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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (3): 531-541    DOI: 10.3785/j.issn.1008-973X.2022.03.012
计算机与控制工程     
多角色多策略多目标粒子群优化算法
王万良(),金雅文,陈嘉诚,李国庆,胡明志,董建杭
浙江工业大学 计算机科学与技术学院，浙江 杭州 310023
Multi-objective particle swarm optimization algorithm with multi-role and multi-strategy
Wan-liang WANG(),Ya-wen JIN,Jia-cheng CHEN,Guo-qing LI,Ming-zhi HU,Jian-hang DONG
College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
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摘要：

针对粒子群算法在解决复杂多目标问题时存在过早收敛和多样性不足的问题，提出多角色多策略多目标粒子群优化算法(MOPSO_RS). 该算法根据粒子的角色划分指标,给不同性能的粒子赋予不同角色；提出多策略的学习参数调整方法和多策略的全局最优粒子选取方法，帮助种群执行各种搜索策略. 不同的学习参数使各角色粒子获得不同的搜索策略，以调整粒子的探索和开发能力. 不同的全局最优粒子使各角色粒子搜索不同区域，提高种群的搜索效率. 为了避免算法陷入局部最优，引入带有高斯函数的变异算子，使粒子根据其角色朝向不同的全局最优粒子变异，提高算法的求解精度. 实验结果表明，对比其他改进多目标算法，MOPSO_RS具有良好的收敛性和多样性，并验证了所提策略的有效性.
关键词： 多角色;  多目标优化;  粒子群优化算法;  多策略;  收敛性;  多样性    
Abstract:

A multi-objective particle swarm optimization algorithm with multi-role and multi-strategy (MOPSO_RS) was proposed, in view of the immature convergence and poor diversity of particle swarm optimization in solving complex multi-objective problems. According to index-based role, the particles with different performances were assigned for different roles. A multi-strategy parameter adjustment method and global optimal particle selection method were proposed to help the population carry out various search mechanisms. Different learning parameters enabled particles with different performances to obtain different search strategies so as to adjust the exploration and exploitation capabilities of the particles. Different global optimal particles made particles search different regions to improve the search efficiency of the population. To avoid the algorithm from falling into the local optimal, a mutation operator with Gaussian function was introduced to make particles mutate toward different global optimal particles and increase accuracy of the algorithm. The experiment results indicate that MOPSO_RS has better convergence and diversity than other improved multi-objective optimization algorithms, and verifies the effectiveness of the proposed strategy.
Key words: multi-role    multi-objective optimization    particle swarm optimization algorithm    multi-strategy    convergence    diversity
收稿日期: 2021-04-21 出版日期: 2022-03-29
CLC:  TP 301  
基金资助: 国家自然科学基金资助项目(61873240)
作者简介: 王万良（1957—），男，教授，从事人工智能及其自动化、网络控制研究. orcid.org/0000-0002-1552-5075.E-mail： zjutwwl@zjut.edu.cn
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引用本文:

王万良,金雅文,陈嘉诚,李国庆,胡明志,董建杭. 多角色多策略多目标粒子群优化算法[J]. 浙江大学学报(工学版), 2022, 56(3): 531-541.

