Source
Sequential
p-value
Lack of Fit
p-value
Adjusted
R²
Predicted
R²
Linear < 0.0001 0.9315 0.9005 Suggested
2FI 0.8686 0.9181 0.8363
Quadratic 0.0121 0.9693 0.6939 Suggested
Cubic 0.7200 0.9585 Aliased
Source
Sum of
Squares
df
Mean
Square
F-value p-value
Model 0.0000 9 2,24E-03 60.54 < 0.0001 significant
A-NTU de 5,11E-03 1 5,11E-03 138.09 < 0.0001
B-NTU re 7,36E-05 1 7,36E-05 1.99 0.1961
C-m solution 2,20E-04 1 2,20E-04 5.94 0.0408
AB 8,87E-06 1 8,87E-06 0.2400 0.6374
AC 2,64E-05 1 2,64E-05 0.7146 0.4225
BC 3,33E-05 1 3,33E-05 0.8991 0.3708
A² 6,59E-04 1 6,59E-04 17.81 0.0029
B² 1,08E-07 1 1,08E-07 0.0029 0.9582
C² 1,47E-05 1 1,47E-05 0.3974 0.5460
Residual 2,96E-04 8 3,70E-05
Lack of Fit 2,96E-04 6 4,93E-05
Pure Error 0.0000 2 0.0000
Cor Total 0.0000 17
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Diagnostic:
(a) (b)
(c) (d)
Figure 5. Normal plot (a); residual vs predicted (b); predicted vs actual (c); residual vs A: NTU de (d)
Table 7. Report
Run
Order
Actual
Value
Predicte
d Value
Residual Leverage
Internally
Studentized
Residuals
Externally
Studentized
Residuals
Cook's
Distance
Influence
on Fitted
Value
DFFITS
Standard
Order
1 0.0073 0.0072 0.0001 0.688 1.295 1.362 0.370 2.023 1
2 0.0048 0.0048 -0.0000 0.181 -0.191 -0.179 0.001 -0.084 2
3 0.0031 0.0030 0.0001 0.689 1.129 1.152 0.283 1.716 3
4 0.0068 0.0069 -0.0001 0.688 -1.295 -1.362 0.370 -2.023 4
5 0.0046 0.0047 -0.0001 0.234 -0.740 -0.717 0.017 -0.396 5
6 0.0029 0.0030 -0.0001 0.689 -1.129 -1.152 0.283 -1.716 6
7 0.0049 0.0048 0.0001 0.688 0.550 0.525 0.067 0.779 7
8 0.0048 0.0048 -0.0000 0.181 -0.191 -0.179 0.001 -0.084 8
9 0.0049 0.0048 0.0001 0.689 0.569 0.544 0.072 0.810 9
10 0.0048 0.0049 -0.0001 0.688 -0.550 -0.525 0.067 -0.779 10
11 0.0046 0.0047 -0.0001 0.234 -0.740 -0.717 0.017 -0.396 11
12 0.0045 0.0046 -0.0001 0.689 -0.569 -0.544 0.072 -0.810 12
13 0.0049 0.0050 -0.0001 0.565 -0.690 -0.665 0.062 -0.759 13
14 0.0051 0.0048 0.0003 0.209 2.040 2.756 0.110 1.416 14
15 0.0046 0.0045 0.0001 0.975 1.786 2.154 12.632⁽¹⁾ 13.557⁽¹⁾ 15
16 0.0038 0.0039 -0.0001 0.697 -1.176 -1.210 0.318 -1.835 16
17 0.0039 0.0037 0.0002 0.388 1.151 1.178 0.084 0.938 17
18 0.0034 0.0034 -0.0000 0.827 -0.608 -0.583 0.177 -1.273 18
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3.4 Multi Objective Genetic Algorithm (MOGA) uses RSM equations .
Optimization using MATLAB R2015a Software. By inputting variables x1, x2, x3 as input. And f1 and f2
as objective functions of the actual equations RSM. For Optimization using the Optimization tool, choose solver
"gamultiobj", the number of variables "3", Lower Bounds "1 1 0.0037", Upper Bonds "8 8 0.0224", choose Pareto
front plot, then "start". Then you will get the pareto front plot, the number of iterations, and the final point table.
3.5. Multi Objective Genetic Algorithm (MOGA) uses the ANN equation.
Randomize the data first for the type of training, validation, testing. Where training must have the largest
range while testing and validation are included in the range of training. After input the data factor and response into
the workspace. Select "Neural Network Pattern Recognition Tools". Number of hidden neurons = 10, dividing the
data as 70% training, 15% validation, 15% testing. Choose Levenberg-Marquard as the training algorithm (Factor
& Grossman, 1980). Then the results of Performance, Training State, Error Histogram, Regression are obtained. After
that, use the Optimization tool to optimize the ANN equation that has been generated.
