Research Article
A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization
Table 1
Test results of the FW method, MDY method, JHS method, and MHS method.
| | n | FW | MDY | JHS | MHS | | I | NF | NG | TCpu | I | NF | NG | TCpu | I | NF | NG | TCpu | I | NF | NG | TCpu |
| | badscp | 2 | 3 | 58 | 5 | 0.0189 | 3 | 58 | 5 | 0.0144 | 3 | 58 | 5 | 0.1081 | 3 | 58 | 5 | 0.0116 | | beale | 2 | 17 | 57 | 29 | 0.0290 | 21 | 62 | 34 | 0.0094 | 23 | 79 | 40 | 0.0140 | 19 | 60 | 31 | 0.0239 | | jensam | 2 | 2 | 52 | 3 | 0.0054 | 2 | 52 | 3 | 0.0079 | 2 | 52 | 3 | 0.0091 | 2 | 52 | 3 | 0.0098 | | helix | 3 | 63 | 465 | 245 | 0.0855 | 79 | 648 | 339 | 0.1265 | 113 | 756 | 401 | 0.2044 | 70 | 467 | 226 | 0.1752 | | bard | 3 | 37 | 99 | 58 | 0.0214 | 86 | 199 | 122 | 0.0909 | 49 | 161 | 71 | 0.0538 | 47 | 94 | 61 | 0.0454 | | gauss | 3 | 4 | 9 | 5 | 0.0144 | 4 | 9 | 5 | 0.0388 | 4 | 9 | 5 | 0.0154 | 4 | 9 | 5 | 0.0138 | | meyer | 3 | 3 | 56 | 5 | 0.0187 | 3 | 56 | 5 | 0.0156 | 3 | 56 | 5 | 0.0176 | 3 | 56 | 5 | 0.0230 | | gulf | 3 | 2 | 52 | 4 | 0.0115 | 2 | 52 | 4 | 0.0138 | 2 | 52 | 4 | 0.0162 | 2 | 52 | 4 | 0.0188 | | box | 3 | 1 | 51 | 2 | 0.0166 | 1 | 51 | 2 | 0.0147 | 1 | 51 | 2 | 0.0168 | 1 | 51 | 2 | 0.0214 | | wood | 4 | 111 | 335 | 166 | 0.0865 | 85 | 245 | 136 | 0.0774 | 14 | 146 | 90 | 0.0657 | 85 | 250 | 135 | 0.0567 | | kowosb | 4 | 153 | 332 | 212 | 0.0452 | 15 | 180 | 126 | 0.0821 | 15 | 147 | 95 | 0.0556 | 105 | 317 | 182 | 0.0747 | | osb1 | 5 | 1 | 51 | 2 | 0.0102 | 1 | 51 | 2 | 0.0110 | 1 | 51 | 2 | 0.0142 | 1 | 51 | 2 | 0.0188 | | biggs | 6 | 8 | 65 | 10 | 0.0210 | 8 | 69 | 12 | 0.0066 | 12 | 95 | 22 | 0.0087 | 11 | 89 | 20 | 0.0075 | | osb2 | 11 | 17 | 89 | 23 | 0.0147 | 28 | 117 | 40 | 0.0178 | 16 | 93 | 24 | 0.0136 | 7 | 66 | 10 | 0.0143 | | pen1 | 10 | 2 | 58 | 7 | 0.0156 | 2 | 58 | 7 | 0.0149 | 2 | 58 | 7 | 0.0211 | 2 | 58 | 7 | 0.0194 | | pen1 | 100 | 2 | 101 | 3 | 0.0132 | 2 | 101 | 3 | 0.0216 | 7 | 351 | 8 | 0.1244 | 5 | 251 | 6 | 0.0487 | | pen1 | 200 | 1 | 51 | 2 | 0.0119 | 1 | 51 | 2 | 0.0256 | 1 | 51 | 2 | 0.0213 | 1 | 51 | 2 | 0.0244 | | pen1 | 1000 | 1 | 51 | 2 | 0.9192 | 1 | 51 | 2 | 0.9964 | 1 | 51 | 2 | 0.9902 | 1 | 51 | 2 | 0.9578 | | pen1 | 1500 | 1 | 51 | 2 | 2.0667 | 1 | 51 | 2 | 2.2766 | 1 | 51 | 2 | 2.0790 | 1 | 51 | 2 | 2.1576 | | pen1 | 2000 | 1 | 51 | 2 | 3.6421 | 1 | 51 | 2 | 4.0836 | 1 | 51 | 2 | 3.7250 | 1 | 51 | 2 | 3.7133 | | pen1 | 3000 | 1 | 51 | 2 | 8.2712 | 1 | 51 | 2 | 9.2095 | 1 | 51 | 2 | 8.1979 | 1 | 51 | 2 | 8.5341 | | pen1 | 5000 | 1 | 51 | 2 | 23.0663 | 1 | 51 | 2 | 25.5505 | 1 | 51 | 2 | 22.1556 | 1 | 51 | 2 | 23.6629 | | pen2 | 10 | 2 | 52 | 3 | 0.0160 | 2 | 52 | 3 | 0.0171 | 2 | 52 | 3 | 0.0156 | 2 | 52 | 3 | 0.0180 | | pen2 | 50 | 1 | 51 | 2 | 0.0165 | 2 | 52 | 3 | 0.0266 | 1 | 51 | 2 | 0.0210 | 1 | 51 | 2 | 0.0197 | | vardim | 2 | 4 | 27 | 10 | 0.0024 | 4 | 30 | 11 | 0.0035 | 5 | 25 | 10 | 0.0034 | 5 | 25 | 10 | 0.0033 | | vardim | 100 | 1 | 51 | 2 | 0.0119 | 1 | 51 | 2 | 0.0218 | 1 | 51 | 2 | 0.0131 | 1 | 51 | 2 | 0.0116 | | vardim | 500 | 1 | 51 | 2 | 0.0776 | 1 | 51 | 2 | 0.1024 | 1 | 51 | 2 | 0.0982 | 1 | 51 | 2 | 0.1105 | | vardim | 1000 | 1 | 51 | 2 | 0.2908 | 1 | 51 | 2 | 0.3441 | 1 | 51 | 2 | 0.3951 | 1 | 51 | 2 | 0.3326 | | vardim | 2000 | 1 | 51 | 2 | 0.9955 | 1 | 51 | 2 | 1.0401 | 1 | 51 | 2 | 1.0591 | 1 | 51 | 2 | 1.0676 | | vardim | 3000 | 1 | 51 | 2 | 1.9162 | 1 | 51 | 2 | 2.1069 | 1 | 51 | 2 | 1.9204 | 1 | 51 | 2 | 2.0107 | | vardim | 4000 | 1 | 51 | 2 | 3.1114 | 1 | 51 | 2 | 3.4843 | 1 | 51 | 2 | 3.3016 | 1 | 51 | 2 | 3.3019 | | vardim | 5000 | 1 | 51 | 2 | 4.6175 | 1 | 51 | 2 | 5.2175 | 1 | 51 | 2 | 4.8257 | 1 | 51 | 2 | 4.9972 | | trig | 10 | 42 | 80 | 50 | 0.0130 | 40 | 70 | 45 | 0.0169 | 41 | 73 | 46 | 0.0182 | 48 | 94 | 60 | 0.0153 | | trig | 50 | 56 | 101 | 64 | 0.0294 | 49 | 108 | 65 | 0.0538 | 51 | 112 | 67 | 0.0436 | 52 | 114 | 68 | 0.0482 | | trig | 150 | 62 | 110 | 71 | 0.1451 | 54 | 112 | 69 | 0.1962 | 61 | 113 | 73 | 0.1620 | 81 | 185 | 113 | 0.2364 | | trig | 200 | 54 | 103 | 65 | 0.2280 | 60 | 124 | 77 | 0.3072 | 67 | 176 | 85 | 0.3789 | 68 | 230 | 102 | 0.3682 | | ie | 10 | 7 | 15 | 8 | 0.0231 | 6 | 13 | 7 | 0.0398 | 7 | 15 | 8 | 0.0314 | 7 | 15 | 8 | 0.0287 | | ie | 100 | 9 | 18 | 10 | 0.1928 | 7 | 16 | 9 | 0.2051 | 7 | 14 | 8 | 0.1332 | 11 | 21 | 12 | 0.2035 | | ie | 500 | 8 | 18 | 10 | 2.8779 | 8 | 18 | 10 | 3.2010 | 8 | 18 | 10 | 2.9477 | 8 | 18 | 10 | 2.9802 | | ie | 1000 | 8 | 18 | 10 | 11.3304 | 7 | 16 | 9 | 11.2570 | 8 | 18 | 10 | 12.0797 | 8 | 18 | 10 | 11.9909 | | ie | 2000 | 8 | 18 | 10 | 45.4075 | 8 | 18 | 10 | 50.2927 | 7 | 16 | 9 | 40.4006 | 7 | 16 | 9 | 42.0180 | | ie | 4000 | 8 | 21 | 11 | 200.1344 | 8 | 21 | 11 | 216.9107 | 7 | 19 | 10 | 179.2517 | 7 | 19 | 10 | 195.2297 | | trid | 100 | 36 | 74 | 40 | 0.0350 | 32 | 69 | 36 | 0.0562 | 33 | 69 | 37 | 0.0544 | 38 | 78 | 43 | 0.0438 | | trid | 500 | 33 | 74 | 39 | 0.3026 | 32 | 70 | 38 | 0.3045 | 32 | 71 | 38 | 0.3125 | 35 | 90 | 47 | 0.3451 | | band | 10 | 21 | 58 | 26 | 0.0229 | 25 | 66 | 31 | 0.0072 | 18 | 56 | 23 | 