Research Article
An Integrated Method Based on PSO and EDA for the Max-Cut Problem
Table 4
Comparison of the results obtained by the GPSO-CDHNN, DHNN-EDA, THNN-EDA, and PSO-EDA on instances from the first set.
| | Instances | GPSO-CDHNN [10] | DHNN-EDA [25] | THNN-EDA [9] | PSO-EDA | | | time | | | Std. | | | Std. | time | | | Std. | time |
| | G1 | — | — | — | 11614 | 11580.6 | 16.58 | 11624 | 11621.6 | 6.9 | 9.76 | 11624 | 11624.0 | 0.0 | 23.714 | | G2 | — | — | — | 11599 | 11584.3 | 10.22 | 11620 | 11612.6 | 7.0 | 9.76 | 11620 | 11613.3 | 4.84 | 24.067 | | G3 | — | — | — | 11617 | 11582.5 | 20.50 | 11622 | 11619.5 | 2.6 | 9.76 | 11622 | 11620.0 | 2.45 | 24.091 | | G11 | 564 | 562.56 | 9.51 | 494 | 476.9 | 5.41 | 564 | 563.7 | 0.7 | 9.76 | 564 | 564.0 | 0.0 | 2.281 | | G12 | 556 | 554.4 | 9.46 | 476 | 464.7 | 7.07 | 556 | 554.7 | 0.9 | 9.76 | 556 | 556.0 | 0.0 | 2.378 | | G13 | 580 | 579.92 | 9.30 | 520 | 501.9 | 7.35 | 582 | 579.8 | 1.4 | 9.76 | 582 | 582.0 | 0.0 | 2.273 | | G14 | 3058 | 3057.43 | 9.47 | 3027 | 3017.3 | 3.86 | 3061 | 3055.5 | 3.3 | 9.76 | 3061 | 3057.3 | 2.58 | 4.296 | | G15 | 3047 | 3046.67 | 9.90 | 2988 | 2980.9 | 2.67 | 3050 | 3043.2 | 4.5 | 9.76 | 3050 | 3045.4 | 3.84 | 4.521 | | G16 | — | — | — | 3001 | 2991.1 | 5.72 | 3052 | 3043.0 | 3.5 | 9.76 | 3052 | 3045.2 | 4.54 | 4.003 | | G20 | 940 | 939.58 | 9.90 | — | — | — | — | — | — | — | 941 | 941.0 | 0.0 | 3.702 | | G21 | 928 | 926.65 | 9.79 | — | — | — | — | — | — | — | 931 | 927.9 | 1.60 | 3.643 | | G22 | 13346 | 13344.4 | 56.70 | 13318 | 13271.7 | 19.34 | 13359 | 13354.0 | 9.7 | 65.04 | 13359 | 13347.4 | 9.97 | 28.986 | | G23 | 13323 | 13321.3 | 58.70 | 13306 | 13273.6 | 19.45 | 13344 | 13337.8 | 4.0 | 65.04 | 13339 | 13327.6 | 9.36 | 28.747 | | G24 | 13329 | 13321.8 | 58.72 | 13296 | 13265.7 | 16.48 | 13337 | 13333.7 | 2.6 | 65.04 | 13337 | 13323.0 | 9.36 | 30.084 | | G30 | 3405 | 3394.62 | 56.90 | — | — | — | — | — | — | — | 3413 | 3407.5 | 5.19 | 29.905 | | G31 | 3293 | 3290.73 | 58.65 | — | — | — | — | — | — | — | 3306 | 3298.0 | 5.27 | 33.429 | | G32 | 1392 | 1391.86 | 56.52 | 1218 | 1198.8 | 9.43 | 1408 | 1406.1 | 1.6 | 65.04 | 1410 | 1406.6 | 1.90 | 6.304 | | G33 | 1368 | 1367.58 | 58.41 | 1200 | 1160.7 | 10.69 | 1382 | 1377.2 | 2.0 | 65.04 | 1382 | 1377.0 | 3.16 | 6.236 | | G34 | 1370 | 1367.57 | 58.58 | 1180 | 1158.2 | 8.46 | 1384 | 1380.8 | 1.9 | 65.04 | 1384 | 1380.8 | 1.69 | 6.453 | | G35 | — | — | — | 7528 | 7512.5 | 7.41 | 7680 | 7670.0 | 3.7 | 65.04 | 7667 | 7658.2 | 6.91 | 17.696 | | G36 | — | — | — | 7532 | 7518.3 | 5.75 | 7671 | 7663.3 | 4.7 | 65.04 | 7657 | 7643.7 | 6.81 | 17.988 | | G37 | — | — | — | 7533 | 7525.8 | 3.28 | 7687 | 7677.5 | 6.6 | 65.04 | 7672 | 7657.8 | 9.05 | 17.953 | | G43 | — | — | — | 6655 | 6625.9 | 13.26 | 6660 | 6658.0 | 2.5 | 19.51 | 6660 | 6658.3 | 1.89 | 8.556 | | G44 | — | — | — | 6641 | 6623.0 | 11.23 | 6650 | 6644.6 | 4.3 | 19.51 | 6650 | 6650.0 | 0.0 | 8.268 | | G45 | — | — | — | 6633 | 6616.1 | 11.49 | 6654 | 6646.3 | 6.0 | 19.51 | 6654 | 6648.6 | 2.46 | 8.758 | | G48 | — | — | — | 6000 | 5899.3 | 58.02 | 6000 | 6000.0 | 0.0 | 9.76 | 6000 | 6000.0 | 0.0 | 7.799 | | G49 | — | — | — | 6000 | 5928.2 | 41.79 | 6000 | 6000.0 | 0.0 | 9.76 | 6000 | 6000.0 | 0.0 | 7.892 | | G50 | — | — | — | 5868 | 5815.0 | 29.40 | 5880 | 5880.0 | 0.0 | 9.76 | 5880 | 5880.0 | 0.0 | 7.653 |
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