Author Contributions
Conceptualization, B.C., F.C.-C. and R.S.; methodology, B.C., F.C.-C., C.P.T.M.-l., J.L.A. and F.S.-P.; software, F.C.-C., C.P.T.M.-l., J.L.A. and F.S.-P.; validation, B.C., F.C.-C., R.S., G.A. and G.G.; formal analysis, C.P.T.M.-l., J.L.A. and F.S.-P.; investigation, B.C., F.C.-C., R.S., C.P.T.M.-l., J.L.A., F.S.-P., G.A. and G.G.; resources, C.P.T.M.-l., J.L.A., F.S.-P. and G.A.; writing—original draft preparation, C.P.T.M.-l., J.L.A., F.S.-P. and G.A.; writing—review and editing, B.C., F.C.-C., R.S. and G.G.; supervision, B.C., F.C.-C. and R.S.; funding acquisition, B.C. and R.S. All authors have read and agreed to the published version of the manuscript.
Figure 1.
S-shaped and V-shaped transfer functions.
Figure 1.
S-shaped and V-shaped transfer functions.
Figure 2.
Convergence analysis of the instances Scp 41, Scp 51 and Scp 61.
Figure 2.
Convergence analysis of the instances Scp 41, Scp 51 and Scp 61.
Figure 3.
Convergence analysis of the instances Scp a1, Scp b1 and Scp c1.
Figure 3.
Convergence analysis of the instances Scp a1, Scp b1 and Scp c1.
Figure 4.
Convergence analysis of the instances Scp d1, Scp nre1 and Scp nrf1.
Figure 4.
Convergence analysis of the instances Scp d1, Scp nre1 and Scp nrf1.
Figure 5.
Convergence analysis of the instances Scp nrg1 and Scp nrh1.
Figure 5.
Convergence analysis of the instances Scp nrg1 and Scp nrh1.
Figure 6.
Time analysis of the instances Scp 41, Scp 51 and Scp 61.
Figure 6.
Time analysis of the instances Scp 41, Scp 51 and Scp 61.
Figure 7.
Time analysis of the instances Scp a1, Scp b1 and Scp c1.
Figure 7.
Time analysis of the instances Scp a1, Scp b1 and Scp c1.
Figure 8.
Time analysis of the instances Scp d1, Scp nre1 and Scp nrf1.
Figure 8.
Time analysis of the instances Scp d1, Scp nre1 and Scp nrf1.
Figure 9.
Time analysis of the instances Scp nrg1, Scp nre1 and Scp nrh1.
Figure 9.
Time analysis of the instances Scp nrg1, Scp nre1 and Scp nrh1.
Figure 10.
Convergence analysis of the instances UScp 41, UScp 51 and UScp 61.
Figure 10.
Convergence analysis of the instances UScp 41, UScp 51 and UScp 61.
Figure 11.
Convergence analysis of the instances UScp a1, UScp b1 and UScp c1.
Figure 11.
Convergence analysis of the instances UScp a1, UScp b1 and UScp c1.
Figure 12.
Convergence analysis of the instances UScp d1, UScp unre1 and UScp unrg1.
Figure 12.
Convergence analysis of the instances UScp d1, UScp unre1 and UScp unrg1.
Figure 13.
Convergence analysis of the instances UScp unrh1, UScp clr10 and UScp clr11.
Figure 13.
Convergence analysis of the instances UScp unrh1, UScp clr10 and UScp clr11.
Figure 14.
Convergence analysis of the instances UScp clr12, UScp cyc06 and UScp cyc07.
Figure 14.
Convergence analysis of the instances UScp clr12, UScp cyc06 and UScp cyc07.
Figure 15.
Convergence analysis of the instance UScp cyc08.
Figure 15.
Convergence analysis of the instance UScp cyc08.
Figure 16.
Time analysis of the instances UScp 41, UScp 51 and UScp 61.
Figure 16.
Time analysis of the instances UScp 41, UScp 51 and UScp 61.
Figure 17.
Time analysis of the instances UScp a1, UScp b1 and UScp c1.
Figure 17.
Time analysis of the instances UScp a1, UScp b1 and UScp c1.
Figure 18.
Time analysis of the instances UScp nre1, UScp nrf1 and UScp nrg1.
Figure 18.
Time analysis of the instances UScp nre1, UScp nrf1 and UScp nrg1.
Figure 19.
Time analysis of the instances UScp nrh1, UScp clr10 and UScp clr11.
Figure 19.
