Table 3. The testing results of the three algorithms for the benchmark functions.
| Benchmark function | algorithm | Best value | Worst value | Median | Means | Std | Average Time |
|---|---|---|---|---|---|---|---|
| Function1 | CIFOA | 0 | 0 | 0 | 0 | 0 | 0.333530448 |
| FOA | 0.0015 | 0.00152954 | 0.0015 | 0.00150353 | 8.84E-06 | 0.52567952 | |
| PSO | 46.9277844 | 81.03940203 | 68.43008378 | 66.31215476 | 9.35121111 | 0.45106818 | |
| TVPSO | 2.57011182 | 5.2530343 | 3.78153176 | 3.78214492 | 0.59961592 | 0.44296219 | |
| IFOA | 0.00076774 | 19864.6401877 | 9616.25445419 | 9362.67965422 | 5031.54002686 | 0.35860204 | |
| Function2 | CIFOA | 1.36E-06 | 2.24E-06 | 1.7E-06 | 1.74E-06 | 2E-07 | 0.44376986 |
| FOA | 5.24264069 | 5.27943571 | 5.24264069 | 5.2450921 | 0.00838239 | 0.52798553 | |
| PSO | 6.65597556 | 10.60347546 | 8.3545127 | 8.46327962 | 0.82543197 | 0.48126274 | |
| TVPSO | 2.38107103 | 4.56606483 | 2.83587925 | 2.86573324 | 0.36354308 | 0.43581129 | |
| IFOA | 1.00025496 | 140.36636921 | 105.44044879 | 90.37246037 | 40.410495 | 0.38489129 | |
| Function3 | CIFOA | 0.00449358 | 0.03248204 | 0.01318236 | 0.01449095 | 0.00568992 | 0.68978405 |
| FOA | 43.30650025 | 46.71584693 | 43.30651904 | 43.49609982 | 0.66045093 | 0.59677812 | |
| PSO | 0.00321914 | 0.01473364 | 0.00747975 | 0.00815546 | 0.00279545 | 0.52370546 | |
| TVPSO | 0.01473127 | 0.08926477 | 0.04285198 | 0.04482646 | 0.01604868 | 0.5350807 | |
| IFOA | 2.40641005 | 23.99233763 | 6.74487223 | 8.03879967 | 4.12276149 | 0.41276481 | |
| Function4 | CIFOA | 0 | 0 | 0 | 0 | 0 | 0.57697321 |
| FOA | 2.325 | 2.39218054 | 2.325 | 2.33120108 | 0.01761902 | 0.5846384 | |
| PSO | 7.05952412 | 23.0391778 | 10.76372186 | 11.10410763 | 2.66095101 | 0.54813436 | |
| TVPSO | 0.44603836 | 1.45367321 | 0.74444863 | 0.79692551 | 0.22996596 | 0.42469803 | |
| IFOA | 1E-08 | 4098.6359684 | 1838.34544005 | 1659.55963896 | 1133.78585088 | 0.42638859 | |
| Function5 | CIFOA | 0 | 1E-08 | 1E-08 | 1E-08 | 0 | 0.55225223 |
| FOA | 2.41413989 | 3394.56423246 | 2.41413989 | 70.26851999 | 474.89938952 | 0.59365665 | |
| PSO | 1.575E-05 | 0.00015636 | 6.267E-05 | 6.729E-05 | 3.338E-05 | 0.54133758 | |
| TVPSO | 4.2E-06 | 6.882E-05 | 2.244E-05 | 2.244E-05 | 1.43E-05 | 0.34650514 | |
| IFOA | 4.8E-06 | 0.51766163 | 0.08901473 | 0.14419936 | 0.16207673 | 0.42880364 | |
| Function6 | CIFOA | 27.77849226 | 224.36102113 | 28.88771013 | 59.65823219 | 56.14181148 | 0.71561607 |
| FOA | 28.93055914 | 29.20904117 | 29.18509567 | 29.17464782 | 0.03776031 | 0.65413263 | |
| PSO | 535.21563267 | 2092.59725654 | 857.02902308 | 935.18812368 | 310.56775915 | 0.61079594 | |
| TVPSO | 50.0915007 | 260.09250574 | 68.0914448 | 100.19315468 | 53.63689523 | 0.4791295 | |
