ACCQPSO：一种改进的量子粒子群优化算法及其应用

doi:10.3969/j.issn.1671-1122.2024.04.008

摘要/Abstract

摘要：

针对量子粒子群优化算法前期易陷入局部极值点、后期寻优精度不高等问题，文章提出一种自适应交叉算子的混沌量子粒子群优化算法，并将其应用于BP神经网络超参数寻优。首先，利用Logistics映射初始种群为混沌序列进行最优解搜索，增强初始种群的随机性与遍历性，提高算法寻优能力；然后，通过纵向交叉操作进行种群中个体的信息交换，并引入自适应交叉概率公式，增加种群多样性，提高算法的寻优精度；最后，在实验中，一方面，选取8个函数在高低两个维度进行验证，同时进行Wilcoxon秩和检验分析以及消融实验，验证该算法相较其他算法的有效性；另一方面，通过算法优化BP神经网络应用到网络安全态势预测任务中，实验结果表明该算法收敛速度相较于对比算法有大幅度提升。

关键词: 量子粒子群优化算法, 混沌映射, 交叉算子, 自适应调整策略, BP神经网络

Abstract:

In order to solve the problems of quantum particle swarm optimization (QPSO), such as easy to fall into local extreme point in the early stage and low accuracy in the later stage, a chaotic quantum particle swarm optimization algorithm with adaptive crossover operator (ACCQPSO) was proposed and used in the hyper-parameter optimization of the BP neural network. Firstly, the initial population of Logistics map was used as chaotic sequence to search the optimal solution, which enhanced the randomness and ergodicity of the initial population and improved the optimization ability of the algorithm. Secondly, the information of individuals in the population was exchanged through vertical crossover operation, and the adaptive crossover probability formula was introduced to increase the population diversity and improved the optimization accuracy of the algorithm. In the experiment, on the one hand, eight functions were selected for validation in both high and low dimensions, while Wilcoxon rank sum test analysis and ablation experiments were performed to verify the effectiveness of the algorithm compared to other algorithms; on the other hand, the parameters optimization of BP neural network were applied to the network security situation prediction task, and the results show that the convergence speed is greatly improved compared with the contrast algorithm.

Key words: quantum particle swarm optimization algorithm, chaotic mapping, crossover operator, adaptive adjustment strategy, BP neural network

中图分类号:

TP309

孙隽丰, 李成海, 宋亚飞. ACCQPSO：一种改进的量子粒子群优化算法及其应用[J]. 信息网络安全, 2024, 24(4): 574-586.

SUN Junfeng, LI Chenghai, SONG Yafei. ACCQPSO: An Improved Quantum Particle Swarm Optimization Algorithm and Its Applications[J]. Netinfo Security, 2024, 24(4): 574-586.

