基于多核数据合成的离线小数据驱动的进化算法
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李二超,刘昀
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Offline small data-driven evolutionary algorithm based on multi-kernel data synthesis
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Erchao LI,Yun LIU
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| 表 1 DDEA-MKDS与各对比算法在6个测试问题上的优化结果 |
| Tab.1 Optimization result of DDEA-MKDS and other comparison algorithms on six test problems |
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| 问题 | d | DDEA-MKDS | TT-DDEA | SRK-DDEA | CC-DDEA | CL-DDEA | DDEA-SE | | Ellipsoid | 10 | 0.79±0.73 | 4.52±6.36(+) | 1.91±2.52(≈) | 1.91±1.12(+) | 114.41±97.15(+) | 2.81±1.38(+) | | 30 | 5.58±2.99 | 18.68±14.99(+) | 11.40±11.59(+) | 9.05±5.60(+) | 451.17±394.59(+) | 48.57±21.00(+) | | 50 | 27.88±9.13 | 110.19±84.30(+) | 23.99±14.62(−) | 32.19±12.61(+) | 1181.39±1035.79(+) | 195.13±57.46(+) | | 100 | 252.72±52.58 | 1380.95±1237.13(+) | 269.84±54.97(≈) | 49.60±22.66(−) | 4908.28±5817.24(+) | 1399.45±377.21(+) | | Rosenbrock | 10 | 16.22±7.00 | 20.84±10.33(≈) | 23.90±12.02(+) | 31.33±15.88(+) | 941.78±796.76(+) | 31.81±14.69(+) | | 30 | 39.82±9.80 | 57.50±25.14(+) | 65.48±29.53(+) | 61.12±16.51(+) | 1170.28±1082.81(+) | 80.95±28.13(+) | | 50 | 69.24±18.95 | 125.76±37.03(+) | 85.74±20.65(≈) | 104.91±51.58(+) | 1298.44±1265.39(+) | 217.48±61.36(+) | | 100 | 209.61±36.64 | 373.37±68.49(+) | 189.10±24.13(≈) | 178.94±42.90(≈) | 1907.06±1789.96(+) | 714.23±121.78(+) | | Ackley | 10 | 5.78±1.73 | 9.71±4.75(+) | 6.42±1.90(≈) | 7.57±2.24(+) | 10.27±4.71(≈) | 6.35±1.63(≈) | | 30 | 4.25±0.69 | 6.91±1.98(+) | 6.10±2.17(+) | 8.19±4.71(+) | 16.19±2.45(+) | 8.96±1.35(+) | | 50 | 4.73±0.47 | 7.63±0.81(+) | 5.94±1.65(≈) | 5.73±1.98(≈) | 11.51±3.09(+) | 10.25±0.86(+) | | 100 | 7.20±0.57 | 11.02±2.01(+) | 7.28±0.60(≈) | 4.95±0.85(−) | 13.01±4.70(+) | 11.59±0.52(+) | | Levy | 10 | 1.60±0.36 | 3.19±3.00(≈) | 2.30±1.22(≈) | 2.48±2.42(≈) | 18.56±9.85(+) | 2.95±2.53(≈) | | 30 | 3.57±0.76 | 10.18±10.03(+) | 4.39±1.33(≈) | 4.02±0.87(≈) | 51.71±39.59(+) | 8.62±3.44(+) | | 50 | 5.94±0.77 | 16.57±11.72(+) | 6.01±1.06(≈) | 10.30±4.54(+) | 109.68±64.49(+) | 20.91±6.25(+) | | 100 | 13.70±3.59 | 106.97±66.70(+) | 13.88±3.64(≈) | 11.03±1.97(≈) | 154.60±79.65(+) | 73.42±17.79(+) | | Griewank | 10 | 1.21±0.28 | 3.51±3.64(+) | 1.12±0.11(≈) | 1.19±0.21(≈) | 26.32±25.28(+) | 2.26±0.54(+) | | 30 | 3.32±1.00 | 5.72±3.12(+) | 1.47±0.14(−) | 1.70±0.33(−) | 96.19±122.65(+) | 12.34±4.19(+) | | 50 | 6.24±1.81 | 9.23±6.83(≈) | 3.04±0.51(−) | 2.21±0.40(−) | 136.93±114.01(+) | 22.87±6.96(+) | | 100 | 21.39±4.12 | 61.68±30.82(+) | 18.56±3.96(≈) | 3.61±0.74(−) | 148.10±168.05(+) | 90.66±20.69(+) | | Rastrigin | 10 | 42.23±26.46 | 58.47±28.90(≈) | 64.47±35.35(+) | 89.87±37.44(+) | 138.64±34.53(+) | 76.92±26.52(≈) | | 30 | 95.41±61.47 | 242.85±162.46(+) | 152.73±104.34(≈) | 195.63±60.41(+) | 322.84±68.42(+) | 219.82±36.95(+) | | 50 | 184.75±61.41 | 397.02±89.28(+) | 245.34±101.93(+) | 280.60±89.96(+) | 570.56±47.71(+) | 431.38±57.44(+) | | 100 | 692.34±122.68 | 1061.33±190.85(+) | 697.66±128.78(≈) | 319.72±271.23(−) | 1307.19±388.38(+) | 953.94±51.30(+) | | +/≈/− | NA | 20/4/0 | 6/15/3 | 12/6/6 | 23/1/0 | 21/3/0 | | Friedman Rank | 1.63 | 4.04 | 2.40 | 2.40 | 6.00 | 4.54 |
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