Time analysis of the instances UScp nrh1, UScp clr10 and UScp clr11.
Figure 20.
Time analysis of the instances UScp clr12, UScp cyc06 and UScp cyc07.
Figure 20.
Time analysis of the instances UScp clr12, UScp cyc06 and UScp cyc07.
Figure 21.
Time analysis of the instance cyc08.
Figure 21.
Time analysis of the instance cyc08.
Table 1.
Incidence Matrix (A), where if consultant j covers requirement i.
Table 1.
Incidence Matrix (A), where if consultant j covers requirement i.
| C1 (Anne) | C2 (Ben) | C3 (Carla) | C4 (David) | C5 (Elena) | C6 (Frank) |
---|
R1 (Fin.) | 1 | 0 | 0 | 0 | 1 | 0 |
R2 (Legal) | 1 | 0 | 1 | 0 | 0 | 1 |
R3 (Tech.) | 0 | 1 | 1 | 0 | 1 | 0 |
R4 (Mkt.) | 0 | 1 | 0 | 1 | 0 | 1 |
R5 (Log.) | 0 | 0 | 1 | 1 | 0 | 0 |
Table 2.
S-shaped and V-shaped transfer functions.
Table 2.
S-shaped and V-shaped transfer functions.
S-Shaped | V-Shaped |
---|
Name | Equation | Name | Equation |
---|
S1 | | V1 | |
S2 | | V2 | |
S3 | | V3 | |
S4 | | V4 | |
Table 3.
Instances used for parameter configuration.
Table 3.
Instances used for parameter configuration.
Instance | Type Problem | M | N | Density (%) | Optimum |
---|
41 | SCP | 200 | 1000 | 2.00 | 429 |
61 | SCP | 200 | 2000 | 5.00 | 138 |
b1 | SCP | 300 | 3000 | 5.00 | 69 |
d1 | SCP | 400 | 4000 | 5.00 | 60 |
clr10 | USCP | 511 | 210 | 12.30 | 25 |
clr11 | USCP | 1023 | 330 | 12.40 | 23 |
cyc06 | USCP | 240 | 192 | 2.10 | 60 |
cyc07 | USCP | 672 | 448 | 0.90 | 144 |
Table 4.
Parameter selection.
Table 4.
Parameter selection.
Pop | Iter | Instance | Best Fitness | Worst Fitness | Average | Time Seconds | Time Minutes |
---|
10 | 500 | 41 | 433 | 433 | 433 | 104.18 | 1.74 |
10 | 70 | 61 | 141 | 141 | 141 | 10.32 | 0.17 |
10 | 400 | b1 | 69 | 69 | 69 | 233.97 | 3.9 |
10 | 600 | clr10 | 25 | 27 | 25.43 | 51.69 | 0.86 |
10 | 900 | clr11 | 23 | 26 | 24.57 | 185.9 | 3.1 |
10 | 600 | cyc06 | 60 | 60 | 60 | 52.07 | 0.87 |
10 | 500 | cyc07 | 144 | 154 | 149.71 | 240.98 | 4.02 |
10 | 1000 | d1 | 60 | 61 | 60.43 | 1297.6 | 21.63 |
Table 5.
Configuration of parameters.
Table 5.
Configuration of parameters.
Parameter | Value | |
---|
All MH | Population size | 10 |
Iterations | 600 |
Independent runs | 31 |
Transfer functions | V3 |
Method of discretization | Elitist |
PSO | | 0.1 |
| 0.9 |
| 2 |
| 2 |
GWO | a | linearly decreases from 2 to 0 |
SBOA | CF | potentially decreases at 0 |
Table 6.
Instances used for the SCP.
Table 6.
Instances used for the SCP.
Instance | M | N | Density (%) | Optimum |
---|
41 | 200 | 1000 | 2.00 | 429 |
42 | 200 | 1000 | 2.00 | 512 |
51 | 200 | 2000 | 2.00 | 253 |
52 | 200 | 2000 | 2.00 | 302 |
61 | 200 | 1000 | 5.00 | 138 |
62 | 200 | 1000 | 5.00 | 146 |
A1 | 300 | 3000 | 2.00 | 253 |
A2 | 300 | 3000 | 2.00 | 252 |
B1 | 300 | 3000 | 5.00 | 69 |
B2 | 300 | 3000 | 5.00 | 76 |
C1 | 400 | 4000 | 2.00 | 227 |
C2 | 400 | 4000 | 2.00 | 219 |
D1 | 400 | 4000 | 5.00 | 60 |
D2 | 400 | 4000 | 5.00 | 66 |
NRE1 | 500 | 5000 | 10.00 | 29 |
NRE2 | 500 | 5000 | 10.00 | 30 |
NRF1 | 500 | 5000 | 20.00 | 14 |
NRF2 | 500 | 5000 | 20.00 | 15 |
NRG1 | 1000 | 10,000 | 2.00 | 176 |
NRG2 | 1000 | 10,000 | 2.00 | 154 |
NRH1 | 1000 | 10,000 | 5.00 | 63 |
NRH2 | 1000 | 10,000 | 5.00 | 63 |
Table 7.