图/表 14

图1

表1

表2

基准函数结果对比

函数	算法	最佳值	平均值	标准差
${{f}_{1}}$	GA	1.179E-03	1.736E-01	2.813E-01
	PSO	3.386E-10	4.002E-01	1.960E+00
	QPSO	5.645E-02	2.103E+00	2.164E+00
	CPSO	1.011E-11	7.403E-11	5.883E-11
	CQPSO	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{1}}$	GA	4.423E+00	1.162E+01	3.618E+00
	PSO	5.687E+01	1.091E+02	2.618E+01
	QPSO	2.567E+01	5.530E+01	2.056E+01
	CPSO	2.773E-06	2.217E-05	2.408E-05
	CQPSO	0.000E+00	1.042E-13	2.210E-13
	ACCQPSO	0.000E+00	3.631E-14	1.260E-13
${{f}_{2}}$	GA	2.756E-04	6.721E+00	2.336E+01
	PSO	7.081E-18	2.926E-16	6.654E-16
	QPSO	1.815E-01	1.052E+02	1.209E+02
	CPSO	8.601E-22	2.624E-19	5.639E-19
	CQPSO	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{2}}$	GA	3.549E+02	1.444E+03	1.018E+03
	PSO	1.151E+04	3.308E+04	1.105E+04
	QPSO	2.895E+03	1.143E+04	5.316E+03
	CPSO	1.329E-11	1.807E-10	2.482E-10
	CQPSO	2.829E-27	1.862E-24	3.215E-24
	ACCQPSO	8.078E-28	2.568E-26	6.697E-26
${{f}_{3}}$	GA	1.943E+00	1.434E+02	2.823E+02
	PSO	1.674E-01	1.355E+04	3.118E+04
	QPSO	4.713E+00	2.839E+03	4.986E+03
	CPSO	5.082E-04	1.433E+00	1.270E+00
	CQPSO	1.222E-04	9.922E-01	2.318E+00
	ACCQPSO	7.023E-12	3.789E-02	6.724E-02
${{{f}'}_{3}}$	GA	3.286E-01	7.356E+02	3.046E+03
	PSO	3.383E-01	2.768E+03	1.363E+04
	QPSO	4.475E-01	6.759E+03	1.931E+04
	CPSO	4.267E-03	1.386E+00	7.884E-01
	CQPSO	1.275E-03	1.232E+00	2.070E+00
	ACCQPSO	4.234E-06	2.260E-01	2.458E-01
${{f}_{4}}$	GA	2.495E-03	2.495E-03	2.495E-03
	PSO	2.849E-04	4.653E-03	3.535E-03
	QPSO	4.743E-04	2.088E-02	3.474E-02
	CPSO	7.831E-05	6.496E-04	4.900E-04
	CQPSO	4.897E-05	5.269E-04	3.328E-04
	ACCQPSO	1.320E-05	1.603E-04	1.171E-04
${{{f}'}_{4}}$	GA	4.687E-01	1.695E+00	1.476E+00
	PSO	5.139E+00	6.141E+01	3.582E+01
	QPSO	2.707E-01	4.380E+00	4.426E+00
	CPSO	3.467E-03	1.093E-02	9.228E-03
	CQPSO	6.994E-04	1.984E-03	1.027E-03
	ACCQPSO	1.455E-04	8.092E-04	4.409E-04
${{f}_{5}}$	GA	4.073E-07	2.639E-02	9.343E-02
	PSO	2.047E-19	2.586E-18	3.293E-18
	QPSO	5.151E-03	1.403E+00	2.659E+00
	CPSO	2.729E-23	1.964E-21	4.335E-21
	CQPSO	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{5}}$	GA	1.334E+00	1.096E+01	8.915E+00
	PSO	1.231E+02	3.142E+02	1.110E+02
	QPSO	2.694E+01	9.791E+01	4.704E+01
	CPSO	3.377E-14	1.201E-12	1.211E-12
	CQPSO	6.942E-29	8.962E-27	1.949E-26
	ACCQPSO	0.000E+00	1.628E-28	3.936E-28
${{f}_{6}}$	GA	5.863E-02	1.700E+00	2.434E+00
	PSO	2.464E-02	1.030E-01	5.637E-02
	QPSO	1.142E-01	2.019E+00	2.088E+00
	CPSO	8.216E-15	1.098E-01	5.315E-02
	CQPSO	1.616E-07	5.068E-02	2.686E-02
	ACCQPSO	0.000E+00	1.555E-02	1.308E-02
${{{f}'}_{6}}$	GA	4.014E+00	1.351E+01	6.839E+00
	PSO	3.908E+01	2.884E+02	1.146E+02
	QPSO	2.400E+01	1.021E+02	4.404E+01
	CPSO	1.093E-09	6.062E-02	1.728E-01
	CQPSO	0.000E+00	1.073E-03	3.599E-03
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{f}_{7}}$	GA	1.990E+00	6.125E+00	3.009E+00
	PSO	9.950E-01	6.706E+00	5.596E+00
	QPSO	1.775E+00	7.903E+00	4.252E+00
	CPSO	0.000E+00	1.708E+00	2.545E+00
	CQPSO	0.000E+00	2.410E-02	1.682E-01
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{7}}$	GA	4.506E+01	7.801E+01	1.296E+01
	PSO	1.374E+02	2.379E+02	5.328E+01
	QPSO	1.336E+02	2.184E+02	4.345E+01
	CPSO	1.480E+02	1.960E+02	2.032E+01
	CQPSO	0.000E+00	2.979E+01	2.087E+01
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{f}_{8}}$	GA	9.980E-03	1.418E+00	1.740E+00
	PSO	3.488E-09	1.369E-08	1.043E-08
	QPSO	4.044E-01	5.817E+00	2.909E+00
	CPSO	3.251E-11	2.183E-10	1.365E-10
	CQPSO	4.441E-16	4.441E-16	3.451E-31
	ACCQPSO	4.441E-16	4.441E-16	3.451E-31
${{{f}'}_{8}}$	GA	5.248E+00	8.624E+00	1.812E+00
	PSO	1.993E+01	1.997E+01	3.995E-02
	QPSO	1.011E+01	1.570E+01	1.943E+00
	CPSO	8.715E-07	1.400E+01	9.166E+00
	CQPSO	2.176E-14	5.746E-13	1.818E-12
	ACCQPSO	4.441E-16	2.908E-14	2.262E-14

