基于改进差分进化算法的动态防空资源分配优化

doi:10.16182/j.issn1004731x.joss.24-0116

系统仿真学报 ›› 2024, Vol. 36 ›› Issue (6): 1285-1297.doi: 10.16182/j.issn1004731x.joss.24-0116

基于改进差分进化算法的动态防空资源分配优化

罗天羽¹(), 邢立宁²(), 王锐¹, 王凌³, 石建迈¹, 孙昕¹

^1.国防科技大学系统工程学院, 湖南长沙 410073
^2.西安电子科技大学电子工程学院, 陕西西安 710071
^3.清华大学自动化系, 北京 100084

收稿日期:2024-01-30 修回日期:2024-04-27 出版日期:2024-06-28 发布日期:2024-06-19
通讯作者: 邢立宁 E-mail:luotianyu951005@163.com;lnxing@xidian.edu.cn
第一作者简介:罗天羽(1995-)，男，博士生，研究方向为复杂系统建模优化。E-mail：luotianyu951005@163.com
基金资助:
国家自然科学基金重点项目(62036006);陕西省重点科技创新团队项目(2023-CX-TD-07);陕西省重点研发计划(2024GH-ZDXM-48)

Dynamic Air Defense Resource Allocation Optimization Based on Improved Differential Evolution Algorithm

Luo Tianyu¹(), Xing Lining²(), Wang Rui¹, Wang Ling³, Shi Jianmai¹, Sun Xin¹

^1.College of Systems Engineering, National University of Defense Science and Technology, Changsha 410073, China
^2.College of Electronic Engineering, Xi'an University of Electronic Science and Technology, Xi'an 710071, China
^3.Department of Automation, Tsinghua University, Beijing 100084, China

Received:2024-01-30 Revised:2024-04-27 Online:2024-06-28 Published:2024-06-19
Contact: Xing Lining E-mail:luotianyu951005@163.com;lnxing@xidian.edu.cn

摘要/Abstract

摘要：

面对动态防空资源分配问题中存在的空袭目标突现和雷达、发射车等资源受干扰现象，在综合考虑雷达、发射车和导弹等武器装备性能的基础上，基于目标集、资源集建立了最小化目标总拦截价值与生存概率的混合整数决策模型。提出了一种新的改进差分进化算法进行求解，采用反向学习策略生成初始解，确保初始种群的质量，设计了一种快速修复与重构的启发式规则作用于多阶段，以提升算法的搜索能力。仿真实验验证了该算法具有求解时间和求解精度上的优越性。该研究能使武器系统在动态事件的随机影响下，保持高效的作战能力和决策效果。

关键词: 防空作战, 动态防空资源分配, 反向学习, 改进差分进化算法

Abstract:

Based on the integrated performance of weapon equipments such as radars, launchers and missiles, a mixed-integer decision model that minimizes the total target intercept value and the probability of survival based on Target-Set, Resource-Set is developed. A new improved differential evolutionary algorithm has been introduced to solve the problem, and the initial solutions is generated by using the reverse learning strategies to ensure the quality of the initial populations. An inspiration rule for the fast repair and reconstruction is designed to work at multi-stage to improve the search capability of the algorithm. The simulation experiment results show the algorithm's superiority in search time and search accuracy, which can maintain the efficient combat capabilities and decision-making under the random influence of dynamic events.

Key words: air defense operations, dynamic air defense resource allocation, opposition-based learning, improved differential evolution algorithm

中图分类号:

TP391.9

罗天羽,邢立宁,王锐等 . 基于改进差分进化算法的动态防空资源分配优化[J]. 系统仿真学报, 2024, 36(6): 1285-1297.

Luo Tianyu,Xing Lining,Wang Rui,et al . Dynamic Air Defense Resource Allocation Optimization Based on Improved Differential Evolution Algorithm[J]. Journal of System Simulation, 2024, 36(6): 1285-1297.

