多目标粒子群优化算法及其应用研究综述

叶倩琳,王万良,王铮

Survey of multi-objective particle swarm optimization algorithms and their applications

Qianlin YE,Wanliang WANG,Zheng WANG

表 2 7个MOPSO算法在3类基准问题上的IGD

Tab.2 IGD of seven MOPSO algorithms on three benchmark problems

问题 传统 基于Pareto支配 基于分解 基于指标 MOPSO NMPSO CMOPSO dMOPSO EGCCMOPSO ESMOPSO R2HMOPSO ZDT1 1.64×100 (9.58×10−2) 3.16×10−2 (9.92×10−3) 4.11×10−3 (7.60×10−5) 3.90×10−3 (3.84×10−5) 3.91×10−3 (4.89×10−5) 3.86×10−3 (6.05×10−7) 3.90×10−3 (6.21×10−5) ZDT2 3.15×100 (1.57×10−1) 6.25×10−2 (1.32×10−1) 4.08×10−3 (7.02×10−5) 6.44×10−2 (1.85×10−1) 3.88×10−3 (3.86×10−5) 3.80×10−3 (9.45×10−7) 3.83×10−3 (4.20×10−5) ZDT3 1.19×100 (8.60×10−2) 9.79×10−2 (7.02×10−3) 4.66×10−3 (6.74×10−5) 1.06×10−2 (7.10×10−4) 4.57×10−3 (4.83×10−5) 9.99×10−3 (3.59×10−4) 6.12×10−2 (1.58×10−1) ZDT4 1.02×101 (4.52×100) 1.37×10−2 (2.71×10−1) 3.84×10−3 (2.96×10−5) 5.97×100 (4.48×100) 3.87×10−3 (3.87×10−5) 3.77×10−3 (6.15×10−6) 4.52×10−3 (3.73×10−3) ZDT6 5.38×100 (5.10×10−1) 2.21×10−3 (1.60×10−4) 3.74×10−3 (1.39×10−4) 1.88×10−3 (8.55×10−6) 3.07×10−3 (1.75×10−5) 1.90×10−3 (7.21×10−7) 1.89×10−3 (4.33×10−5) DTLZ1 1.55×100 (1.02×100) 4.25×101 (6.56×100) 3.25×100 (4.50×100) 1.53×101 (1.18×101) 2.47×100 (3.46×100) 1.28×10−2 (7.85×10−6) 1.99×10−2 (2.08×10−3) DTLZ2 1.57×10−1 (3.83×10−2) 7.68×10−2 (2.69×10−3) 6.71×10−2 (1.94×10−3) 4.72×10−2 (1.49×10−3) 5.48×10−2 (5.68×10−4) 3.56×10−2 (1.67×10−4) 4.37×10−2 (1.20×10−3) DTLZ4 3.61×10−1 (2.70×10−1) 1.07×10−1 (1.18×10−1) 1.29×10−1 (2.22×10−1) 1.18×10−1 (7.63×10−2) 5.63×10−2 (8.29×10−4) 4.68×10−2 (9.35×10−4) 5.20×10−2 (2.01×10−3) DTLZ6 9.21×100 (6.60×10−2) 7.57×10−2 (3.11×10−3) 5.31×10−1 (2.52×10−4) 1.27×10−1 (6.73×10−3) 4.18×10−3 (4.54×10−5) 7.85×10−2 (3.16×10−3) 7.04×10−2 (8.44×10−3) UF2 1.26×10−1 (1.41×10−2) 8.19×10−2 (7.06×10−3) 6.38×10−2 (4.76×10−3) 4.73×10−2 (8.12×10−3) 5.83×10−2 (7.68×10−3) 1.54×10−2 (2.55×10−3) 1.84×10−2 (7.15×10−3) UF3 4.89×10−1 (2.35×10−2) 3.64×10−1 (5.59×10−2) 3.97×10−1 (2.56×10−2) 5.01×10−1 (2.56×10−1) 3.45×10−1 (7.31×10−2) 2.59×10−1 (7.62×10−2) 6.20×10−1 (1.77×10−1) UF4 1.73×10−1 (6.65×10−3) 6.39×10−2 (8.78×10−3) 1.09×10−1 (1.12×10−2) 9.21×10−2 (4.96×10−3) 7.97×10−2 (5.31×10−3) 3.28×10−2 (2.90×10−3) 3.76×10−2 (2.64×10−3) UF5 2.43×100 (3.40×10−1) 1.69×100 (4.19×10−1) 8.45×10−1 (1.75×10−1) 7.01×10−1 (1.73×10−1) 8.27×10−1 (3.27×10−1) 1.62×10−1 (7.93×10−3) 1.75×10−1 (2.73×10−2) UF8 4.65×10−1 (3.84×10−2) 4.48×10−1 (1.18×10−1) 5.54×10−1 (1.05×10−1) 1.97×10−1 (3.14×10−2) 2.68×10−1 (3.84×10−3) 1.81×10−1 (6.89×10−2) 4.14×10−1 (5.22×10−2) UF9 6.12×10−1 (4.81×10−2) 4.70×10−1 (6.12×10−2) 8.45×10−1 (1.14×10−1) 1.14×10−1 (2.88×10−2) 4.52×10−1 (2.49×10−2) 6.29×10−2 (5.04×10−3) 2.36×10−1 (5.91×10−2) UF10 1.32×100 (1.94×10−1) 1.50×100 (3.41×100) 4.51×100 (4.79×10−1) 1.01×100 (1.74×10−1) 3.30×10−1 (2.03×10−2) 2.26×10−1 (1.06×10−1) 2.38×10−1 (5.69×10−2)