Table. 8 Randomized Experiment Data
NTU de NTU re
m
solution
e laten
m flux
rate
(kg/s)
1 4 0.009 0.251 0.0073
1 4 0.012 0.249 0.0068
4 4 0.0056 0.689 0.0049
6 6 0.0037 0.79 0.0038
4 4 0.0224 0.667 0.0046
8 4 0.012 0.833 0.0029
4 4 0.0112 0.718 0.0051
4 8 0.012 0.676 0.0045
4 8 0.009 0.678 0.0049
4 1 0.009 0.702 0.0049
4 1 0.012 0.699 0.0048
8 4 0.009 0.85 0.0031
4 4 0.012 0.702 0.0046
6 6 0.0074 0.831 0.0039
4 4 0.009 0.708 0.0048
4 4 0.012 0.682 0.0046
6 6 0.0148 0.807 0.0034
4 4 0.009 0.698 0.0048
Training
Validation
Testing
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(a) (b) (c)
Gambar 6. Performance (a); Training State (b); Error Histogram (c)
Figure 7. Regression
3.6 TOPSIS
By using the results of objective function 1 and objective function 2 from MOGA-RSM and MOGA-ANN,
TOPSIS will be carried out using Microsoft Excel 2019 software with the following steps:(Chen et al., 2014)
1. Calculates a normalized matrix using the following equation:.
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data ke e laten moisture flux rate
1 0,182350328 0,090535746
2 0,145246787 0,090535746
3 0,182350328 0,090535746
4 0,070134741 0,135803619
5 0,116287926 0,090535746
6 0,091401405 0,135803619
7 0,059275169 0,135803619
8 0,141626929 0,090535746
9 0,155201396 0,090535746
10 0,03484113 0,135803619
11 0,045700702 0,135803619
12 0,057012758 0,135803619
13 0,109048211 0,135803619
14 0,168323379 0,090535746
15 0,083256725 0,135803619
16 0,102260978 0,135803619
17 0,131219839 0,090535746
18 0,080994314 0,135803619
Table 9. results for MOGA-RSM
Table 10. results for MOGA-ANN
1. Calculate the weight of a normalized matrix
Table 11. results for MOGA-RSM Table 12. results for
MOGA-ANN
2. Calculate ideal best and ideal worst value. Because both objective functions want to be maximized, the
maximum value for the ideal best value and the minimum value for the ideal worst value
data ke e laten moisture flux rate
1 0,364700655 0,181071492
2 0,290493574 0,181071492
3 0,364700655 0,181071492
4 0,140269483 0,271607238
5 0,232575852 0,181071492
6 0,18280281 0,271607238
7 0,118550337 0,271607238
8 0,283253859 0,181071492
9 0,310402791 0,181071492
10 0,069682259 0,271607238
11 0,091401405 0,271607238
12 0,114025515 0,271607238
13 0,218096422 0,271607238
14 0,336646759 0,181071492
15 0,166513451 0,271607238
16 0,204521956 0,271607238
17 0,262439678 0,181071492
18 0,161988629 0,271607238
data ke e laten moisture flux rate
1 0,300573394 0,181443685
2 0,349367776 0,090721842
3 0,248851349 0,226804606
4 0,32692236 0,181443685
5 0,197129304 0,226804606
6 0,291302461 0,181443685
7 0,280079753 0,181443685
8 0,314723765 0,181443685
9 0,124425674 0,272165527
10 0,209327899 0,226804606
11 0,178099495 0,226804606
12 0,114178854 0,317526448
13 0,098076708 0,317526448
14 0,228845652 0,226804606
15 0,132720719 0,272165527
16 0,340584787 0,136082763
17 0,094661101 0,317526448
18 0,094661101 0,317526448
data ke e laten moisture flux rate
1 0,150286697 0,090721842
2 0,174683888 0,045360921
3 0,124425674 0,113402303
4 0,16346118 0,090721842
5 0,098564652 0,113402303
6 0,145651231 0,090721842
7 0,140039877 0,090721842
8 0,157361882 0,090721842
9 0,062212837 0,136082763
10 0,10466395 0,113402303
11 0,089049747 0,113402303
12 0,057089427 0,158763224
13 0,049038354 0,158763224
14 0,114422826 0,113402303
15 0,06636036 0,136082763
16 0,170292394 0,068041382
17 0,047330551 0,158763224
18 0,047330551 0,158763224
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Table 13. V+ and V- for MOGA-RSM Table 14. V+ and V- for MOGA-ANN