| IFOA | 802.05974855 | 45938931.0951 | 727748.6591 | 5352910.575355 | 7140960.545249 | 0.51228287 | |
| Function7 | CIFOA | 6.4E-07 | 1.08E-06 | 9E-07 | 8.9E-07 | 8E-08 | 0.57037173 |
| FOA | 0.11422539 | 0.11543086 | 0.11422539 | 0.11429541 | 0.00025334 | 0.62419126 | |
| PSO | 3.08891225 | 3.62000336 | 3.40850015 | 3.40552595 | 0.11909537 | 0.46736982 | |
| TVPSO | 0.76043029 | 1.20173887 | 1.05696236 | 1.03287373 | 0.10292351 | 0.46470978 | |
| IFOA | 1.17177655 | 19.9050933 | 15.82120214 | 15.23704712 | 3.30422523 | 0.35988503 | |
| Function8 | CIFOA | 0 | 0.44987534 | 0 | 0.03734983 | 0.10842514 | 0.57705417 |
| FOA | 2.78E-06 | 3.2E-06 | 2.78E-06 | 2.81E-06 | 8E-08 | 0.4975661 | |
| PSO | 1.39171802 | 1.75384585 | 1.59891445 | 1.59947527 | 0.07868131 | 0.53438732 | |
| TVPSO | 1.01901183 | 1.04766821 | 1.03285273 | 1.03320413 | 0.00631144 | 0.36616112 | |
| IFOA | 0 | 236.66796911 | 81.29755439 | 79.95490768 | 45.98983574 | 0.42762164 | |
| Function9 | CIFOA | 0.01096023 | 0.02905256 | 0.01921427 | 0.01997557 | 0.00384017 | 0.63945682 |
| FOA | 0.36200707 | 0.36648511 | 0.36200707 | 0.36251395 | 0.00127768 | 0.41726704 | |
| PSO | 0.5555723 | 6.23583619 | 1.28688615 | 1.57415173 | 0.92606614 | 0.50687815 | |
| TVPSO | 0.04691413 | 1.54387105 | 0.37571847 | 0.44654829 | 0.33720773 | 0.35788392 | |
| IFOA | 2.60785268 | 36.26263065 | 14.15463627 | 14.38035363 | 6.59076109 | 0.42133829 | |
| Function10 | CIFOA | 0.03284302 | 0.37756413 | 0.12941583 | 0.13837669 | 0.06016914 | 0.6612283 |
| FOA | 16.9428 | 16.9428 | 16.9428 | 16.9428 | 0 | 0.4228202 | |
| PSO | 11.64524961 | 48.61811606 | 22.3435454 | 24.03177247 | 7.51416269 | 0.53200057 | |
| TVPSO | 0.42406271 | 1.10909011 | 0.81222728 | 0.83037475 | 0.15005306 | 0.38975869 | |
| IFOA | 6.78668492 | 4598.52176616 | 1397.19974052 | 1501.61570182 | 813.57738831 | 0.44357287 | |
| Function11 | CIFOA | 0 | 3.98897514 | 1.01794575 | 1.68499896 | 1.11403793 | 0.5554832 |
| FOA | 104.06037467 | 107.96149003 | 106.60893982 | 106.58501952 | 0.40733199 | 0.41106256 | |
| PSO | 46.34092901 | 106.83098785 | 63.68310374 | 64.51160886 | 11.54041507 | 0.51115152 | |
| TVPSO | 24.52376268 | 167.32843182 | 57.97808999 | 61.63611782 | 27.60762214 | 0.52063316 | |
| IFOA | 47.37883985 | 266.00413696 | 122.01030039 | 140.14453027 | 49.05889799 | 0.43695702 | |
| Function12 | CIFOA | 0.09987335 | 0.59987336 | 0.29987335 | 0.28595637 | 0.1020944 | 0.40908259 |
| FOA | 0.03333597 | 0.03396079 | 0.03333597 | 0.03336861 | 0.00013189 | 0.39189368 | |
| PSO | 0.80004655 | 1.09991055 | 0.92589667 | 0.94091837 | 0.05730999 | 0.42242791 | |
| TVPSO | 0.29987827 | 0.40146745 | 0.39987345 | 0.35680167 | 0.04630805 | 0.41691559 | |
| IFOA | 7.63407942 | 23.40037258 | 12.72564107 | 13.46440787 | 3.27607954 | 0.32941129 |