Instances used for the USCP.
Table 7.
Instances used for the USCP.
Instance | M | N | Density (%) | Optimum |
---|
U41 | 200 | 1000 | 2.00 | 38 |
U51 | 200 | 2000 | 2.00 | 34 |
U61 | 200 | 1000 | 5.00 | 21 |
UA1 | 300 | 3000 | 2.00 | 39 |
UB1 | 300 | 3000 | 5.00 | 22 |
UC1 | 400 | 4000 | 2.00 | 43 |
UD1 | 400 | 4000 | 5.00 | 24 |
UNRE1 | 500 | 5000 | 10.00 | 17 |
UNRF1 | 500 | 5000 | 20.00 | 10 |
UNRG1 | 1000 | 10,000 | 2.00 | 61 |
UNRH1 | 1000 | 10,000 | 5.00 | 34 |
CLR10 | 511 | 210 | 12.30 | 25 |
CLR11 | 1023 | 330 | 12.40 | 23 |
CLR12 | 2047 | 495 | 12.50 | 23 |
CYC06 | 240 | 192 | 2.10 | 60 |
CYC07 | 672 | 448 | 0.90 | 144 |
CYC08 | 1792 | 1024 | 0.40 | 344 |
Table 8.
Fitness results per SCP instance.
Table 8.
Fitness results per SCP instance.
MH | Instance | Opt. | Best | Worst | Avg. Fitness | Std. Fitness |
---|
SBOA | 41 | 429 | 433.0 | 433.0 | 433.0 | 0.0 |
GWO | 433.0 | 438.0 | 433.419 | 1.29 |
PSO | 433.0 | 437.0 | 433.258 | 0.983 |
SBOA | 42 | 512 | 525.0 | 527.0 | 525.968 | 0.999 |
GWO | 525.0 | 527.0 | 525.935 | 0.982 |
PSO | 525.0 | 527.0 | 526.29 | 0.957 |
SBOA | 51 | 253 | 267.0 | 269.0 | 267.29 | 0.52 |
GWO | 267.0 | 268.0 | 267.194 | 0.395 |
PSO | 267.0 | 269.0 | 267.323 | 0.59 |
SBOA | 52 | 302 | 315.0 | 322.0 | 318.387 | 1.979 |
GWO | 315.0 | 323.0 | 319.677 | 2.74 |
PSO | 315.0 | 323.0 | 318.742 | 2.17 |
SBOA | 61 | 138 | 141.0 | 145.0 | 141.935 | 1.605 |
GWO | 141.0 | 145.0 | 142.968 | 1.926 |
PSO | 141.0 | 145.0 | 141.839 | 1.568 |
SBOA | 62 | 146 | 148.0 | 154.0 | 149.677 | 2.277 |
GWO | 148.0 | 154.0 | 150.323 | 2.085 |
PSO | 148.0 | 154.0 | 149.387 | 2.058 |
SBOA | A1 | 253 | 257.0 | 257.0 | 257.0 | 0.0 |
GWO | 257.0 | 257.0 | 257.0 | 0.0 |
PSO | 257.0 | 257.0 | 257.0 | 0.0 |
SBOA | A2 | 252 | 258.0 | 265.0 | 260.387 | 1.58 |
GWO | 256.0 | 265.0 | 260.452 | 1.997 |
PSO | 258.0 | 265.0 | 261.355 | 1.976 |
SBOA | B1 | 69 | 69.0 | 71.0 | 69.387 | 0.79 |