表2

图2

表3

表4

模型消融实验结果

	${{f}_{1}}$		${{{f}'}_{1}}$		${{f}_{2}}$		${{{f}'}_{2}}$
	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
QPSO	2.103E+ 00	2.164E+ 00	5.530E+ 01	2.056E+ 01	1.052E+ 02	1.209E+ 02	1.143E+ 04	5.316E+ 03
ACQPSO	0.000E+ 00	0.000E+ 00	7.532E-14	1.838E-13	0.000E+ 00	0.000E+ 00	4.268E-25	1.335E-24
ChaoticQPSO	7.771E-11	6.008E-11	2.243E-05	2.664E-05	2.949E-19	6.207E-19	1.916E-10	2.712E-10
ACCQPSO	0.000E+ 00	0.000E+ 00	3.631E-14	1.260E-13	0.000E+ 00	0.000E+ 00	2.568E-26	6.697E-26
	${{f}_{3}}$		${{{f}'}_{3}}$		${{f}_{4}}$		${{{f}'}_{4}}$
	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
QPSO	2.839E+ 03	4.986E+ 03	6.759E+ 03	1.931E+ 04	2.088E-02	3.474E-02	4.380E+ 00	4.426E+ 00
ACQPSO	2.343E-01	1,447E+ 00	9,813E-01	1.270E+ 00	4.139E-04	2.368E-04	7.390E-03	3.214E-03
ChaoticQPSO	1.297E+ 00	8.171E-01	1.402E+ 00	8.329E-01	5.986E-04	3.497E-04	1.186E-02	1.008E-02
ACCQPSO	3.789E-02	6.724E-02	2.260E-01	2.458E-01	1.603E-04	1.171E-04	8.092E-04	4.409E-04
	${{f}_{5}}$		${{{f}'}_{5}}$		${{f}_{6}}$		${{{f}'}_{6}}$
	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
QPSO	1.403E+ 00	2.659E+ 00	9.791E+ 01	4.704E+ 01	2.019E+ 00	2.088E+ 00	1.021E+ 02	4.404E+ 01
ACQPSO	0.000E+ 00	0.000E+ 00	3.872E-27	7.893E-27	3.138E-02	2.131E-02	1.068E-13	3.674E-13
ChaoticQPSO	1.541E-21	3.729E-21	1.175E-12	1.087E-12	1.125E-01	5.540E-02	7.577E-02	1.902E-01
ACCQPSO	0.000E+ 00	0.000E+ 00	1.628E-28	3.936E-28	1.555E-02	1.308E-02	0.000E+ 00	0.000E+ 00
	${{f}_{7}}$		${{{f}'}_{7}}$		${{f}_{8}}$		${{{f}'}_{8}}$
	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
QPSO	7.903E+ 00	4.252E+ 00	2.184E+ 02	4.345E+ 01	5.817E+ 00	2.909E+ 00	1.570E+ 01	1.943E+ 00
ACQPSO	3.026E-11	1.734E-10	2.643E-04	2.047E-04	4.441E-16	3.451E-31	1.756E-13	1.963E-12
ChaoticQPSO	1.848E+ 00	2.573E+ 00	1.944E+ 02	1.961E+ 01	2.300E-10	1.432E-10	1.400E+ 01	9.164E+ 00
ACCQPSO	0.000E+ 00	0.000E+ 00	0.000E+ 00	0.000E+ 00	4.441E-16	3.451E-31	2.908E-14	2.262E-14

