数据驱动的智能计算及其应用研究综述

戴瑞,介婧,王万良,叶倩琳,吴菲

Review of data-driven intelligent computation and its application

Rui DAI,Jing JIE,Wanliang WANG,Qianlin YE,Fei WU

表 3 10个最新多目标DDICs在DTLZ和WFG测试问题上获得IGD的均值和标准差

Tab.3 Mean and standard deviation of IGD values obtained by ten multi-objective DDICs on DTLZ and WFG problems

测试函数 GCS-PSO REMO θ-DAE-DP ABMOEA CSEA HeEMOEA EDNMOEA KRVEA ParEGO KTA2 DTLZ1 1.430×103 (7.70×101) 1.260×103 (9.63×101)(−) 1.462×103 (8.67×101)(=) 1.440×103 (7.13×101)(=) 1.299×103 (2.72×101)(−) 1.471×103 (6.34×100)(=) 1.502×103 (3.04×101)(+) 1.395×103 (1.55×102)(−) 1.455×103 (9.87×101)(=) 8.246×102 (2.40×100)(−) DTLZ2 3.299×10-1 (5.82×10-3) 2.765×100 (2.82×101)(+) 3.563×100 (2.79×10−1)(+) 3.475×100 (2.08×10−1)(+) 2.948×100 (4.99×10−1)(+) 8.328×10−1 (2.26×10−2)(+) 3.154×100 (1.42×10−1)(+) 3.421×100 (4.23×10−2)(+) 3.203×100 (1.98×10−1)(+) 6.644×10−1 (1.31×10−1)(+) DTLZ3 4.441×103 (1.97×102) 3.972×103 (2.90×102)(−) 4.409×103 (2.24×102)(=) 4.472×103 (1.21×102)(=) 3.940×103 (1.99×102)(=) 4.600×103 (1.87×102)(=) 4.639×103 (4.84×100)(=) 4.342×103 (2.36×101)(=) 4.568×103 (5.63×101)(=) 2.737×103 (2.45×100)(−) DTLZ4 1.258×100 (1.14×10−1) 2.579×100 (2.32×10−1)(+) 3.544×100 (3.80×10−1)(+) 3.457×100 (1.33×10−1)(+) 2.526×100 (8.60×10−2)(+) 1.547×100 (7.89×10−2)(=) 3.595×100 (7.98×10−2)(+) 3.181×100 (1.12×10−1)(+) 3.666×100 (1.03×10−1)(+) 1.447×100 (9.39×10-3)(+) DTLZ5 2.372×10-1 (4.83×10−2) 2.631×100 (2.58×10−1)(+) 2.969×100 (3.43×10−1)(+) 3.345×100 (1.61×10−2)(+) 2.739×100 (3.83×10-3)(+) 8.551×10−1 (3.75×10−2)(+) 3.167×100 (1.89×10−2)(+) 3.508×100 (6.06×10−2)(+) 3.248×100 (1.90×10−1)(+) 5.355×10−1 (4.92×10−2)(+) DTLZ6 4.456×101 (1.38×10−1) 3.258×101 (1.45×10-2)(−) 4.852×101 (3.51×10−2)(+) 5.092×101 (2.12×10−1)(+) 4.835×101 (3.59×10−1)(+) 5.102×101 (7.25×10−2)(+) 5.005×101 (7.60×10−1)(+) 4.579×101 (7.54×10−1)(=) 4.729×101 (3.19×10−1)(+) 3.333×101 (1.97×100)(−) DTLZ7 4.912×10-1 (6.41×10-3) 6.575×101 (5.83×10−1)(+) 7.439×101 (6.33×10−1)(+) 9.862×100 (1.41×10−1)(+) 7.380×100 (7.45×10−1)(+) 8.263×100 (4.03×10−1)(+) 4.312×100 (1.93×10−1)(+) 8.265×10−1 (5.98×10−1)(+) 2.069×100 (5.50×10−1)(+) 6.206×10−1 (3.28×10−1)(+) WFG1 2.182×100 (3.97×10−2) 1.797×100 (6.10×10−2)(−) 1.804×100 (8.26×10−2)(−) 2.409×100 (7.57×10−2)(+) 1.668×100 (1.52×10−2)(−) 2.355×100 (5.03×10−2)(+) 1.659×100 (3.49×10−2)(−) 1.643×100 (4.82×10-3)(−) 1.687×100 (4.98×10−2)(−) 2.056×100 (1.13×10−2)(−) WFG2 5.132×10-1 (4.74×10−2) 7.437×10−1 (2.64×10−2)(+) 8.407×10−1 (3.95×10−2)(+) 9.977×10−1 (5.90×10−2)(+) 1.0630×100 (2.12×10-2)(+) 8.844×10−1 (1.08×10−1)(+) 1.024×100 (5.08×10−2)(+) 9.647×10−1 (9.93×10−2)(+) 9.064×10−1 (3.59×10−2)(+) 1.174×100 (3.54×10−2)(+) WFG3 4.694×10-1 (3.75×10-3) 7.612×10−1 (8.24×10−3)(+) 8.187×10−1 (2.28×10−2)(+) 7.756×10−1 (1.45×10−2)(+) 8.005×10−1 (6.48×10−3)(+) 5.077×10−1 (1.28×10−2)(+) 7.875×10−1 (9.31×10−3)(+) 7.871×10−1 (1.40×10−2)(+) 7.759×10−1 (7.10×10−3)(+) 8.091×10−1 (1.12×10−1)(+) WFG4 4.479×10-1 (2.87×10−2) 5.153×10−1 (1.59×10−2)(+) 5.332×10−1 (1.19×10−2)(+) 8.674×10−1 (5.17×10−2)(+) 7.384×10−1 (1.21×10−1)(+) 7.320×10−1 (4.94×10−2)(+) 6.466×10−1 (1.54×10-3)(+) 8.060×10−1 (2.65×10−2)(+) 7.955×10−1 (7.37×10−2)(+) 1.192×100 (1.86×10−1)(+) WFG5 7.514×10−1 (4.15×10−3) 7.118×10-1 (1.08×10−2)(−) 8.667×10−1 (2.52×10−2)(+) 8.680×10−1 (9.44×10−3)(+) 8.421×10−1 (8.99×10-3)(+) 8.499×10−1 (1.92×10−2)(+) 7.966×10−1 (1.23×10−2)(+) 8.567×10−1 (3.36×10−2)(+) 8.694×10−1 (4.78×10−2)(+) 1.074×100 (6.19×10−2)(+) WFG6 7.067×10-1 (5.15×10-3) 8.849×10−1 (1.80×10−2)(+) 1.005×100 (1.91×10−2)(+) 1.020×100 (2.22×10−2)(+) 9.376×10−1 (2.18×10−2)(+) 9.552×10−1 (6.49×10−2)(+) 9.506×10−1 (9.03×10−3)(+) 1.022×100 (2.26×10−2)(+) 1.050×100 (1.04×10−2)(+) 1.177×100 (1.67×10−2)(+) WFG7 4.891×10-1 (2.21×10-3) 6.705×10−1 (1.39×10−2)(+) 6.744×10−1 (1.69×10−2)(+) 6.684×10−1 (1.13×10−2)(+) 7.467×10−1 (7.27×10−2)(+) 6.378×10−1 (1.30×10−2)(+) 6.788×10−1 (4.60×10−3)(+) 6.911×10−1 (5.11×10−3)(+) 7.013×10−1 (4.11×10−2)(+) 6.016×10−1 (1.29×10−2)(+) WFG8 5.743×10-1 (3.63×10-3) 7.288×10−1 (1.13×10−2)(+) 7.220×10−1 (1.21×10−2)(+) 7.415×10−1 (1.66×10−2)(+) 7.355×10−1 (1.59×10−2)(+) 6.903×10−1 (2.04×10−2)(+) 7.308×10−1 (8.46×10−3)(+) 7.243×10−1 (1.53×10−2)(+) 7.916×10−1 (2.12×10−2)(+) 5.781×10−1 (2.27×10−2)(=) WFG9 6.573×10-1 (9.88×10-3) 7.288×10−1 (1.13×10−2)(+) 9.203×10−1 (1.48×10−2)(+) 9.387×10−1 (2.54×10−2)(+) 9.114×10−1 (2.92×10−2)(+) 9.022×10−1 (3.36×10−2)(+) 9.515×10−1 (1.61×10−2)(+) 9.380×10−1 (1.69×10−2)(+) 9.708×10−1 (3.85×10−2)(+) 6.672×10−1 (6.40×10−2)(=) +/=/− NA 11/0/5 13/2/1 14/2/0 13/1/2 13/3/0 14/1/1 12/2/2 13/2/1 10/2/4