GWO | 69.0 | 71.0 | 69.645 | 0.9 |
PSO | 69.0 | 71.0 | 69.387 | 0.79 |
SBOA | B2 | 76 | 76.0 | 77.0 | 76.129 | 0.335 |
GWO | 76.0 | 82.0 | 76.419 | 1.185 |
PSO | 76.0 | 77.0 | 76.161 | 0.368 |
SBOA | C1 | 227 | 231.0 | 234.0 | 233.065 | 0.504 |
GWO | 231.0 | 235.0 | 232.806 | 0.858 |
PSO | 231.0 | 234.0 | 232.968 | 0.647 |
SBOA | C2 | 219 | 221.0 | 226.0 | 222.387 | 1.559 |
GWO | 221.0 | 228.0 | 222.516 | 1.949 |
PSO | 221.0 | 229.0 | 222.645 | 2.088 |
SBOA | D1 | 60 | 60.0 | 65.0 | 61.387 | 1.006 |
GWO | 60.0 | 63.0 | 61.161 | 0.919 |
PSO | 60.0 | 63.0 | 61.323 | 1.028 |
SBOA | D2 | 66 | 67.0 | 69.0 | 67.71 | 0.727 |
GWO | 67.0 | 69.0 | 67.774 | 0.791 |
PSO | 67.0 | 69.0 | 67.677 | 0.69 |
SBOA | NRE1 | 29 | 29.0 | 29.0 | 29.0 | 0.0 |
GWO | 29.0 | 30.0 | 29.032 | 0.177 |
PSO | 29.0 | 29.0 | 29.0 | 0.0 |
SBOA | NRE2 | 30 | 30.0 | 32.0 | 31.0 | 0.803 |
GWO | 30.0 | 33.0 | 31.065 | 0.878 |
PSO | 30.0 | 32.0 | 30.71 | 0.632 |
SBOA | NRF1 | 14 | 14.0 | 14.0 | 14.0 | 0.0 |
GWO | 14.0 | 15.0 | 14.032 | 0.177 |
PSO | 14.0 | 14.0 | 14.0 | 0.0 |
SBOA | NRF2 | 15 | 15.0 | 15.0 | 15.0 | 0.0 |
GWO | 15.0 | 16.0 | 15.032 | 0.177 |
PSO | 15.0 | 15.0 | 15.0 | 0.0 |
Table 9.
Fitness results per SCP instance.
Table 9.
Fitness results per SCP instance.
MH | Instance | Opt. | Best | Worst | Avg. Fitness | Std. Fitness |
---|
SBOA | NRG1 | 176 | 178.0 | 184.0 | 180.968 | 1.492 |
GWO | 179.0 | 185.0 | 181.484 | 1.72 |
PSO | 179.0 | 184.0 | 181.0 | 1.666 |
SBOA | NRG2 | 154 | 158.0 | 161.0 | 159.355 | 0.598 |
GWO | 158.0 | 162.0 | 159.677 | 0.929 |
PSO | 158.0 | 162.0 | 159.516 | 1.043 |
SBOA | NRH1 | 63 | 64.0 | 67.0 | 65.0 | 1.016 |
GWO | 64.0 | 67.0 | 65.581 | 0.943 |
PSO | 64.0 | 67.0 | 65.484 | 0.875 |
SBOA | NRH2 | 63 | 64.0 | 67.0 | 65.065 | 1.014 |
GWO | 64.0 | 67.0 | 65.161 | 0.954 |
PSO | 64.0 | 66.0 | 65.194 | 0.895 |
Table 10.
Time per SCP instance.
Table 10.
Time per SCP instance.
