Skip to main content
Have a personal or library account? Click to login
Multiobjective fuzzy-GSK algorithm in uncertain project management environments Cover

Multiobjective fuzzy-GSK algorithm in uncertain project management environments

International Journal on Smart Sensing and Intelligent Systems
Volume 18 (2025): Issue 1 (January 2025)
By:  and    
Open Access
|Jun 2025
Figures & tables

Figures & Tables

Figure 1:

FIS for linguistic antecedent and consequent variables. FIS, fuzzy inference system.

Figure 2:

Membership function for ME. ME, managerial expertise.

Figure 3:

Membership function for LE. LE, labor expertise.

Figure 4:

Membership function for WC. WC, weather conditions.

Figure 5:

Membership function for activity time.

Figure 6:

Membership function for activity cost.

Figure 7:

Set of fuzzy rules.

Pseudo-code for designing FIS

1, Set the number of activities of project network = act (say) and i = 1 (i is for increment). 2. Using FIS-Editor, add three antecedent variables namely, ME, LE, and WC in range [0, 1] and two consequent variables namely, “activity time” and “activity cost” in range “(T − 0.2 × T to T + 0.2 × T)” and “(P − 0.2 × P to P + 0.2 × P)”, respectively, as shown in Figure 1. 3. Add five membership functions for each antecedent linguistic variable as shown in Figures 2–4, respectively, and add seven membership functions for each consequent linguistic variable as shown in Figures 5 and 6, respectively. 4. Design “252” fuzzy rules set for ith activity as mentioned in Section “Set of fuzzy rules” 5. Defuzzification is applied to obtain the “precise time–cost” pair. 6. i = i +1. 7. Repeat steps 2–5 until i ≠ act.
Figure 8:

Vector xij during junior gaining and sharing of knowledge phase.

Pseudo-code 1:

Junior gaining and sharing of knowledge phase

fori = 1: Ndo   forj = 1: Djuniordo     ifrandomnumber ≤ Krthen         ifrank(xi) < rank (xr) then        xi,jnew=xi,j+Kfxi−1'−xi,+1'+xr,j'−xi,j         else        xi,jnew=xi,j+Kfxi−1'−xi,+1'+xr,j'−xi,j         end if     else          xi,jnew=xi,jold     end if   end forend for
Figure 9:

Vector xij during senior gaining and sharing of knowledge phase.

Pseudo-code 2:

Senior gaining and sharing of knowledge phase

fori = 1 : Ndo   forj = 1: Dseniordo     ifrandomnumber ≤ Krthen       ifrank(xi) < rank (xmiddle) then    xi,jnew=xi,j+Kfxpbest,j'−xpworst,j'+xmiddle,j'−xi,j       else    xijnew=xi,j+Kfxpbest,j'−xpworst,j'+xi,j−xmiddle,j'     end if       else      xi,jnew=xi,jold     end if   end forend for
Figure 10:

Working methodology of fuzzy-GSK. fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 11:

ZDT1 using fuzzy-GSK. fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 12:

ZDT2 using fuzzy-GSK. fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 13:

ZDT3 using fuzzy-GSK. fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 14:

ZDT6 using fuzzy-GSK. fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 15:

Linear TCT relationship of the project activity. TCT, time–cost trade-off.

Figure 16:

Network of seven activity test problem.

Figure 17:

Network of 13 activity test problem.

Figure 18:

Network of 18 activity test problem.

Figure 19:

Comparative analysis using fuzzy-GSK, fuzzy-NSGA-II and fuzzy-iMOGA (for seven activities). Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; Fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; Fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Figure 20:

Comparative analysis using fuzzy-GSK, fuzzy-NSGA-II, and fuzzy-iMOGA (for 13 activities). Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; Fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; Fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Figure 21:

Comparative analysis using fuzzy-GSK, fuzzy-NSGA-II, and fuzzy-iMOGA (for 18 activities). Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Table 1:

Test problem alternatives

ActivitiesCTNTCCNC
114242,4001,500
215253,0001,000
315334,5003,200
4122045,00030,000
5223020,00010,000
6142440,00018,000
7091830,00020,000

[i] CC, crash cost; CT, crash time; NC, normal cost; NT, normal time.