3. Calculate Euclidean distance from ideal best and ideal worst with the following equation.
Table 15. Si+ and Si- for MOGA-RSM Table 16. Si+ and Si- for MOGA-ANN
4. Calculate performance with the following equation and determine the ranking.
e laten moisture flux rate
V+ 0,18235 0,135803619
V- 0,034841 0,090535746
e laten moisture flux rate
V+ 0,174684 0,158763224
V- 0,047331 0,045360921
Si+ Si-
0,045267873 0,147509198
0,058530787 0,110405657
0,045267873 0,147509198
0,112215586 0,057400517
0,080083839 0,081446796
0,090948923 0,072444773
0,123075159 0,051441254
0,060889864 0,1067858
0,052784892 0,120360266
0,147509198 0,045267873
0,136649625 0,046552236
0,12533757 0,050405966
0,073302117 0,086924515
0,047391303 0,13348225
0,099093602 0,066281598
0,08008935 0,081207243
0,068289876 0,096378709
0,101356013 0,064647481
Si+ Si-
0,072283142 0,112505916
0,113402303 0,127353337
0,06770156 0,102826493
0,068960705 0,124675323
0,088610108 0,085173721
0,073976515 0,10828005
0,07635337 0,10321159
0,070211691 0,119014735
0,114735089 0,091934407
0,083429041 0,088976111
0,096906239 0,079813038
0,117594461 0,11382143
0,125645534 0,113415162
0,075425518 0,095556282
0,110672445 0,092696204
0,090828068 0,125036067
0,127353337 0,113402303
0,127353337 0,113402303
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Table 17. Performance MOGA-RSM Table18. Performance MOGA-ANN
3. Results and Discussions
3.1 RSM
RSM results show the largest response value and the smallest response value due to input factors. In figure
(a), namely with the input factor NTU dehumidifier and NTU regenerator, for the response, namely e latent and
moisture flux rate. If the NTU dehumidifier is larger, the latent e will tend to be larger, while the moisture flux rate
tends to be smaller. In figure (b), namely with the input factor NTU dehumidifier and mass solution. In figure (c),
namely with the input factor NTU regenerator and mass solution(Elsayed et al., 1993).
(a) NTU dehumidifer dan NTU regenerator (a) NTU dehumidifer dan NTU regenerator
Pi Ranking
0,608834298 3
0,528973432 9
0,602988725 4
0,643864288 1
0,490113041 12
0,594107817 5
0,574786917 7
0,628954093 2
0,444837815 18
0,516087307 10
0,451637417 17
0,491847944 11
0,474419943 13
0,558868149 8
0,455803806 16
0,579235023 6
0,471026568 14
0,471026568 14
Pi Ranking
0,765180201 1
0,653533686 5
0,765180201 1
0,338414313 14
0,504218883 9
0,443375569 11
0,294764561 15
0,636859265 6
0,695140813 4
0,234819799 18
0,254103509 17
0,286815476 16
0,54250978 8
0,737986553 3
0,400795269 12
0,503465333 10
0,585288984 7
0,389434458 13
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\
(b) NTU dehumidifier dan mass solution (b) NTU dehumidifier dan mass solution
(c) NTU regenerator dan mass solution (c) NTU regenerator dan mass solution
Figure 8. Response surface contours from Figure 9. Response surface contours of
factors against latent. (a) NTU de factor - factor against moisture flux rate.
and NTU re, (b) NTU de and m solution, (c) (a) NTU de and NTU re, (b) NTU de and
NTU re and m solution. m solution, (c) NTU re and m solution.
The results of Design Expert Optimization can also be in the form of tables. Design Expert has a large
selection of optimization goals. Because in the liquid desiccant dehumidifier system is to get the largest possible
response, we can choose "maximize" for response and "in range" for factors(Elsayed et al., 1993). The results of
Design Expert optimization can be seen in table 19. There are 32 types of choices and the best choice is at number one.
Table 19. Design Expert optimization results
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3.2 Multi Objective Genetic Algorithm (MOGA)
For MOGA Optimization, use the equation from Design Expert and the EN equation. The results of pareto
front optimization MOGA with RSM equation and optimization MOGA with ANN equation are presented in the
form of pareto front in figure 10 and presented in table 20 and table 21. For pareto a and b have similarities in form
but differ in value. (FACTOR & GROSSMAN, n.d.)