MH | Instance | Min. Time (s) | Max. Time (s) | Avg. Time (s) | Std. Time (s) |
---|
SBOA | 41 | 157.704 | 213.129 | 183.116 | 16.07 |
GWO | 153.028 | 187.257 | 173.556 | 9.494 |
PSO | 154.711 | 170.525 | 165.33 | 4.352 |
SBOA | 42 | 142.817 | 218.333 | 174.875 | 19.872 |
GWO | 158.63 | 182.134 | 171.814 | 6.122 |
PSO | 158.201 | 167.463 | 164.051 | 2.481 |
SBOA | 51 | 253.613 | 374.187 | 313.787 | 30.033 |
GWO | 236.581 | 282.194 | 267.529 | 14.559 |
PSO | 237.17 | 271.079 | 259.171 | 8.931 |
SBOA | 52 | 253.449 | 379.583 | 314.932 | 34.542 |
GWO | 233.655 | 283.615 | 266.88 | 13.466 |
PSO | 231.334 | 271.309 | 258.577 | 10.615 |
SBOA | 61 | 98.435 | 157.754 | 122.681 | 13.947 |
GWO | 110.113 | 123.04 | 116.26 | 3.258 |
PSO | 102.526 | 116.973 | 109.84 | 2.943 |
SBOA | 62 | 97.503 | 142.421 | 119.435 | 13.442 |
GWO | 107.432 | 121.659 | 114.606 | 3.808 |
PSO | 104.62 | 115.671 | 110.325 | 3.257 |
SBOA | A1 | 776.617 | 992.96 | 886.21 | 52.953 |
GWO | 548.174 | 603.27 | 583.829 | 19.38 |
PSO | 547.932 | 583.488 | 564.821 | 7.163 |
SBOA | A2 | 760.15 | 978.413 | 885.575 | 58.469 |
GWO | 559.968 | 613.854 | 589.377 | 14.932 |
PSO | 540.209 | 587.692 | 569.523 | 11.293 |
SBOA | B1 | 492.081 | 598.676 | 549.83 | 29.989 |
GWO | 340.665 | 377.974 | 355.276 | 7.95 |
PSO | 331.606 | 369.327 | 355.788 | 7.879 |
SBOA | B2 | 509.619 | 609.138 | 566.107 | 27.889 |
GWO | 345.028 | 399.848 | 368.475 | 9.286 |
PSO | 339.963 | 369.457 | 350.85 | 6.382 |
SBOA | C1 | 1624.884 | 2006.59 | 1800.822 | 104.886 |
GWO | 1055.171 | 1174.378 | 1109.42 | 26.687 |
PSO | 1057.741 | 1215.157 | 1083.767 | 32.262 |
SBOA | C2 | 1494.119 | 1967.28 | 1785.954 | 136.993 |
GWO | 1019.127 | 1169.176 | 1117.342 | 30.362 |
PSO | 1034.299 | 1112.982 | 1075.741 | 15.09 |
SBOA | D1 | 932.527 | 1160.315 | 1073.955 | 65.504 |
GWO | 640.738 | 702.894 | 661.201 | 13.484 |
PSO | 605.31 | 667.894 | 638.656 | 13.116 |
SBOA | D2 | 943.902 | 1147.318 | 1060.202 | 52.619 |
GWO | 608.824 | 691.086 | 646.158 | 16.23 |
PSO | 594.241 | 664.729 | 628.357 | 20.317 |
Table 11.
Time per SCP instance.
Table 11.
Time per SCP instance.
MH | Instance | Min. Time (s) | Max. Time (s) | Avg. Time (s) | Std. Time (s) |
---|
SBOA | NRE1 | 1163.322 | 1343.931 | 1301.288 | 43.887 |
GWO | 709.169 | 820.318 | 756.539 | 27.69 |
PSO | 681.815 | 749.788 | 714.205 | 14.854 |
SBOA | NRE2 | 1111.717 | 1419.179 | 1314.766 | 74.668 |
GWO | 683.767 | 845.554 | 754.179 | 40.734 |
PSO | 669.604 | 855.131 | 758.741 | 49.429 |
SBOA | NRF1 | 1032.868 | 1327.712 | 1225.842 | 70.654 |
GWO | 565.83 | 681.723 | 619.619 | 26.624 |
PSO | 546.366 | 661.886 | 604.704 | 28.136 |
SBOA | NRF2 | 1099.421 | 1391.446 | 1272.068 | 76.519 |
GWO | 573.592 | 701.44 | 633.946 | 30.842 |
PSO | 588.031 | 713.309 | 635.212 | 26.661 |
SBOA | NRG1 | 17,984.637 | 54,355.97 | 26,594.345 | 12,842.352 |
GWO | 30,569.108 | 62,689.422 | 53,273.186 | 11,121.198 |
PSO | 32,644.973 | 61,491.48 | 55,582.678 | 6414.388 |
SBOA | NRG2 | 17,185.131 | 52,717.745 | 27,342.828 | 9971.869 |
GWO | 25,719.309 | 61,376.891 | 53,300.762 | 10,461.981 |
PSO | 31,367.547 | 59,373.087 | 54,333.041 | 5643.738 |
SBOA | NRH1 | 10,512.106 | 32,739.219 | 16,587.815 | 6416.691 |
GWO | 15,165.461 | 34,183.717 | 30,025.251 | 4855.541 |
PSO | 21,114.651 | 35,256.654 | 31,207.508 | 2997.95 |
SBOA | NRH2 | 10,276.136 | 29,402.972 | 15,774.859 | 5539.228 |
GWO | 14,111.582 | 34,673.103 | 29,343.299 | 5608.793 |
PSO | 19,751.687 | 34,721.174 | 30,023.669 | 3445.378 |
Table 12.