Table 2:

Test problem alternatives

ActivitiesCTNTCCNC
A114101,0001,600
A218154,0004,540
A319191,2001,200
A41513200440
A5808600600
A619162,1002,490
A722204,0004,600
A824241,2001,200
A927245,0005,450
A1020162,0002,200
A1122181,4001,900
A1218157001,150
A1320181,0001,200

[i] CC, crash cost; CT, crash time; NC, normal cost; NT, normal time.

Table 3:

Test problem alternatives

ActivitiesCTNTCCNC
114242,4001,500
215253,0001,000
315334,5003,200
4122045,00030,000
5223020,00010,000
6142440,00018,000
7091830,00020,000
81424220120
91525300100
101533450320
111220450300
1222302,0001,000
1314244,0001,800
1409183,0002,200
1516163,5003,500
1620303,0001,000
1714244,0001,800
1809183,0002,200

[i] CC, crash cost; CT, crash time; NC, normal cost; NT, normal time.

Figure 22:

Trade-off profiles using fuzzy-GSK for seven activities. Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 23:

Trade-off profiles using fuzzy-GSK for 13 activities. Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Figure 24:

Trade-off profiles using fuzzy-GSK for 18 activities. Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm.

Table 4:

Statistical analysis of fuzzy-GSK, fuzzy-NSGA-II, and fuzzy-iMOGA (for seven activities)

AlgorithmProject timeProject cost
MinMaxMeanMedianModeStdMinMaxMeanMedianModeStd
Fuzzy-GSK601057775.36013.059.62e+041.417e+051.137e+051.105e+059.62e+041.449e+04
Fuzzy-NSGA-II6010577.474.6810513.359.62e+041.418e+051.134e+051.112e+059.62e+041.419e+04
Fuzzy-iMOGA60.695.5674.773.0460.610.419.733e+041.422e+051.156e+051.137e+059.733e+051.334e+04

[i] Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; Fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; Fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Table 5:

Statistical Analysis of fuzzy-GSK, fuzzy-NSGA-II, and fuzzy-iMOGA (for 13 activities)

AlgorithmProject timeProject cost
MinMaxMeanMedianModeStdMinMaxMeanMedianModeStd
Fuzzy-GSK108125115.5115.31084.9512.44e+042.684e+042.543e+042.536e+042.44e+04729.3
Fuzzy-NSGA-II108125115.7115.51085.0142.44e+042.684e+042.541e+042.534e+042.44e+04735.9
Fuzzy-iMOGA108121.1114.11141083.942.46e+042.689e+042.562e+042.556e+042.46e+04672.3

[i] Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Table 6:

Statistical Analysis of fuzzy-GSK, fuzzy-NSGA-II, and fuzzy-iMOGA (for 18 activities)

AlgorithmProject timeProject cost
MinMaxMeanMedianModeStdMinMaxMeanMedianModeStd
Fuzzy-GSK104169125.7116.716920.079.804e+041.267e+051.07e+051.027e+059.084e+049,068
Fuzzy-NSGA-II104169123.8113.810419.239.81e+041.274e+051.077e+051.038e+059.81e+049,298
Fuzzy-iMOGA104136.6113.5111.11048.6911.029e+051.321e+051.16e+051.15e+051.029e+058,930

[i] Fuzzy-GSK, fuzzy-gaining sharing knowledge-based algorithm; Fuzzy-iMOGA, fuzzy-improved multi-objective genetic algorithm; Fuzzy-NSGA-II, fuzzy-non-dominated sorting genetic algorithm-II.