Pareto Front:
Number NTU de NTU re m solution e laten m flux rate Desirability
1 3.605 8.000 0.004 0.612 0.006 0.621 Selected
2 3.580 8.000 0.004 0.609 0.006 0.621
3 3.602 7.957 0.004 0.612 0.006 0.621
4 3.600 7.942 0.004 0.612 0.006 0.621
5 3.648 8.000 0.004 0.616 0.006 0.621
6 3.604 7.897 0.004 0.613 0.006 0.621
7 3.642 7.945 0.004 0.616 0.006 0.621
8 3.610 7.851 0.004 0.614 0.006 0.621
9 3.585 7.824 0.004 0.612 0.006 0.621
10 3.681 7.999 0.004 0.620 0.006 0.621
11 3.613 7.740 0.004 0.615 0.006 0.621
12 3.556 7.797 0.004 0.609 0.006 0.621
13 3.526 7.897 0.004 0.604 0.006 0.621
14 3.580 7.996 0.004 0.610 0.006 0.620
15 3.566 7.364 0.004 0.614 0.006 0.620
16 3.618 6.436 0.004 0.627 0.006 0.618
17 3.981 7.522 0.004 0.655 0.005 0.616
18 3.679 5.772 0.004 0.639 0.005 0.615
19 3.594 5.689 0.004 0.630 0.006 0.614
20 3.621 4.887 0.004 0.637 0.005 0.610
21 3.729 2.630 0.004 0.656 0.005 0.592
22 4.574 1.000 0.022 0.707 0.005 0.588
23 4.523 1.000 0.022 0.702 0.005 0.588
24 4.496 1.015 0.022 0.700 0.005 0.587
25 4.636 1.022 0.022 0.712 0.005 0.587
26 4.524 1.031 0.022 0.703 0.005 0.587
27 4.506 1.063 0.022 0.701 0.005 0.586
28 4.194 1.000 0.020 0.690 0.005 0.584
29 4.150 1.000 0.018 0.699 0.005 0.582
30 4.089 1.000 0.018 0.693 0.005 0.582
31 3.885 1.000 0.017 0.675 0.005 0.581
32 3.843 1.000 0.013 0.681 0.005 0.580
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(a) MOGA - RSM (b) MOGA - ANN
Figure 10. Pareto Front. (a) MOGA – RSM, (b) MOGA - ANN
Tabel:
f1 = laten; f2 = moisture flux rate; x1 = NTU dehumidifier; x2 = NTU regenerator; x3 = mass solution.
Tabel 20. MOGA - RSM
Tabel 21. MOGA - ANN
data ke f1 f2 x1 x2 x3
1 0,616 0,004 3,603 7,904 0,022
2 0,716 0,002 7,944 7,942 0,022
3 0,51 0,005 2,641 7,601 0,022
4 0,67 0,004 4,221 7,835 0,022
5 0,404 0,005 1,883 7,814 0,022
6 0,597 0,004 3,412 7,892 0,022
7 0,574 0,004 3,185 7,809 0,022
8 0,645 0,004 3,9 7,4 0,022
9 0,255 0,006 1,151 3,363 0,022
10 0,429 0,005 2,058 7,321 0,022
11 0,365 0,005 1,636 7,468 0,022
12 0,234 0,007 1,194 1,03 0,022
13 0,201 0,007 1 1 0,021
14 0,469 0,005 2,337 7,7 0,022
15 0,272 0,006 1,205 4,127 0,022
16 0,698 0,003 4,643 7,855 0,022
17 0,194 0,007 1 1 0,022
18 0,194 0,007 1 1 0,022
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Figure 11. Pareto Front for 3 types of optimization. RSM, MOGA – RSM, MOGA – ANN
From figure 11 shows the most optimal objective function is through the RSM Design Expert method. Where
to get the maximum possible value is latent e of 0.006 and moisture flux rate of 0.006. The input factor is NTU
Dehumidifier of 3.605, NTU Regenerator of 8, and mass solution of 0.004.
data ke f1 f2 x1 x2 x3
1 0,403 0,002 1,687 4,246 0,004
2 0,321 0,002 1,055 5,541 0,006
3 0,403 0,002 1,687 4,246 0,004
4 0,155 0,003 1,016 7,902 0,012
5 0,257 0,002 1,097 6,735 0,008
6 0,202 0,003 1,042 7,491 0,009
7 0,131 0,003 1,021 7,96 0,013
8 0,313 0,002 1,115 5,97 0,006
9 0,343 0,002 1,194 5,43 0,006
10 0,077 0,003 1 7,995 0,016
11 0,101 0,003 1,011 7,972 0,014
12 0,126 0,003 1,013 7,96 0,013
13 0,241 0,003 1,099 6,816 0,009
14 0,372 0,002 1,306 5,156 0,004
15 0,184 0,003 1,139 7,812 0,011
16 0,226 0,003 1,063 7,106 0,009
17 0,29 0,002 1,051 5,905 0,007
18 0,179 0,003 1,106 7,828 0,011
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3.3 TOPSIS.