Fitness results per USCP instance.
Table 12.
Fitness results per USCP instance.
MH | Instance | Opt. | Best | Worst | Avg. Fitness | Std. Fitness |
---|
SBOA | U41 | 38 | 39.0 | 41.0 | 39.839 | 0.627 |
GWO | 39.0 | 43.0 | 40.871 | 1.07 |
PSO | 39.0 | 41.0 | 39.645 | 0.598 |
SBOA | U51 | 34 | 35.0 | 37.0 | 35.581 | 0.555 |
GWO | 35.0 | 38.0 | 36.29 | 0.681 |
PSO | 35.0 | 36.0 | 35.613 | 0.487 |
SBOA | U61 | 21 | 21.0 | 22.0 | 21.29 | 0.454 |
GWO | 21.0 | 23.0 | 21.839 | 0.514 |
PSO | 21.0 | 22.0 | 21.29 | 0.454 |
SBOA | UA1 | 39 | 39.0 | 41.0 | 40.323 | 0.642 |
GWO | 40.0 | 43.0 | 41.387 | 0.656 |
PSO | 40.0 | 41.0 | 40.452 | 0.498 |
SBOA | UB1 | 22 | 22.0 | 24.0 | 22.806 | 0.591 |
GWO | 22.0 | 24.0 | 23.387 | 0.605 |
PSO | 22.0 | 23.0 | 22.774 | 0.418 |
SBOA | UC1 | 43 | 43.0 | 45.0 | 44.323 | 0.532 |
GWO | 44.0 | 48.0 | 46.387 | 0.79 |
PSO | 44.0 | 46.0 | 44.774 | 0.551 |
SBOA | UD1 | 24 | 25.0 | 26.0 | 25.226 | 0.418 |
GWO | 25.0 | 27.0 | 26.194 | 0.47 |
PSO | 25.0 | 26.0 | 25.065 | 0.246 |
SBOA | UNRE1 | 17 | 17.0 | 18.0 | 17.516 | 0.5 |
GWO | 17.0 | 18.0 | 17.774 | 0.418 |
PSO | 17.0 | 17.0 | 17.0 | 0.0 |
SBOA | UNRF1 | 10 | 10.0 | 11.0 | 10.903 | 0.296 |
GWO | 10.0 | 11.0 | 10.774 | 0.418 |
PSO | 10.0 | 11.0 | 10.29 | 0.454 |
SBOA | UNRG1 | 61 | 62.0 | 63.0 | 62.484 | 0.5 |
GWO | 63.0 | 68.0 | 66.194 | 0.895 |
PSO | 62.0 | 64.0 | 63.29 | 0.579 |
SBOA | UNRH1 | 34 | 34.0 | 35.0 | 34.323 | 0.467 |
GWO | 35.0 | 37.0 | 35.839 | 0.514 |
PSO | 34.0 | 35.0 | 34.935 | 0.246 |
SBOA | CLR10 | 24 | 25.0 | 27.0 | 25.097 | 0.39 |
GWO | 25.0 | 27.0 | 25.387 | 0.748 |
PSO | 25.0 | 27.0 | 25.29 | 0.632 |
SBOA | CLR11 | 23 | 23.0 | 23.0 | 23.0 | 0.0 |
GWO | 23.0 | 27.0 | 24.839 | 1.919 |
PSO | 23.0 | 27.0 | 23.387 | 1.183 |
SBOA | CLR12 | 23 | 23.0 | 28.0 | 24.258 | 1.586 |
GWO | 23.0 | 29.0 | 24.774 | 2.121 |
PSO | 23.0 | 26.0 | 23.968 | 1.257 |
SBOA | CYC06 | 60 | 60.0 | 62.0 | 61.097 | 0.817 |
GWO | 60.0 | 63.0 | 61.452 | 0.978 |
PSO | 60.0 | 62.0 | 61.226 | 0.831 |
SBOA | CYC07 | 144 | 147.0 | 153.0 | 150.871 | 1.362 |
GWO | 147.0 | 154.0 | 151.903 | 1.399 |
PSO | 144.0 | 153.0 | 150.484 | 1.563 |
SBOA | CYC08 | 344 | 357.0 | 365.0 | 361.129 | 2.324 |
GWO | 358.0 | 372.0 | 363.419 | 2.721 |
PSO | 358.0 | 367.0 | 362.258 | 1.883 |
Table 13.
Time per USCP instance.
Table 13.
Time per USCP instance.
