Direct Position Updating-based Trying-mutation Particle Swarm Optimization Algorithm and its Application on Reliability Optimization
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摘要: 为了提升粒子群优化(Particle swarm optimization, PSO)算法的全局寻优能力，增强PSO算法在处理复杂的、高维的、多模态优化问题的寻优性能，提升PSO算法在可靠性优化应用中的优化效果，提出了一种基于直接位置更新策略的试变异(Direct position updating-based trying-mutation PSO, DTPSO)算法。设计了直接位置更新策略和试变异策略，有效维持了种群的多样性，维持了探索和开发的平衡，提升了获得全局最优解的概率。通过9种复杂测试函数的验证和比较，证明了DTSPO算法设计的合理性，以及算法拥有的优异的全局寻优能力。对可靠性冗余分配和可靠度分配问题进行了优化，并和其它先进的改进算法进行比较，结果证明了DTPSO算法的稳定性和寻优性能。Abstract: In order to improve the global optimization ability of particle swarm optimization (PSO), enhance the performance of PSO in dealing with those complex, high-dimensional, multimodal optimization problems, and furthermore, promote the optimization effect in reliability optimization applications, a direct position updating-based trying-mutation PSO (DTPSO) is proposed in this paper. In this algorithm, the direct position updating strategy and trying mutation strategy are designed, which can effectively maintain the diversity of population, balance the exploitation and exploration, and increase the probability of obtaining the global optimal solution. After being verified and compared by 9 complex test functions, the rationality of DTPSO algorithm design and the excellent global optimization performances are proved. In the reliability optimization, the reliability redundancy allocation and reliability allocation are optimized by different advanced improved algorithms, and the comparison results prove the stability and optimization performance of DTPSO.
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表 1 典型测试函数特征
测试函数 搜索范围 维数 最优解 全局极值 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (1, 1, …, 1)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (0, 0, …, 0)100 0 
[-100, 100] 100 (1, 1, …, 1)100 0 
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表 2 不同惯性权重对寻优性能的影响
函数 ω1-DTPSO ω2-DTPSO ω3-DTPSO Mean StD Mean StD Mean StD f1 0 0 7.094 9×10-309 0 0 0 f2 0 0 0 0 0 0 f3 0 0 0 0 0 0 f4 0 0 0 0 0 0 f5 0 0 0 0 0 0 f6 0.001 6 0.002 5 1.701 7×10-5 5.480 5×10-5 2.051 6×10-7 5.108 8×10-7 f7 0 0 7.736 1×10-313 0 0 0 f8 0 0 2.608 7×10-309 0 0 0 f9 5.503 4×10-5 8.930 3×10-5 1.590 9×10-7 1.912 9×10-7 5.691 7×10-10 1.183 24×10-9
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表 3 试变异策略对寻优性能的影响
函数 TPSO DPSO DTPSO Mean StD Mean StD Mean StD f1 2.029 0×103 432.309 7 0 0 0 0 f2 0.485 4 0.004 4 0 0 0 0 f3 1.483 5 0.119 9 0 0 0 0 f4 20.214 2 1.149 5 0 0 0 0 f5 3.284 3×103 435.924 0 0 0 0 0 f6 6.416 5×106 2.809 1×106 98.744 2 0.0047 2.051 6×10-7 5.108 8×10-7 f7 1.383 4×1088 7.576 3×1088 0 0 0 0 f8 5.407 2×104 2.286 8×104 0 0 0 0 f9 855.031 9 191.828 5 8.722 6 0.369 8 5.691 7×10-10 1.183 24×10-9
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表 4 不同PSO改进型算法的寻优性能比较
函数 MELPSO SRPSO DNPSO MAPSO DTPSO Mean StD Mean StD Mean StD Mean StD Mean StD f1 2.7021×10-88 1.4797×10-87 1.3597 0.7925 5.3732×10-32 2.6408×10-31 2.6081 1.0807 0 0 f2 0 0 0.4900 0.0026 0.4999 2.6756×10-5 0.4842 0.0073 0 0 f3 0 0 0.0266 0.0141 0.1620 0.0928 0.0465 0.0217 0 0 f4 0 0 21.3397 0.0538 20.1824 0.0549 19.7378 1.2965 0 0 f5 0 0 742.2342 97.0136 1.6505×103 285.1539 803.6139 141.3295 0 0 f6 93.8743 1.3185 1.3941×103 470.5492 3.8874×103 2.2049×103 2.0078 ×103 1.3292×103 2.0516×10-7 5.1088×10-7 f7 3.9447×10-188 0 2.0038×1053 1.0181×1054 3.6985×1033 2.0051×1034 2.2577×1048 1.0191×1049 0 0 f8 1.0269×10-76 3.4135×10-76 1.1436×104 4.5527×103 8.9545×103 7.8814×103 9.0510×103 2.9310×103 0 0 f9 4.1419 0.5041 480.5421 88.6011 6.2407×103 2.2854×103 450.1516 90.6516 5.6917×10-10 1.1834×10-9
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表 6 在可靠性冗余分配优化中各算法性能比较
算法 最优解 系统最优总成本 系统最优可靠度 最优解比例/% 最优解时平均迭代步数 时间开销/s DTPSO [1, 1, 3, 1, 2] 16 0.994 5 100 22.4 33.413 QPSO [1, 1, 3, 1, 2] 16 0.994 5 88 60.3 27.732 ACO [2, 1, 2, 1, 2] 16 0.993 9 84 45.7 25.983 GA [2, 1, 2, 1, 2] 16 0.993 9 78 56.3 32.871 SAA [2, 1, 3, 1, 1] 17 0.993 9 75 79.4 21.325
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表 7 在可靠度分配优化中各算法性能比较
算法 系统总成本比较 最优输出解比较(各单元分配可靠度) 系统可靠度 时间开销/s DTPSO Mean 260.1879 Min 259.9945 0.8309 0.9375 0.5000 0.6070 0.99 35.332 StD 0.2287 Max 261.3611 0.8575 0.9348 0.5020 0.5447 0.99 H-PSO Mean 261.3318 Min 259.9923 0.8299 0.9377 0.5000 0.6086 0.99 30.757 StD 4.0935 Max 275.9935 0.7586 0.9900 0.5000 0.6049 0.99 ALCPSO Mean 260.2271 Min 259.9917 0.8305 0.9373 0.5000 0.6087 0.99 24.374 StD 0.5970 Max 263.1432 0.8695 0.9335 0.5053 0.5078 0.99 MELPSO Mean 261.9232 Min 259.9916 0.8302 0.9374 0.5000 0.6089 0.99 59.137 StD 3.8856 Max 276.3871 0.7358 0.9897 0.5000 0.6395 0.99
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