Table 7:

Statistical results for seven activities

Statistical ValuesCompletion timeTotal costUnpredictable Factors
Min56.027.815e+04ME = 0.9, LE = 0.8, WC = 0.1
Good conditions
Max98.021.148e+05
Mean70.489.11e+04
Median66.448.813e+04
Mode56.027.815e+04
Std12.691.174e+04
Range423.663e+04
Min608.372e+04ME = 0.5, LE = 0.5, WC = 0.5
Normal conditions
Max1051.23e+05
Mean76.19.717e+04
Median72.399.305e+04
Mode608.372e+04
Std13.861.275e+04
Range453.923e+04
Min66.329.253e+04ME = 0.9, LE = 0.5, WC = 0.1
Average conditions
Max116.11.338e+05
Mean84.471.062e+05
Median80.421.026e+05
Mode116.19.253e+04
Std14.771.259e+04
Range49.744.127e+04
Min68.799.594e+04ME = 0.1, LE = 0.1, WC = 0.1
Worst conditions
Max120.41.388e+05
Mean86.91.107e+05
Median83.331.063e+05
Mode68.799.594e+05
Std14.781.37e+04
Range51.584.285e+04

[i] LE, labor expertise; ME, managerial expertise; WC, weather conditions.

Table 8:

Statistical results for 13 activities

Statistical valuesCompletion timeTotal costUnpredictable factors
Min100.82.278e+04ME = 0.9, LE = 0.8, WC = 0.1
Good conditions
Max116.72.507e+04
Mean107.32.382e+04
Median106.82.38e+04
Mode100.82.278e+04
Std4.429676.5
Range15.852288
Min1082.44e+04ME = 0.5, LE = 0.5, WC = 0.5
Normal conditions
Max1252.708e+04
Mean1152.555e+04
Median114.22.544e+04
Mode1252.44e+04
Std5.068783.6
Range172677
Min119.42.684e+04ME = 0.9, LE = 0.5, WC = 0.1
Average conditions
Max138.22.967e+04
Mean127.22.809e+04
Median126.42.808e+04
Mode119.42.967e+04
Std5.522834.5
Range18.82822
Min123.82.779e+04ME = 0.1, LE = 0.1, WC = 0.1
Worst conditions
Max143.33.078e+04
Mean132.12.907e+04
Median131.92.899e+04
Mode123.82.799e+04
Std5.68878.2
Range19.482983

[i] LE, labor expertise; ME, managerial expertise; WC, weather conditions.

Table 9:

Statistical results for 18 activities

Statistical valuesCompletion timeTotal costUnpredictable factors
Min97.19.185e+04ME = 0.9, LE = 0.8, WC = 0.1
Good conditions
Max1411.45e+05
Mean112.41.028e+04
Median108.39.611e+04
Mode97.19.185e+04
Std13.591.294e+04
Range43.865.32e+04
Min1049.88e+04ME = 0.5, LE = 0.5, WC = 0.5
Normal conditions
Max1611.296e+05
Mean122.51.079e+05
Median113.91.036e+05
Mode1049.88e+04
Std17.029372
Range56.983.077e+04
Min114.91.089e+05ME = 0.9, LE-0.5, WC = 0.1
Average Conditions
Max182.81.528e+05
Mean137.61.196e+05
Median129.21.138e+05
Mode114.91.089e+05
Std21.361.142e+04
Range67.834.393e+04
Min119.21.124e+05ME = 0.1, LE = 0.1, WC = 0.1
Worst conditions
Max193.71.475e+05
Mean143.81.23e+05
Median1341.177e+05
Mode193.71.124e+05
Std23.151.102e+04
Range74.513.509e+04

[i] LE, labor expertise; ME, managerial expertise; WC, weather conditions.

DOI: https://doi.org/10.2478/ijssis-2025-0027 | Journal eISSN: 1178-5608
Journal RSS Feed
Language: English
Submitted on: Mar 26, 2025
Published on: Jun 7, 2025
Published by: International Journal on Smart Sensing and Intelligent Systems
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
Project Management,
Fuzzy logic,
Multiobjective optimization problems,
Fuzzy Inference System,
Gaining Sharing Knowledge-based algorithm
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2025 Talal A. Alshammari, Ali Wagdy Mohamed, published by International Journal on Smart Sensing and Intelligent Systems
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 18 (2025): Issue 1 (January 2025)
Previous article
Next article