MH | Instance | Min. Time (s) | Max. Time (s) | Avg. Time (s) | Std. Time (s) |
---|
SBOA | U41 | 127.133 | 165.55 | 144.041 | 9.186 |
GWO | 122.253 | 138.701 | 128.183 | 3.852 |
PSO | 117.762 | 144.135 | 128.764 | 5.967 |
SBOA | U51 | 240.841 | 298.561 | 261.01 | 14.843 |
GWO | 212.336 | 229.391 | 219.389 | 4.053 |
PSO | 219.169 | 248.563 | 233.324 | 8.576 |
SBOA | U61 | 87.424 | 119.14 | 98.912 | 7.76 |
GWO | 68.666 | 86.004 | 77.182 | 4.104 |
PSO | 62.444 | 78.625 | 73.111 | 3.677 |
SBOA | UA1 | 596.009 | 988.713 | 718.132 | 81.884 |
GWO | 271.85 | 342.57 | 299.673 | 21.205 |
PSO | 155.901 | 331.492 | 281.74 | 35.986 |
SBOA | UB1 | 261.626 | 572.229 | 354.131 | 96.36 |
GWO | 163.543 | 178.737 | 169.919 | 3.133 |
PSO | 163.947 | 189.483 | 177.069 | 6.403 |
SBOA | UC1 | 43.0 | 45.0 | 44.323 | 0.532 |
GWO | 44.0 | 48.0 | 46.387 | 0.79 |
PSO | 44.0 | 46.0 | 44.774 | 0.551 |
SBOA | UD1 | 466.161 | 1065.89 | 691.041 | 212.326 |
GWO | 280.281 | 314.57 | 292.719 | 6.333 |
PSO | 280.569 | 329.153 | 302.325 | 12.853 |
SBOA | UNRE1 | 863.663 | 1732.248 | 1337.399 | 330.758 |
GWO | 410.564 | 705.947 | 434.391 | 50.715 |
PSO | 423.553 | 497.961 | 460.517 | 18.005 |
SBOA | UNRF1 | 1070.355 | 1650.344 | 1551.32 | 130.705 |
GWO | 424.606 | 683.387 | 589.47 | 95.124 |
PSO | 449.775 | 535.65 | 485.254 | 25.765 |
SBOA | UNRG1 | 5414.287 | 14,309.31 | 7441.461 | 3000.263 |
GWO | 8737.818 | 18,034.46 | 15,638.192 | 3071.343 |
PSO | 13,479.719 | 21,729.841 | 18,346.111 | 2374.816 |
SBOA | UNRH1 | 4168.711 | 16,435.724 | 7474.938 | 3805.651 |
GWO | 4775.536 | 11,231.733 | 9150.029 | 1921.657 |
PSO | 6517.542 | 14,954.869 | 11,776.28 | 1780.385 |
Table 14.
Time per USCP instance.
Table 14.
Time per USCP instance.
Metaheuristic | Instance | Min. Time (s) | Max. Time (s) | Avg. Time (s) | Std. Time (s) |
---|
SBOA | CLR10 | 58.212 | 86.825 | 75.066 | 6.622 |
GWO | 23.831 | 29.506 | 26.374 | 1.434 |
PSO | 29.711 | 36.123 | 32.689 | 1.824 |
SBOA | CLR11 | 126.482 | 196.981 | 141.176 | 11.534 |
GWO | 53.558 | 69.384 | 61.066 | 4.716 |
PSO | 66.438 | 85.256 | 71.301 | 4.728 |
SBOA | CLR12 | 604.751 | 1064.573 | 801.739 | 149.713 |
GWO | 338.341 | 500.013 | 407.826 | 43.52 |
PSO | 501.697 | 604.357 | 550.129 | 22.986 |
SBOA | CYC06 | 53.307 | 93.846 | 68.63 | 8.254 |
GWO | 22.638 | 26.964 | 24.317 | 1.085 |
PSO | 23.312 | 28.313 | 25.79 | 1.229 |
SBOA | CYC07 | 282.102 | 319.146 | 306.65 | 6.968 |
GWO | 138.408 | 163.015 | 148.045 | 6.521 |
PSO | 146.28 | 175.9 | 158.426 | 5.986 |
SBOA | CYC08 | | 5163.509 | 4655.015 | 226.937 |
GWO | 3080.423 | 3591.295 | 3391.635 | 126.319 |
PSO | 3562.642 | 3902.347 | 3747.505 | 84.342 |
Table 15.