Wan-liang WANG,Ya-wen JIN,Jia-cheng CHEN,Guo-qing LI,Ming-zhi HU,Jian-hang DONG. Multi-objective particle swarm optimization algorithm with multi-role and multi-strategy. Journal of ZheJiang University (Engineering Science), 2022, 56(3): 531-541.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.03.012    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I3/531

图 1  非支配解集的极端粒子图
图 2  不同角色的粒子在迭代前、后期选取的全局最优粒子图
图 3  外部归档集更新示意图
测试问题 MOEADCMA CAMOEA NSGAII MMOPSO CMOPSO MOPSO_RS
DTLZ1 2.068 6×10?2
(1.13×10?4) ? 		2.136 4×10?2
(3.22×10?4) ? 		2.739 6×10?2
(1.11×10?3) ? 		1.157 7×10?1
(2.41×10?1) ? 		7.869 8×10?1
(1.57×10+0) ? 		2.026 2×10?2
(1.79×10?4)
DTLZ2 5.549 4×10?2
(3.97×10?4) +		 5.706 2×10?2
(7.67×10?4) ? 		6.902 1×10?2
(2.77×10?3) ? 		7.143 9×10?2
(2.00×10?3) ? 		5.803 3×10?2
(1.15×10?3) ? 		5.595 1×10?2
(8.06×10?4)
DTLZ3 1.810 6×10+0
(3.39×10+0) ? 		5.838 6×10?2
(3.03×10?3) ? 		6.947 4×10?2
(2.78×10?3) ? 		2.371 7×10?1
(3.61×10?1) ? 		3.773 6×10+1
(2.67×10+1) ? 		5.471 1×10?2
(7.28×10?4)
DTLZ4 9.455 3×10?2
(6.45×10?2) ? 		5.734 0×10?2
(9.37×10?4) ? 		9.490 2×10?2
(1.58×10?1) ? 		7.185 8×10?2
(2.92×10?3) ? 		6.037 4×10?2
(1.24×10?3) ? 		5.629 6×10?2
(1.02×10?3)
DTLZ5 2.277 5×10?2
(5.66×10?5) ? 		5.073 2×10?3
(1.53×10?4) ? 		5.854 1×10?3
(3.42×10?4) ? 		6.532 5×10?3
(9.75×10?4) ? 		5.909 7×10?3
(7.55×10?4) ? 		4.360 3×10?3
(9.46×10?5)
DTLZ6 2.288 7×10?2
(2.19×10?5) ? 		4.633 2×10?3
(1.28×10?4) ? 		5.882 0×10?3
(3.01×10?4) ? 		6.889 7×10?3
(6.76×10?4) ? 		4.215 9×10?3
(4.69×10?5) ? 		4.084 1×10?3
(2.39×10?5)
DTLZ7 1.512 8×10?1
(5.13×10?3) ? 		6.190 9×10?2
(1.64×10?3) = 		7.584 4×10?2
(3.65×10?3) ? 		1.206 6×10?1
(9.00×10?2) ? 		1.554 6×10?1
(2.27×10?1) ? 		6.176 5×10?2
(1.45×10?3)
WFG2 2.453 4×10?1
(1.67×10?2) ? 		1.827 0×10?1
(7.41×10?3) ? 		2.173 0×10?1
(9.22×10?3) ? 		2.324 9×10?1
(1.28×10?2) ? 		1.807 3×10?1
(6.13×10?3) ? 		1.735 8×10?1
(4.34×10?3)
WFG4 3.312 3×10?1
(2.11×10?2) ? 		2.329 7×10?1
(3.73×10?3) ? 		2.788 7×10?1
(8.35×10?3) ? 		3.113 3×10?1
(8.35×10?3) ? 		2.670 6×10?1
(5.75×10?3) ? 		2.275 9×10?1
(3.37×10?3)
WFG9 3.036 8×10?1
(2.52×10?2) ? 		2.314 3×10?1
(4.11×10?3) ? 		2.744 4×10?1
(1.20×10?2) ? 		2.877 0×10?1
(2.18×10?2) ? 		2.186 2×10?1
(3.26×10?3) = 		2.172 7×10?1
(3.62×10?3)
+/?/= 1/9/0 0/9/1 0/10/0 0/10/0 0/9/1 　
表 1  MOPSO_RS和其他5种多目标算法在不同测试问题得到的IGD结果
测试问题 MOEADCMA CAMOEA NSGAII MMOPSO CMOPSO MOPSO_RS
DTLZ1 8.403 8×10?1