表4

表5

实验结果对比

函数	算法	最佳值	平均值	标准差
${{f}_{1}}$	GWO	2.028E-29	1.736E-27	1.993E-27
	WOA	2.586E-87	6.443E-73	2.588E-72
	SSA1	2.648E-08	1.303E-07	1.164E-07
	SSA	0.000E+00	1.235E-51	7.886E-51
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{1}}$	GWO	2.342E-17	8.124E-17	3.938E-17
	WOA	4.813E-23	1.668E-20	7.640E-20
	SSA1	4.260E-02	2.371E+00	1.860E+00
	SSA	1.149E-33	5.265E-31	3.385E-31
	ACCQPSO	0.000E+00	3.631E-14	1.260E-13
${{f}_{2}}$	GWO	2.635E-09	7.353E-06	1.336E-06
	WOA	3.682E-06	4.626E-05	1.673E-06
	SSA1	2.324E-23	1.453E-21	7.639E-21
	SSA	2.443E-76	4.622E-29	1.669E-28
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{2}}$	GWO	7.463E-05	7.012E-01	3.679E-01
	WOA	7.441E-02	4.006E-01	2.182E-01
	SSA1	2.345E-08	2.012E-07	2.793E-07
	SSA	1.180E-14	1.538E-11	3.735E-11
	ACCQPSO	8.078E-28	2.568E-26	6.697E-26
${{f}_{3}}$	GWO	4.936E+00	2.434E+02	3.856E+02
	WOA	5.384E-01	4.572E+04	2.159E+04
	SSA1	7.736E+00	2.351E+03	3.436E+03
	SSA	3.832E-04	2.463E+00	3.274E+00
	ACCQPSO	7.023E-12	3.789E-02	6.724E-02
${{{f}'}_{3}}$	GWO	2.611E+01	2.694E+01	6.458E-01
	WOA	2.708E+01	2.799E+01	4.643E-01
	SSA1	2.431E+01	1.660E+02	2.594E+02
	SSA	6.712E-03	3.420E+00	3.144E-01
	ACCQPSO	4.234E-06	2.260E-01	2.458E-01
${{f}_{4}}$	GWO	6.427E-03	1.495E-02	4.495E-03
	WOA	1.850E-04	4.742E-03	4.545E-03
	SSA1	3.753E-04	6.483E-02	7.394E-02
	SSA	5.836E-05	4.493E-04	4.357E-04
	ACCQPSO	1.320E-05	1.603E-04	1.171E-04
${{{f}'}_{4}}$	GWO	4.314E-02	1.794E-01	5.151E-02
	WOA	3.826E-04	1.960E-03	8.779E-04
	SSA1	6.170E-02	1.766E-01	6.366E-02
	SSA	8.348E-04	1.705E-03	1.403E-03
	ACCQPSO	1.455E-04	8.092E-04	4.409E-04
${{f}_{5}}$	GWO	3.023E-04	5.639E-04	3.344E-04
	WOA	7.047E-06	4.585E-05	4.233E-05
	SSA1	3.143E-03	5.486E+00	2.639E+00
	SSA	1.733E-24	1.284E-22	5.315E-22
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{5}}$	GWO	1.230E-02	3.400E-02	1.372E-02
	WOA	4.555E-03	2.942E-02	4.120E-02
	SSA1	2.614E+00	6.731E+00	3.705E+00
	SSA	2.387E-16	9.771E-13	3.221E-12
	ACCQPSO	0.000E+00	1.628E-28	3.936E-28
${{f}_{6}}$	GWO	0.000E+00	0.000E+00	0.000E+00
	WOA	0.000E+00	0.000E+00	0.000E+00
	SSA1	0.000E+00	0.000E+00	0.000E+00
	SSA	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{6}}$	GWO	0.000E+00	3.220E-03	8.209E-03
	WOA	0.000E+00	0.000E+00	0.000E+00
	SSA1	6.555E-04	1.303E-02	1.250E-02
	SSA	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{f}_{7}}$	GWO	0.000E+00	0.000E+00	0.000E+00
	WOA	0.000E+00	0.000E+00	0.000E+00
	SSA1	0.000E+00	3.550E-03	4.239E-03
	SSA	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{{f}'}_{7}}$	GWO	0.000E+00	3.175E+00	4.446E+00
	WOA	0.000E+00	0.000E+00	0.000E+00
	SSA1	2.336E+01	5.184E+01	2.078E+01
	SSA	0.000E+00	0.000E+00	0.000E+00
	ACCQPSO	0.000E+00	0.000E+00	0.000E+00
${{f}_{8}}$	GWO	4.441E-16	4.441E-16	3.451E-31
	WOA	4.441E-16	4.441E-16	3.451E-31
	SSA1	2.043E-01	2.833E+00	1.209E+00
	SSA	4.441E-16	4.441E-16	3.451E-31
	ACCQPSO	4.441E-16	4.441E-16	3.451E-31
${{{f}'}_{8}}$	GWO	7.551E-14	1.022E-13	1.670E-14
	WOA	8.882E-16	4.530E-15	2.955E-15
	SSA1	9.311E-01	2.570E+00	1.943E+00
	SSA	8.882E-16	8.882E-16	0.000E+00
	ACCQPSO	4.441E-16	2.908E-14	2.262E-14