Average p-value of the SBOA compared with PSO and GWO for SCP41, ScP42, SCP51, SCP52, SCP61 and SCP62.
Table 15.
Average p-value of the SBOA compared with PSO and GWO for SCP41, ScP42, SCP51, SCP52, SCP61 and SCP62.
| 4.1 | 4.2 | 5.1 | 5.2 | 6.1 | 6.2 |
---|
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | 0.03 | - | ≥0.05 | ≥0.05 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.02 | ≥0.05 | - | ≥0.05 |
GWO | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.03 | 0.02 | - | ≥0.05 | ≥0.05 | - |
Table 16.
Average p-value of the SBOA compared with PSO and GWO for a1, a2, b1, b2, c1, c2, d1 and d2.
Table 16.
Average p-value of the SBOA compared with PSO and GWO for a1, a2, b1, b2, c1, c2, d1 and d2.
| a.1 | a.2 | b.1 | b.2 |
---|
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | ≥0.05 | - | 0.05 | - | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | 1.0 | - | ≥0.05 | ≥0.05 | - | ≥0.05 |
GWO | ≥0.05 | ≥0.05 | - | - | ≥0.05 | - | 0.2 | ≥0.05 | - | ≥0.05 | ≥0.05 | - |
| c.1 | c.2 | d.1 | d.2 |
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 |
GWO | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - |
Table 17.
Average p-value of the SBOA compared with PSO and GWO for nre1, nre2, nrf1, nrf2, nrg1, nrg2, nrh1 and nrh2.
Table 17.
Average p-value of the SBOA compared with PSO and GWO for nre1, nre2, nrf1, nrf2, nrg1, nrg2, nrh1 and nrh2.
| nre1 | nre2 | nrf1 | nrf2 |
---|
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 |
GWO | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.33 | ≥0.05 | - |
| nrg1 | nrg2 | nrh1 | nrh2 |
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.003 | 0.02 | - | ≥0.05 | ≥0.05 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | 0.03 | - | ≥0.05 | ≥0.05 | - | ≥0.05 |
GWO | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.02 | ≥0.05 | - | ≥0.05 | ≥0.05 | - |
Table 18.
Average p-value of the SBOA compared with PSO and GWO for u41, u51, u61, ua1, ub1, uc1, uclr10, uclr12, ucyc06, ucyc07, ud1, unre1, unrf1, unre1 and unrh1.
Table 18.
Average p-value of the SBOA compared with PSO and GWO for u41, u51, u61, ua1, ub1, uc1, uclr10, uclr12, ucyc06, ucyc07, ud1, unre1, unrf1, unre1 and unrh1.
| u41 | u51 | u61 | ua1 |
---|
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | 0.0 | - | ≥0.05 | 0.0 | - | ≥0.05 | 0.0 | - | ≥0.05 | 0.0 |
PSO | ≥0.05 | - | 0.0 | ≥0.05 | - | 0.0 | ≥0.05 | - | 0.0 | ≥0.05 | - | 0.0 |
GWO | 0.0 | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - |
| ub1 | uc1 | uclr10 | uclr12 |
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | 0.0 | - | 0.0 | 0.0 | - | ≥0.05 | ≥0.05 | - | 0.5 | ≥0.05 |
PSO | ≥0.05 | - | 0.0 | 0.0 | - | 0.0 | ≥0.05 | - | ≥0.05 | ≥0.05 | - | ≥0.05 |
GWO | 0.0 | 0.0 | - | 0.0 | 0.0 | - | ≥0.05 | ≥0.05 | - | ≥0.05 | ≥0.05 | - |
| ucyc06 | ucyc07 | ucyc07 | ud1 |
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | ≥0.05 | 0.12 | - | ≥0.05 | 0.0 | - | ≥0.05 | 0.0 | - | ≥0.05 | 0.0 |
PSO | ≥0.05 | - | ≥0.05 | ≥0.05 | - | 0.0 | ≥0.05 | - | 0.0 | ≥0.05 | - | 0.0 |
GWO | ≥0.05 | ≥0.05 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - |
| unre1 | unrf1 | unre1 | unrh1 |
| SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO | SBO | PSO | GWO |
SBO | - | 0.0 | 0.04 | - | 0.0 | ≥0.05 | - | 0.0 | 0.0 | - | 0.0 | 0.0 |
PSO | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - | 0.0 |
GWO | 0.04 | 0.0 | - | ≥0.05 | 0.0 | - | 0.0 | 0.0 | - | 0.0 | 0.0 | - |