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算例		目标信息		发射车			雷达
算例		数量	出现时间/s	数量	导弹数量	故障数量/时间(s)	数量	通道上限	故障数量/时间(s)
小规模	S0	24	0	6	24	/	6	1	/
	S1	15/5/4	0/10/20	4	20	/	4	1	/
	S2	15/5/4	0/10/20	4	40	/	4	2	/
	S3	24	0	6	24	1/10	5	2	1/15
	S4	24	0	6	48	1/10	5	2	1/15
	S5	15/5/4	0/10/20	8	32	1/10	5	3	1/15
	S6	15/5/4	0/10/20	8	64	1/5	5	3	1/15
中规模	M1	40/5/15	0/10/20	8	56	/	7	1	/
	M2	40/5/15	0/10/20	8	112	/	7	1	/
	M3	60	0	10	60	1/10	8	2	1/15
	M4	60	0	10	120	1/10	8	2	1/15
	M5	40/5/15	0/10/20	12	72	1/10	8	3	1/15
	M6	40/5/15	0/10/20	12	132	1/5	8	3	1/15
大规模	L1	60/20/20	0/10/20	14	98	/	14	1	/
	L2	60/20/20	0/10/20	14	168	/	14	1	/
	L3	100	0	16	112	1/10	16	2	1/15
	L4	100	0	16	208	1/10	16	2	1/15
	L5	60/20/20	0/10/20	18	144	1/10	18	3	1/15
	L6	60/20/20	0/10/20	18	198	1/5	18	3	1/15

算例	DE				SA				IDE
算例	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s
S0	23.186	23.540	1.999	8.530	29.448	31.878	3.147	27.980	21.208	22.179	1.939
S1	30.594	31.233	1.422	2.920	32.192	33.285	2.253	7.740	29.700	30.312	0.782
S2	19.572	20.511	1.896	12.090	27.512	28.934	2.328	37.460	17.206	17.577	0.780
S3	24.436	24.818	1.754	11.240	28.124	29.560	2.081	22.880	21.690	22.787	1.089
S4	18.750	19.851	1.938	10.500	26.016	27.218	2.269	35.490	16.782	16.966	1.239
S5	19.596	20.622	1.867	11.930	24.198	24.981	2.237	28.680	17.258	17.401	1.323
S6	19.440	20.548	1.847	10.580	25.128	26.882	2.104	30.820	17.384	17.482	1.177
M1	130.732	135.295	3.180	8.810	140.204	147.610	4.719	14.980	119.208	126.814	3.210
M2	104.040	109.532	3.243	10.530	120.638	128.076	4.793	22.840	93.088	99.257	3.131
M3	120.594	126.194	3.802	6.090	138.024	140.968	5.922	17.950	113.248	120.483	4.253
M4	94.402	99.800	4.270	5.360	134.086	139.738	6.118	33.370	89.338	94.270	4.268
M5	105.384	111.063	3.391	1.110	133.684	138.927	4.264	22.050	104.212	107.245	3.289
M6	100.322	106.566	3.422	2.990	137.224	143.133	4.033	29.080	97.318	103.013	3.419
L1	278.544	281.555	5.662	7.620	279.014	290.922	10.012	7.770	257.332	263.581	5.941
L2	250.356	253.103	5.810	15.490	268.276	275.675	10.144	21.140	211.572	230.211	6.230
L3	248.100	250.223	7.716	7.140	259.234	269.988	12.895	11.130	230.394	236.956	7.899
L4	225.410	227.661	8.439	9.860	258.346	264.050	13.482	21.360	203.174	211.253	8.146
L5	223.144	224.941	7.208	13.060	257.184	264.182	8.974	24.560	194.010	206.494	6.619
L6	223.878	228.582	7.261	14.630	252.328	262.629	8.869	24.250	191.130	196.640	6.630

算例	GA				IGA				IDE
算例	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s
S0	23.684	24.351	2.005	10.450	22.486	23.475	2.663	5.680	21.208	22.179	1.939
S1	33.678	33.873	0.823	11.810	30.782	31.045	1.025	3.520	29.700	30.312	0.782
S2	22.688	23.650	1.890	24.160	18.798	19.427	1.065	8.470	17.206	17.577	0.780
S3	27.416	27.801	2.020	20.890	24.712	25.114	1.562	12.230	21.690	22.787	1.089
S4	22.058	23.746	1.821	23.920	19.214	19.806	1.771	12.660	16.782	16.966	1.239
S5	23.138	24.300	1.817	25.410	20.278	20.841	1.758	14.890	17.258	17.401	1.323
S6	23.282	24.116	1.829	25.330	19.792	20.551	1.532	12.170	17.384	17.482	1.177
M1	146.094	149.081	3.587	18.400	129.400	133.362	4.265	7.880	119.208	126.814	3.210
M2	122.730	129.209	3.511	24.150	106.064	110.423	4.226	12.230	93.088	99.257	3.131
M3	133.604	135.879	4.168	15.240	129.538	131.975	4.952	12.580	113.248	120.483	4.253
M4	124.300	126.213	4.584	28.130	113.840	117.509	5.449	21.520	89.338	94.270	4.268
M5	120.808	127.354	3.537	13.740	118.502	123.771	3.946	12.060	104.212	107.245	3.289
M6	124.156	128.557	3.393	21.620	120.212	125.497	3.997	19.040	97.318	103.013	3.419
L1	295.112	300.402	6.292	12.800	262.988	273.304	7.573	2.150	257.332	263.581	5.941
L2	275.074	283.269	7.203	23.090	240.190	244.523	7.573	11.910	211.572	230.211	6.230
L3	264.708	273.724	9.271	12.960	240.290	252.052	10.153	4.120	230.394	236.956	7.899
L4	234.522	245.642	9.925	13.370	226.090	233.112	11.196	10.140	203.174	211.253	8.146
L5	226.352	238.521	7.666	14.290	228.340	236.458	8.446	15.030	194.010	206.494	6.619
L6	229.078	232.032	7.623	16.570	220.300	231.101	8.124	13.240	191.130	196.640	6.630