0.0084 | 20 | 63 | 27 | 0.0074 | | band | 500 | 1 | 51 | 2 | 0.3930 | 1 | 51 | 2 | 0.4692 | 1 | 51 | 2 | 0.4523 | 1 | 51 | 2 | 0.4562 | | band | 5000 | 1 | 51 | 2 | 32.4417 | 1 | 51 | 2 | 37.1887 | 1 | 51 | 2 | 32.5321 | 1 | 51 | 2 | 33.9574 | | lin | 2 | 1 | 4 | 3 | 0.0061 | 1 | 4 | 3 | 0.0091 | 1 | 4 | 3 | 0.0047 | 1 | 4 | 3 | 0.0046 | | lin | 50 | 1 | 4 | 3 | 0.0058 | 1 | 4 | 3 | 0.0047 | 1 | 4 | 3 | 0.0053 | 1 | 4 | 3 | 0.0084 | | lin | 500 | 1 | 4 | 3 | 0.0432 | 1 | 4 | 3 | 0.0646 | 1 | 4 | 3 | 0.0522 | 1 | 4 | 3 | 0.0632 | | lin | 1000 | 1 | 4 | 3 | 0.2213 | 1 | 4 | 3 | 0.2170 | 1 | 4 | 3 | 0.1997 | 1 | 4 | 3 | 0.1960 | | lin | 1500 | 1 | 4 | 3 | 0.4253 | 1 | 4 | 3 | 0.4649 | 1 | 4 | 3 | 0.3651 | 1 | 4 | 3 | 0.3824 | | lin | 2000 | 1 | 4 | 3 | 0.6977 | 1 | 4 | 3 | 0.8611 | 1 | 4 | 3 | 0.7180 | 1 | 4 | 3 | 0.8242 | | lin | 3000 | 1 | 4 | 3 | 1.6127 | 1 | 4 | 3 | 1.9749 | 1 | 4 | 3 | 1.6681 | 1 | 4 | 3 | 1.6817 | | lin | 5000 | 1 | 4 | 3 | 4.7730 | 1 | 4 | 3 | 5.3896 | 1 | 4 | 3 | 4.8142 | 1 | 4 | 3 | 4.8166 | | lin1 | 2 | 2 | 4 | 3 | 0.0086 | 2 | 4 | 3 | 0.0018 | 2 | 4 | 3 | 0.0134 | 2 | 4 | 3 | 0.0096 | | lin1 | 10 | 1 | 4 | 3 | 0.0029 | 1 | 4 | 3 | 0.0034 | 1 | 4 | 3 | 0.0042 | 1 | 4 | 3 | 0.0065 | | lin1 | 100 | 6 | 62 | 9 | 0.0580 | 6 | 62 | 9 | 0.0408 | 6 | 62 | 9 | 0.0530 | 6 | 62 | 9 | 0.0598 | | lin1 | 500 | 3 | 56 | 7 | 0.5768 | 3 | 56 | 7 | 0.6440 | 3 | 56 | 7 | 0.5921 | 3 | 56 | 7 | 0.6223 | | lin1 | 1000 | 3 | 56 | 5 | 2.1466 | 3 | 56 | 5 | 2.5596 | 3 | 56 | 5 | 2.1943 | 3 | 56 | 5 | 2.3149 | | lin1 | 2000 | 3 | 56 | 5 | 9.0047 | 3 | 56 | 5 | 10.9094 | 3 | 56 | 5 | 9.0499 | 3 | 56 | 5 | 9.8109 | | lin1 | 3000 | 3 | 56 | 5 | 25.2678 | 5 | 63 | 8 | 30.5328 | 5 | 63 | 8 | 25.2772 | 5 | 63 | 8 | 27.4500 | | lin0 | 4 | 2 | 4 | 3 | 0.0111 | 2 | 4 | 3 | 0.0096 | 2 | 4 | 3 | 0.0142 | 2 | 4 | 3 | 0.0138 | | lin0 | 500 | 3 | 58 | 6 | 0.7479 | 3 | 58 | 6 | 0.7779 | 3 | 58 | 6 | 0.7604 | 3 | 58 | 6 | 0.6715 | | lin0 | 800 | 3 | 56 | 5 | 1.8232 | 3 | 56 | 5 | 2.1614 | 3 | 56 | 5 | 1.9628 | 3 | 56 | 5 | 1.8111 | | lin0 | 1000 | 7 | 62 | 9 | 3.3620 | 7 | 62 | 9 | 3.6958 | 7 | 62 | 9 | 3.6405 | 7 | 64 | 9 | 3.3911 | | lin0 | 2000 | 3 | 56 | 5 | 11.8533 | 3 | 56 | 5 | 14.5539 | 3 | 56 | 5 | 12.0432 | 3 | 56 | 5 | 12.2544 | | lin0 | 2500 | 3 | 56 | 5 | 19.5770 | 3 | 56 | 5 | 23.3801 | 3 | 56 | 5 | 19.6448 | 3 | 56 | 5 | 22.1141 | | lin0 | 3000 | 3 | 57 | 5 | 28.9680 | 3 | 57 | 5 | 33.4278 | 3 | 57 | 5 | 28.9657 | 3 | 57 | 5 | 30.2009 |
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