非线性多目标概率约束规划免疫优化算法

张仁崇; 张著洪

doi:10.13700/j.bh.1001-5965.2019.0350

非线性多目标概率约束规划免疫优化算法

doi: 10.13700/j.bh.1001-5965.2019.0350

张仁崇¹,
张著洪^2, ,

1.
贵州商学院计算机与信息工程学院, 贵阳 550014
2.
贵州大学大数据与信息工程学院, 贵阳 550025

基金项目:

国家自然科学基金 61563009)

贵州省教育厅青年科技人才成长项目 QJH KY Zi[2018] No.276

贵州省大数据应用工程研究中心 QJH KY Zi[2017] No.022

详细信息

作者简介:
张仁崇男, 硕士, 助教。主要研究方向:智能优化算法

张著洪男, 教授, 博士, 博士生导师。主要研究方向:控制理论与计算智能

通讯作者:
张著洪, E-mail: zhzhang@gzu.edu.cn

中图分类号: TP301.6
计量
- 文章访问数: 779
- HTML全文浏览量: 185
- PDF下载量: 489
- 被引次数: 0
出版历程
- 收稿日期: 2019-07-03
- 录用日期: 2019-09-27
- 网络出版日期: 2020-05-20

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

ZHANG Renchong¹,
ZHANG Zhuhong^{2
, ,}

1.
Computer and Information Engineering College, Guizhou University of Commerce, Guiyang 550014, China
2.
College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China

Funds:

National Natural Science Foundation of China 61563009)

Youth Science and Technology Talent Development Project of Education Department in Guizhou Province QJH KY Zi[2018] No.276

Guizhou Big Data Application Engineering Research Center in Guizhou Province QJH KY Zi[2017] No.022

More Information

Corresponding author: ZHANG Zhuhong, E-mail: zhzhang@gzu.edu.cn

摘要

摘要:
针对噪声信息未知的一般非线性多目标概率约束规划（MOPCP）问题，探讨基于危险理论的多目标免疫优化算法（MOIOA）。算法设计中，借助自适应采样方法估计机会约束的概率和目标值；借助危险理论蕴含的应答模式分割进化种群为已感染、易感染和未感染子群；借助二进制交叉、自适应变异概率、多项式变异策略平衡种群的全局与局部搜索能力。与7种算法相比较获得的数值结果表明，所提算法的搜索效率有明显优势且搜索效果有一定的优越性，同时对复杂工程问题有应用潜力。
- 多目标概率约束规划(MOPCP) /
- 免疫优化 /
- 危险理论 /
- 自适应采样 /
- 随机模拟
Abstract:
This paper investigates a Multi-Objective Immune Optimization Algorithm (MOIOA) based on danger theory to solve the problem of nonlinear Multi-Objective Probabilistic Constrained Programming (MOPCP) with unknown noise information. In the design of the algorithm, adaptive sampling methods are used to estimate each chance constraint's probability and objective values, while each evolving population is divided into infected, susceptible and uninfected sub-populations in terms of one specific immune response mechanism contained by danger theory. The capability of global and local search can be enhanced, relying upon simulated binary crossover, adaptive mutation probability and polynomial mutation strategy. Numerical experiment results show that the proposed multi-objective algorithm has high efficiency and has some advantages over seven comparative methods with regard to solution quality. It has application potential to complex engineering problems.
- Multi-Objective Probabilistic Constrained Programming (MOPCP) /
- immune optimization /
- danger theory /
- adaptive sampling /
- stochastic simulation

HTML全文

图 1 MOIOA的流程图

Figure 1. Flowchart of MOIOA

下载: 全尺寸图片幻灯片

图 2 问题1的非支配面比较与CD、CS值的箱线图比较

Figure 2. Comparison of Pareto fronts and comparison of box plots on CD and CS for Problem 1

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图 3 问题2的非支配面比较与CD、CS值的箱线图比较

Figure 3. Comparison of Pareto fronts and comparison of box plots on CD and CS for Problem 2

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图 4 问题3的非支配面与CD、CS值的箱线图比较

Figure 4. Comparison of Pareto fronts and comparison of box plots on CD and CS for Problem 3

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图 5 问题4的非支配面与CD、CS值的箱线图比较

Figure 5. Comparison of Pareto fronts and comparison of box plots on CD and CS for Problem 4

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图 6 MOIOA的不同参数设置及统计结果比较

Figure 6. Different parameter settings of MOIOA and comparison of statistical results

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表 1 不同算法在α=0.9下求解问题1获得的统计结果比较

Table 1. Comparison of statistical results of different algorithms for Problem 1 with α = 0.9

算法	CR均值/%								CD均值	CS均值	IAE 均值/ 10^-3	FR 均值/ %	AR 均值/ s
算法	AgMOPSO	MOEA/DD	CMIGA	NNIA	MOPSO	NSGA-Ⅱ	SPEA-Ⅱ	MOIOA	CD均值	CS均值	IAE 均值/ 10^-3	FR 均值/ %	AR 均值/ s
AgMOPSO	0	14.69	16.47	14.29	20.49	15.67	15.89	18.68	0.031	1.94	5.59	63.32	19.82
MOEA/DD	14.99	0	16.73	14.44	20.61	14.38	15.72	18.14	0.031	1.94	4.05	69.34	9.24
CMIGA	16.10	17.18	0	15.66	21.02	15.60	15.60	20.69	0.027	1.96	3.98	70.83	15.02
NNIA	13.27	14.13	15.40	0	19.83	13.56	12.77	17.61	0.032	1.82	5.82	59.50	11.13
MOPSO	12.64	13.92	14.11	12.69	0	13.28	12.49	17.57	0.026	1.91	3.90	71.96	8.63
NSGA-Ⅱ	14.21	15.41	15.89	14.81	21.20	0	14.27	19.68	0.031	1.95	4.82	64.73	8.73
SPEA-Ⅱ	13.86	14.78	16.55	14.71	20.38	14.11	0	20.00	0.027	1.89	4.03	68.73	9.38
MOIOA	14.46	14.78	15.29	12.05	20.35	13.44	14.24	0	0.021	1.94	2.33	80.21	1.22