(6.88×10?4) ? 		8.385 4×10?1
(9.40×10?4) ? 		8.242 1×10?1
(3.70×10?3) ? 		6.980 3×10?1
(2.85×10?1) ? 		3.535 1×10?1
(3.69×10?1) ? 		8.422 1×10?1
(4.05×10?4)
DTLZ2 5.564 4×10?1
(4.67×10?4) +		 5.504 6×10?1
(2.22×10?3) + 		5.314 8×10?1
(4.80×10?3) ? 		5.302 2×10?1
(4.38×10?3) ? 		5.412 1×10?1
(3.11×10?3) ? 		5.487 1×10?1
(2.39×10?3)
DTLZ3 3.407 1×10?1
(2.59×10?1) ? 		5.485 8×10?1
(5.15×10?3) ? 		5.293 7×10?1
(5.93×10?3) ? 		4.370 4×10?1
(1.98×10?1) ? 		0.000 0×10+0
(0.00×10+0) ? 		5.574 0×10?1
(2.56×10?3)
DTLZ4 5.450 3×10?1
(2.37×10?2) ? 		5.515 7×10?1
(1.82×10?3) +		 5.212 6×10?1
(8.00×10?2) ? 		5.325 5×10?1
(5.42×10?3) ? 		5.344 1×10?1
(2.78×10?3) ? 		5.498 6×10?1
(2.70×10?3)
DTLZ5 1.904 1×10?1
(3.06×10?5) ? 		1.991 7×10?1
(1.59×10?4) ? 		1.991 4×10?1
(1.76×10?4) ? 		1.991 9×10?1
(1.96×10?4) ? 		1.981 3×10?1
(5.52×10?4) ? 		1.996 5×10?1
(1.34×10?4)
DTLZ6 1.904 7×10?1
(9.91×10?6) ? 		1.998 6×10?1
(1.22×10?4) ? 		1.994 1×10?1
(1.52×10?4) ? 		1.992 2×10?1
(1.63×10?4) ? 		2.001 9×10?1
(3.10×10?5) +		 2.000 9×10?1
(3.36×10?5)
DTLZ7 2.588 5×10?1
(7.17×10?4) ? 		2.736 0×10?1
(1.65×10?3) ? 		2.682 5×10?1
(2.10×10?3) ? 		2.632 6×10?1
(9.77×10?3) ? 		2.603 7×10?1
(2.14×10?2) ? 		2.751 3×10?1
(9.04×10?4)
WFG2 9.007 6×10?1
(1.65×10?2) ? 		9.291 7×10?1
(1.78×10?3) =		 9.205 9×10?1
(2.43×10?3) ? 		9.143 3×10?1
(3.78×10?3) ? 		9.287 5×10?1
(1.41×10?3) = 		9.289 7×10?1
(1.34×10?3)
WFG4 5.062 5×10?1
(1.68×10?2) ? 		5.361 2×10?1
(3.13×10?3) +		 5.023 6×10?1
(4.45×10?3) ? 		4.811 8×10?1
(6.75×10?3) ? 		4.840 6×10?1
(4.67×10?3) ? 		5.253 2×10?1
(4.15×10?3)
WFG9 4.757 7×10?1
(2.81×10?2) ? 		5.136 1×10?1
(4.23×10?3) = 		5.039 3×10?1
(6.93×10?3) ? 		4.995 9×10?1
(1.94×10?2) ? 		5.173 0×10?1
(2.72×10?3) +		 5.123 3×10?1
(5.13×10?3)
+/?/= 1/10/0 3/5/2 0/10/0 0/10/0 2/7/1 　
表 2  MOPSO_RS和其他5种多目标算法在不同测试问题得到的HV结果
图 4  各算法部分测试问题帕累托前沿图
图 5  不同的划分阈值在DTLZ7上的IGD
测试问题 目标数目 NSGA-III RSEA RVEA NMPSO MOPSO_RS
DTLZ1 5 6.337 6×10?2
(8.48×10?5) ? 		7.611 1×10?2
(2.16×10?3) ? 		6.332 7×10?2
(7.81×10?5) ? 		6.512 3×10?2
(1.99×10?3) ? 		5.870 5×10?2
(5.15×10?4)
10 1.493 3×10?1
(4.62×10?2) ? 		1.524 3×10?1
(2.63×10?2) ? 		1.334 2×10?1
(2.68×10?3) ? 		1.687 7×10?1
(1.32×10?2) ? 		1.100 4×10?1
(1.46×10?3)
15 2.030 2×10?1
(8.76×10?2) ? 		2.009 3×10?1
(2.48×10?2) ? 		1.334 4×10?1
(1.12×10?2) +		 1.169 0×10+0
(3.60×10+0) ? 		1.351 8×10?1
(3.20×10?3)
DTLZ2 5 1.949 0×10?1
(1.61×10?5) + 		2.455 6×10?1