算例	SA/wr				GA/wr				IDE
算例	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s	GAP/%	C_best	C_avg	T/s
S0	22.744	24.267	3.597	6.750	22.100	22.509	2.530	4.040	21.208	22.179	1.939
S1	30.594	31.276	3.649	2.800	30.262	30.835	1.900	1.730	29.700	30.312	0.782
S2	19.624	20.415	3.601	12.320	17.920	18.530	3.804	3.980	17.206	17.577	0.780
S3	22.242	24.128	3.118	0.450	23.580	24.607	3.726	6.100	21.690	22.787	1.089
S4	18.750	19.836	3.942	10.500	18.286	19.327	3.379	8.220	16.782	16.966	1.239
S5	19.690	20.499	3.666	12.350	18.942	20.013	3.131	8.890	17.258	17.401	1.323
S6	19.440	20.405	3.555	10.580	18.850	19.694	2.995	7.780	17.384	17.482	1.177
M1	132.124	135.744	6.329	9.780	133.334	136.122	5.210	10.590	119.208	126.814	3.210
M2	107.552	110.099	5.852	13.260	107.680	110.728	5.498	13.370	93.088	99.257	3.131
M3	127.606	131.423	7.238	11.250	125.230	127.266	5.338	9.570	113.248	120.483	4.253
M4	98.314	100.516	7.891	9.130	98.314	100.516	5.842	9.130	89.338	94.270	4.268
M5	120.734	124.774	5.960	13.680	108.574	112.425	4.933	4.020	104.212	107.245	3.289
M6	119.654	125.907	5.159	17.730	102.052	108.754	4.467	3.540	97.318	103.013	3.419
L1	269.386	277.018	11.143	4.470	271.560	277.173	7.976	5.240	257.332	263.581	5.941
L2	243.190	250.130	11.237	13.000	242.016	246.666	8.605	12.580	211.572	230.211	6.230
L3	252.132	256.430	13.903	8.620	242.080	250.143	11.254	4.830	230.394	236.956	7.899
L4	243.410	245.558	14.905	15.790	233.554	236.306	11.328	12.230	203.174	211.253	8.146
L5	219.578	232.414	10.630	11.640	230.346	235.586	9.287	15.770	194.010	206.494	6.619
L6	217.082	225.181	10.592	11.950	218.050	222.727	8.778	12.350	191.130	196.640	6.630

算例	平均值	最优解	相对差	标准差
S0	22.179	21.208	0.971	0.534
S1	30.312	29.700	0.612	0.462
S2	17.577	17.206	0.371	0.476
S3	22.787	21.690	1.097	0.567
S4	16.966	16.782	0.184	0.137
S5	17.401	17.258	0.143	0.143
S6	17.482	17.384	0.098	0.119
M1	126.814	119.208	7.606	4.590
M2	99.257	93.088	6.169	4.168
M3	120.483	113.248	7.235	2.830
M4	94.270	89.338	4.932	2.645
M5	107.245	104.212	3.033	1.760
M6	103.013	97.318	5.695	2.965
L1	263.581	257.332	6.249	5.675
L2	230.211	211.572	18.639	11.240
L3	236.956	230.394	6.562	4.736
L4	211.253	203.174	8.079	3.885
L5	206.494	194.010	12.484	6.201
L6	196.640	191.130	5.510	2.649

基于改进差分进化算法的动态防空资源分配优化

Dynamic Air Defense Resource Allocation Optimization Based on Improved Differential Evolution Algorithm

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