Research Article
Solving Constrained Global Optimization Problems by Using Hybrid Evolutionary Computing and Artificial Life Approaches
Table 9
Comparison of the numerical results of the proposed RGA-PSO and AIA-PSO algorithms and those of the published individual AIA and RGA for TPs 5–13.
| TP number | Global optimum | Methods | Best | Mean | Median | Worst | MAPE% |
| 5 | 1227.1978 | AIA-2 [10] | 1227.3191 | 1228.6097 | 1227.8216 | 1239.5205 | | GA-3 [9] | 1228.5118 | 1279.3825 | 1263.2589 | 1481.3710 |
4.266
| The proposed RGA-PSO | 1227.2321 | 1228.8471 | 1228.3935 | 1231.6003 | | The proposed AIA-PSO | 1227.1598 | 1228.1800 | 1227.9762 | 1229.6590 | | 6 | 3.9511 | AIA-2 [10] | 3.9518 | 4.1005 | 4.0460 | 4.2997 |
3.781
| GA-3 [9] | 3.9697 | 4.1440 | 4.1358 | 4.3743 |
4.881
| The proposed RGA-PSO | 3.9521 | 3.9577 | 3.9566 | 3.9722 | | The proposed AIA-PSO | 3.9516 | 3.9581 | 3.9569 | 3.9735 | | 7 | −5.7398 | AIA-2 [10] | −5.7398 | −5.7398 | −5.7398 | −5.7396 | | GA-3 [9] | −5.7398 | −5.7375 | −5.7383 | −5.7316 | | The proposed RGA-PSO | −5.7398 | −5.7398 | −5.7398 | −5.7398 | | The proposed AIA-PSO | −5.7398 | −5.7398 | −5.7398 | −5.7398 | | 8 | −83.254 | AIA-2 [10] | −83.2504 | −83.2499 | −83.2499 | −83.2496 | | GA-3 [9] | −83.2497 | −83.2490 | −83.2494 | −83.2461 | | The proposed RGA-PSO | −83.2497 | −83.2497 | −83.2497 | −83.2497 | | The proposed AIA-PSO | −83.2497 | −83.2497 | −83.2497 | −83.2497 | | 9 | −6.0482 | AIA-2 [10] | −6.0471 | −5.9795 | −6.0138 | −5.7159 |
1.136
| GA-3 [9] | −6.0417 | −5.8602 | −5.8772 | −5.6815 |
3.108
| The proposed RGA-PSO | −6.0441 | −5.9883 | −5.9968 | −5.8051 |
0.991
| The proposed AIA-PSO | −6.0466 | −5.9808 | −5.9969 | −5.8274 |
1.082
| 10 | 6300 | AIA-2 [10] | 6299.8232 | 6299.8388 | 6299.8403 | 6299.8494 | | GA-3 [9] | 6299.8399 | 6299.8546 | 6299.8453 | 6299.9407 | | The proposed RGA-PSO | 6299.8374 | 6299.8412 | 6299.8419 | 6299.8428 | | The proposed AIA-PSO | 6299.8395 | 6299.8420 | 6299.8423 | 6299.8425 | | 11 | 10122.6964 | AIA-2 [10] | 10122.4343 | 10122.5014 | 10122.5023 | 10122.6271 | | GA-3 [9] | 10122.4809 | 10125.2441 | 10123.9791 | 10155.1349 | | The proposed RGA-PSO | 10122.4732 | 10122.4925 | 10122.4925 | 10122.6444 | | The proposed AIA-PSO | 10122.4852 | 10122.4920 | 10122.4927 | 10122.4931 | | 12 | — | AIA-2 [10] | 0.012665 | 0.012703 | 0.012719 | 0.012725 | — | GA-3 [9] | 0.012665 | 0.012739 | 0.012717 | 0.013471 | — | The proposed RGA-PSO | 0.012692 | 0.012724 | 0.012721 | 0.012784 | — | The proposed AIA-PSO | 0.012667 | 0.012715 | 0.012719 | 0.012778 | — | 13 | — | AIA-2 [10] | 5885.5312 | 5900.4860 | 5894.7929 | 6014.2198 | — | GA-3 [9] | 5885.3076 | 5943.4714 | 5897.2904 | 6289.7314 | — | The proposed RGA-PSO | 5885.3018 | 5895.0381 | 5885.3326 | 6005.4351 | — | The proposed AIA-PSO | 5885.3310 | 5886.5426 | 5885.3323 | 5906.7404 | — |
|
|
(The “—” denotes unavailable information.)
|