下载: 导出CSV

表 2 不同算法在α=0.9下求解问题2获得的统计结果比较

Table 2. Comparison of statistical results of different algorithms for Problem 2 with α=0.9

算法	CR均值/%								CD均值	CS均值	IAE 均值/ 10^-5	FR 均值/ %	AR 均值/ s
算法	AgMOPSO	MOEA/DD	CMIGA	NNIA	MOPSO	NSGA-Ⅱ	SPEA-Ⅱ	MOIOA	CD均值	CS均值	IAE 均值/ 10^-5	FR 均值/ %	AR 均值/ s
AgMOPSO	0	11.77	12.99	9.09	12.89	13.01	24.37	9.07	1.92	241.73	0.39	99.96	20.31
MOEA/DD	3.51	0	10.94	7.08	11.51	11.22	21.44	7.01	4.60	206.70	0.33	99.98	11.35
CMIGA	4.85	10.22	0	7.55	10.27	10.69	21.01	7.17	1.86	237.76	0.48	99.98	17.44
NNIA	4.87	10.97	11.22	0	10.85	11.08	21.79	7.62	1.86	241.21	0.84	99.94	12.36
MOPSO	2.76	9.37	8.63	5.80	0	9.09	17.09	5.76	3.30	192.67	0.30	99.96	11.24
NSGA-Ⅱ	4.49	9.59	9.94	7.39	10.17	0	19.38	7.94	1.91	241.74	0.38	99.96	11.19
SPEA-Ⅱ	2.66	8.07	7.14	4.73	7.93	7.83	0	4.78	2.93	234.86	0.55	99.98	11.30
MOIOA	4.89	10.75	11.30	7.96	11.02	11.40	22.35	0	1.79	239.55	0	100	1.80

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表 3 不同算法在α=0.6下求解问题3获得的统计结果比较

Table 3. Comparison of statistical results of different algorithms for Problem 3 with α=0.6

算法	CR均值/%								CD均值	CS均值	IAE 均值/ 10^-4	FR 均值/ %	AR 均值/ s
算法	AgMOPSO	MOEA/DD	CMIGA	NNIA	MOPSO	NSGA-Ⅱ	SPEA-Ⅱ	MOIOA	CD均值	CS均值	IAE 均值/ 10^-4	FR 均值/ %	AR 均值/ s
AgMOPSO	0	15.61	8.54	18.39	34.82	18.91	21.89	17.39	0.32	13.22	6.61	96.07	26.04
MOEA/DD	24.41	0	9.39	21.02	40.11	21.33	25.70	21.82	0.37	11.26	4.50	97.46	12.20
CMIGA	39.40	30.80	0	34.64	58.93	35.43	41.33	33.28	0.46	13.54	1.70	98.80	20.26
NNIA	25.46	18.23	10.43	0	42.59	21.80	27.97	22.05	0.24	12.06	5.39	96.87	15.19
MOPSO	12.65	7.73	2.75	8.57	0	8.90	11.15	10.12	0.33	12.49	4.80	97.72	11.84
NSGA-Ⅱ	25.38	17.63	9.61	21.25	41.64	0	26.49	21.43	0.29	12.25	4.65	97.28	11.68
SPEA-Ⅱ	20.32	14.28	5.97	17.14	34.82	16.37	0	16.95	0.36	12.17	5.09	97.02	12.69
MOIOA	27.48	20.02	11.06	23.03	42.77	23.89	29.08	0	0.31	12.36	2.18	98.58	2.48

下载: 导出CSV

表 4 不同算法在α=0.9下求解问题4获得的统计结果比较

Table 4. Comparison of statistical results of different algorithms for Problem 4 with α=0.9

算法	CR均值/%								CD均值	CS均值	IAE 均值/ 10^-3	FR 均值/ %	AR 均值/ s
算法	AgMOPSO	MOEA/DD	CMIGA	NNIA	MOPSO	NSGA-Ⅱ	SPEA-Ⅱ	MOIOA	CD均值	CS均值	IAE 均值/ 10^-3	FR 均值/ %	AR 均值/ s
AgMOPSO	0	25.95	21.47	36.51	36.93	32.80	32.84	18.10	2.82	14.94	4.32	71.46	19.07
MOEA/DD	21.79	0	21.66	35.11	36.69	30.20	31.52	17.44	2.99	13.28	0.72	92.35	8.89
CMIGA	25.36	32.19	0	44.98	40.99	34.27	37.27	21.84	2.69	14.30	0.63	90.18	15.34
NNIA	13.89	22.31	13.93	0	23.90	20.88	20.60	10.41	1.50	8.51	1.13	89.42	10.69
MOPSO	11.42	16.62	11.97	27.90	0	22.47	22.90	11.81	1.85	9.33	1.38	86.03	8.83
NSGA-Ⅱ	16.58	21.04	15.69	32.40	30.78	0	24.92	15.61	2.77	14.84	0.70	92.61	9.01
SPEA-Ⅱ	16.00	20.58	18.07	34.25	32.22	28.31	0	15.07	1.66	10.70	0.94	90.15	9.68
MOIOA	29.50	36.62	30.45	49.04	45.93	41.06	40.74	0	3.78	20.12	0.80	90.04	1.30

下载: 导出CSV

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