表5

图3

表6

图4

表7

图5

表8

图6

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函数	函数名称	函数公式	极值点	维度	定义域
${{f}_{1}}$	Schwefel’s	公式（12）	单个	5	[-10,10]
${{{f}'}_{1}}$	Schwefel’s	公式（12）	单个	30	[-10,10]
${{f}_{2}}$	Step	公式（13）	单个	5	[-100,100]
${{{f}'}_{2}}$	Step	公式（13）	单个	30	[-100,100]
${{f}_{3}}$	Rosenbrock	公式（14）	单个	5	[-30,30]
${{{f}'}_{3}}$	Rosenbrock	公式（14）	单个	30	[-30,30]
${{f}_{4}}$	Quartic	公式（15）	单个	5	[-1.28,1.28]
${{{f}'}_{4}}$	Quartic	公式（15）	单个	30	[-1.28,1.28]
${{f}_{5}}$	Alpine	公式（16）	多个	5	[-10,10]
${{{f}'}_{5}}$	Alpine	公式（16）	多个	30	[-10,10]
${{f}_{6}}$	Griewing	公式（17）	多个	5	[-600,600]
${{{f}'}_{6}}$	Griewing	公式（17）	多个	30	[-600,600]
${{f}_{7}}$	Rastrigin	公式（18）	多个	5	[-5.12,5.12]
${{{f}'}_{7}}$	Rastrigin	公式（18）	多个	30	[-5.12,5.12]
${{f}_{8}}$	Ackley	公式（19）	多个	5	[-32,32]
${{{f}'}_{8}}$	Ackley	公式（19）	多个	30	[-32,32]

函数	GA		PSO		QPSO		CPSO		CQPSO
函数	$p$	$R$	$p$	$R$	$p$	$R$	$p$	$R$	$p$	$R$
${{f}_{1}}$	3.3111E-20	+	3.3101E-20	+	3.3111E-20	+	3.3111E-20	+	NAN	=
${{{f}'}_{1}}$	4.4381E-18	+	4.4381E-18	+	4.4381E-18	+	4.4381E-18	+	2.7407E-4	+
${{f}_{2}}$	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	NAN	=
${{{f}'}_{2}}$	7.0629E-18	+	7.0629E-18	+	7.0629E-18	+	7.0629E-18	+	1.3375E-12	+
${{f}_{3}}$	7.2232E-19	+	1.0090E-18	+	7.2232E-19	+	8.9749E-15	+	2.1929E-15	+
${{{f}'}_{3}}$	5.1388E-18	+	4.0923E-17	+	1.4232E-18	+	4.8825E-14	+	7.9311E-11	+
${{f}_{4}}$	7.2102E-19	+	1.5926E-18	+	7.2232E-19	+	4.2452E-13	+	2.8630E-10	+
${{{f}'}_{4}}$	7.2232E-19	+	7.2232E-19	+	7.2232E-19	+	7.2232E-19	+	1.3706E-13	+
${{f}_{5}}$	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	NAN	=
${{{f}'}_{5}}$	6.9868E-18	+	6.9868E-18	+	6.9868E-18	+	6.9868E-18	+	2.4991E-13	+
${{f}_{6}}$	7.0502E-18	+	5.9606E-17	+	7.0502E-18	+	2.6493E-13	+	1.1435E-11	+
${{{f}'}_{6}}$	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	3.3111E-20	+	2.5398E-4	+
${{f}_{7}}$	2.4537E-21	+	2.3412E-21	+	2.4537E-21	+	5.6468E-16	+	5.1287E-4	+
${{{f}'}_{7}}$	2.4537E-21	+	2.4537E-21	+	2.4537E-21	+	2.4537E-21	+	1.5528E-18	+
${{f}_{8}}$	3.5094E-21	+	3.5094E-21	+	3.5094E-21	+	3.5094E-21	+	NAN	=
${{{f}'}_{8}}$	6.9178E-19	+	6.9178E-19	+	6.9178E-19	+	6.9178E-19	+	4.9670E-16	+

网络安全威胁	权重
境内感染网络病毒的主机数量	0.30
境内被篡改网站总数	0.25
境内被植入后门网站总数	0.15
境内网站的仿冒页面数量	0.15
新增信息安全漏洞数量	0.15

实验环境	具体配置
操作系统	Windows 11
CPU	Intel(R) Core(TM) i5-11300H @3.10 GHz 3.11 GHz
内存	16 GB
硬盘	2 TB
开发框架	TensorFlow 2.8.0
开发语言	Python 3.9.12

模型	MAE	RMSE	MAPE	${{R}^{2}}$
BP	0.0051	0.0095	186.25%	0.9642
GA-BP	0.0041	0.0064	157.44%	0.9835
PSO-BP	0.0061	0.0075	222.14%	0.9778
QPSO-BP	0.0122	0.0184	433.91%	0.8658
CPSO-BP	0.0043	0.0063	153.47%	0.9840
CQPSO-BP	0.0035	0.0047	124.86%	0.9913
ACCQPSO-BP	0.0014	0.0024	46.03%	0.9977