(1.99×10?2) ? 		1.948 9×10?1
(8.54×10?6) +		 2.162 3×10?1
(2.31×10?3) ? 		2.099 2×10?1
(2.06×10?3)
10 4.904 3×10?1
(5.93×10?2) ? 		5.338 5×10?1
(3.17×10?2) ? 		4.533 6×10?1
(3.46×10?4) ? 		4.230 0×10?1
(2.20×10?3) ? 		4.198 4×10?1
(2.21×10?3)
15 6.904 7×10?1
(8.99×10?2) ? 		6.701 9×10?1
(2.53×10?2) ? 		5.269 7×10?1
(6.76×10?4) +		 6.565 8×10?1
(7.27×10?2) ? 		5.346 1×10?1
(3.80×10?3)
WFG2 5 4.712 8×10?1
(1.79×10?3) + 		4.958 8×10?1
(1.39×10?2) + 		4.484 9×10?1
(8.61×10?3) +		 1.094 9×10+0
(2.08×10?1) ? 		5.393 7×10?1
(2.20×10?2)
10 1.447 3×10+0
(1.34×10?1) ? 		1.099 6×10+0
(3.44×10?2) ? 		1.133 8×10+0
(3.09×10?2) ? 		1.956 8×10+0
(1.94×10?1) ? 		1.022 4×10+0
(1.94×10?2)
15 2.036 9×10+0
(1.06×10?1) ? 		1.953 8×10+0
(2.25×10?1) ? 		1.722 4×10+0
(1.15×10?1) ? 		2.729 8×10+0
(2.71×10?1) ? 		1.525 0×10+0
(3.04×10?2)
WFG4 5 1.176 6×10+0
(8.31×10?4) +		 1.298 9×10+0
(2.67×10?2) = 		1.177 3×10+0
(9.79×10?4) + 		1.265 5×10+0
(2.30×10?2) + 		1.292 6×10+0
(1.92×10?2)
10 4.769 4×10+0
(3.99×10?2) ? 		4.877 3×10+0
(1.06×10?1) ? 		4.633 0×10+0
(5.26×10?2) ? 		4.219 0×10+0
(2.93×10?2) = 		4.206 1×10+0
(3.27×10?2)
15 8.591 6×10+0
(5.17×10?1) ? 		9.202 0×10+0
(2.42×10?1) ? 		8.856 0×10+0
(1.90×10?1) ? 		7.683 0×10+0
(5.87×10?2) = 		7.658 9×10+0
(5.89×10?2)
WFG9 5 1.127 9×10+0
(6.02×10?3) +		 1.256 2×10+0
(4.88×10?2) ? 		1.149 7×10+0
(2.73×10?3) + 		1.192 4×10+0
(1.66×10?2) + 		1.223 0×10+0
(2.14×10?2)
10 4.521 1×10+0
(3.70×10?2) ? 		4.808 5×10+0
(1.06×10?1) ? 		4.467 2×10+0
(7.60×10?2) ? 		4.147 5×10+0
(3.89×10?2) ? 		4.100 5×10+0
(2.84×10?2)
15 8.127 9×10+0
(1.71×10?1) ? 		9.053 4×10+0
(2.46×10?1) ? 		7.460 2×10+0
(2.77×10?1) =		 7.665 7×10+0
(1.06×10?1) ? 		7.484 3×10+0
(7.46×10?2)
+/?/= 4/11/0 1/13/1 6/8/1 2/11/2
表 3  MOPSO_RS和其他4种高维多目标算法在5、10、15个目标的测试函数上的 $ {\text{IGD}} $指标结果
测试问题 MOPSO_RS-OG MOPSO_R-G MOPSO_R MOPSO_RS
DTLZ3 5.437 4×10?2(1.86×10?3) + 5.471 2×10?2 (7.02×10?4) = 5.591 8×10?2 (2.65×10?3) ? 5.471 1×10?2 (7.28×10?4)
DTLZ4 5.793 9×10?2 (1.81×10?3) ? 5.746 1×10?2 (1.90×10?3) ? 5.690 1×10?2 (1.45×10?3) = 5.629 6×10?2(1.02×10?3)
DTLZ5 4.454 9×10?3 (1.24×10?4) ? 4.368 3×10?3 (1.23×10?4) = 4.423 6×10?3 (1.15×10?4) ? 4.360 3×10?3(9.46×10?5)
DTLZ6 4.107 9×10?3 (2.97×10?5) ? 4.120 2×10?3 (3.51×10?5) ? 4.125 3×10?3 (2.76×10?5) ? 4.084 1×10?3(2.39×10?5)
+/?/= 1/3/2 0/3/3 0/5/1
表 4  不同策略对IGD的影响
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