The purpose of TOPSIS is to determine the most optimal point generated by the equation RSM - DE, MOGA
- equation DE, MOGA - equation ANN. In optimizing the RSM – DE equation, topsis is not done because the value
of the most optimal solution can be determined from desirability(Ru & Yan, 1992). The results of the TOPSIS MOGA
equation DE can be seen in table 22.
The results of the TOPSIS MOGA ANN equation can be seen in table 23.
Table 22. Result TOPSIS MOGA - RSM
Table 23. Result TOPSIS MOGA - ANN
data ke f1 f2 x1 x2 x3 ranking
1 0,616 0,004 3,603 7,904 0,022 3
2 0,716 0,002 7,944 7,942 0,022 9
3 0,51 0,005 2,641 7,601 0,022 4
4 0,67 0,004 4,221 7,835 0,022 1
5 0,404 0,005 1,883 7,814 0,022 12
6 0,597 0,004 3,412 7,892 0,022 5
7 0,574 0,004 3,185 7,809 0,022 7
8 0,645 0,004 3,9 7,4 0,022 2
9 0,255 0,006 1,151 3,363 0,022 18
10 0,429 0,005 2,058 7,321 0,022 10
11 0,365 0,005 1,636 7,468 0,022 17
12 0,234 0,007 1,194 1,03 0,022 11
13 0,201 0,007 1 1 0,021 13
14 0,469 0,005 2,337 7,7 0,022 8
15 0,272 0,006 1,205 4,127 0,022 16
16 0,698 0,003 4,643 7,855 0,022 6
17 0,194 0,007 1 1 0,022 14
18 0,194 0,007 1 1 0,022 14
data ke f1 f2 x1 x2 x3 ranking
1 0,403 0,002 1,687 4,246 0,004 1
2 0,321 0,002 1,055 5,541 0,006 5
3 0,403 0,002 1,687 4,246 0,004 1
4 0,155 0,003 1,016 7,902 0,012 14
5 0,257 0,002 1,097 6,735 0,008 9
6 0,202 0,003 1,042 7,491 0,009 11
7 0,131 0,003 1,021 7,96 0,013 15
8 0,313 0,002 1,115 5,97 0,006 6
9 0,343 0,002 1,194 5,43 0,006 4
10 0,077 0,003 1 7,995 0,016 18
11 0,101 0,003 1,011 7,972 0,014 17
12 0,126 0,003 1,013 7,96 0,013 16
13 0,241 0,003 1,099 6,816 0,009 8
14 0,372 0,002 1,306 5,156 0,004 3
15 0,184 0,003 1,139 7,812 0,011 12
16 0,226 0,003 1,063 7,106 0,009 10
17 0,29 0,002 1,051 5,905 0,007 7
18 0,179 0,003 1,106 7,828 0,011 13
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Table 24. The optimum point in each optimization method.
3.4. Discussion
Based on the results of optimization that has been carried out and TOPSIS as a decision support, the multi-
objective optimization method that produces the most optimal objective function value is optimization with Design
Expert (RSM) software. The most optimal objective function value through the Design Expert software optimization
method is latent of 0.612 and moisture flux rate of 0.006. Both objective function values have fulfilled the
optimization goal, namely the maximum latent value possible with the maximum possible moisture flux rate value
(GROSSMAN, 2002). For the MOGA optimization method with the RSM , quation has an optimum objective function
value that is close to optimization with Design Expert software, namely latent value of 0.67 and a moisture flux
rate of 0.004. While MOGA optimization with the ANN equation has the optimum objective function value that is
most different from the other two optimization methods, namely the latent value of 0.403 and the moisture flux rate
of 0.002. This may be due to differences between the ANN-generated equations and the Design Expert-generated
equations. Errors in data randomization can also affect the ANN equation produced by MATLAB, so the pareto front
also experiences differences.
4. Conclusion
From the optimization of RSM, MOGA – RSM, MOGA – ANN that has been carried out in a complete membrane-
based liquid desiccant dehumidifier system, the following conclusions can be drawn:
1. The RSM method has the most optimal objective function value compared to the other two methods.
2. The MOGA – ANN method has the most different objective function value from the other 2 optimization
methods.
Errors in the data randomization method can affect the results of the generated ANN equation .
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MOGA - RSM 0,67 0,004 4,221 7,835 0,022
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