基于改进NSGA-Ⅲ的多SGSW火力分配优化

doi:10.3969/j.issn.1001-506X.2020.09.15

摘要/Abstract

摘要：

在高维多目标优化中,基于参考点非支配排序遗传算法(non-dominated sorting genetic algorithm-Ⅲ, NSGA-Ⅲ)相比于其他多目标进化算法,具备较强的多样性保持能力,但收敛能力存在一定不足。因此引入遗传K均值(genetic K-means, GKM)聚类算法以提高NSGA-Ⅲ的收敛能力,提出基于NSGA-Ⅲ-GKM算法的多天基对地打击武器(space-to-ground strike weapon, SGSW)火力分配优化方法。首先,建立以转移时间最短、落地点速度最大和落地点侵彻角最大为优化目标的SGSW转移轨道优化模型,为后续优化目标的计算打下基础;其次,建立基于NSGA-Ⅲ-GKM算法的火力分配优化模型;最后,仿真结果表明, NSGA-Ⅲ-GKM算法相比于其他代表性多目标进化算法具备较好的多样性保持能力和收敛能力,总体性能较好,该方法能够更有效地解决多SGSW火力分配优化问题。

关键词: 天基对地打击武器, 多目标进化算法, 基于参考点非支配排序遗传算法, 火力分配, 遗传K均值

Abstract:

In optimizations with higher dimensional objectives, the non-dominated sorting genetic algorithm-Ⅲ (NSGA-Ⅲ) compared to other many-objective evolutionary algorithms, has the strong ability of diversity maintenance, but the convergence ability is still weak. On the basis that the genetic K-means (GKM) clustering algorithm is introduced to improve the convergence ability of the NSGA-Ⅲ, the NSGA-Ⅲ-GKM is proposed to solve the optimization problem of the fire distribution for multiple space-to-ground strike weapon (SGSW). Firstly, taking the minimum duration of the transfer trajectory, the velocity of the SGSW at the landing point, and the penetration angle of the SGSW at the landing point as optimization indexes, the optimization models of transfer trajectories are established, which lays a foundation of the computation for indexes of the fire distribution. Secondly, the optimization model of fire distribution is established based on the NSGA-Ⅲ-GKM. Finally, the simulation results demonstrate that the NSGA-Ⅲ-GKM has better diversity and convergence and optimization results than other representative many-objective evolutionary algorithms, which can effectively solve the fire distribution problem of multiple SGSW.

Key words: space-to-ground strike weapon (SGSW), multi-objective evolutionary algorithms, non-dominated sorting genetic algorithm-Ⅲ (NSGA-Ⅲ), fire distribution, genetic K-means (GKM)

中图分类号:

V474.2

刘庆国, 刘新学, 武健, 李亚雄, 陈豪. 基于改进NSGA-Ⅲ的多SGSW火力分配优化[J]. 系统工程与电子技术, 2020, 42(9): 1995-2002.

Qingguo LIU, Xinxue LIU, Jian WU, Yaxiong LI, Hao CHEN. Optimization of fire distribution for multiple SGSW based on improved NSGA-Ⅲ[J]. Systems Engineering and Electronics, 2020, 42(9): 1995-2002.

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参考文献 19

1	ZIARNICK B . The coming revolution in military space professionalism[J]. Air & Space Power Journal, 2018, 32 (2): 9- 20.
2	ISHIBUCHI H , AKEDO N , NOJIMA Y . Behavior of multi-objective evolutionary algorithms on many-objective knapsack problems[J]. IEEE Trans.on Evolutionary Computation, 2015, 19 (2): 264- 283. doi: 10.1109/TEVC.2014.2315442
3	DEB K , SRINIVAS N . Multi-objective optimization using non-dominated sorting in genetic algorithms[J]. Evolutionary Computation, 1995, 3 (2): 221- 248.
4	DEB K , PRATAP A , AGARWAL S , et al. A fast and elitist multi-objective genetic algorithm: NSGA-Ⅱ[J]. IEEE Trans.on Evolutionary Computation, 2002, 6 (2): 182- 197. doi: 10.1109/4235.996017
5	DEB K , JAIN H . An evolutionary many-objective optimization algorithm using reference-point-based non-dominated sorting approach, part I: solving problems with box constraints[J]. IEEE Trans.on Evolutionary Computation, 2014, 18 (4): 577- 601. doi: 10.1109/TEVC.2013.2281535
6	BI X , WANG C . An improved NSGA-Ⅲ algorithm based on objective space decomposition for many-objective optimization[J]. Soft Computing, 2017, 21 (15): 4269- 4296. doi: 10.1007/s00500-016-2192-0
7	李飞, 刘建昌, 朱佳妮, 等. 基于目标空间分区的稳态高维多目标进化算法[J]. 东北大学学报, 2018, 39 (3): 305- 310.
	LI F , LIU J C , ZHU J N , et al. Steady-state many-objectives evolutionary algorithm based on objective space partition[J]. Journal of Northeastern University, 2018, 39 (3): 305- 310.
8	YUAN Y, XU H, WANG B. An improved NSGA-Ⅲ procedure for evolutionary many-objective optimization[C]//Proc.of the Confe-rence on Genetic and Evolutionary computation, 2014: 661-668.
9	MARWA C , SLIM B , CHIH C H , et al. Multi-objective evolution of oblique decision trees for imbalanced data binary classification[J]. Swarm and Evolutionary Computation, 2019, 49, 1- 22. doi: 10.1016/j.swevo.2019.05.005
10	ALSAYAT A , ELSAYED H . Efficient genetic K-means in healthcare domain[J]. International Journal of Computer & Information Science, 2016, 17 (3): 1- 10.
11	BOUHMALA N , VIKEN A , LONNUM J B . Enhanced genetic algorithm with K-means for the clustering problem[J]. International Journal of Modeling and Optimization, 2015, 5 (2): 150- 154. doi: 10.7763/IJMO.2015.V5.452
12	CHENG Y H , JIANG B , SUN J , et al. Low-thrust orbit transfer by combing genetic algorithm with refined Q-law method[J]. Transactions of Nanjing University of Aeronautics & Astronautics, 2010, 27 (4): 313- 320.
13	唐军刚.天基再入飞行器全程机动制导方法研究[D].哈尔滨:哈尔滨工业大学, 2012.
	TANG J G. Research on omni distance maneuvering guidance of space-based reentry vehicle[D]. Harbin: Harbin Institute of Technology, 2012.
14	SARI C , SUBCHAN S . Application of Pontryagin's minimum principle in optimum time of missile manoeuvring[J]. Cauchy, 2016, 4 (3): 107- 111. doi: 10.18860/ca.v4i3.3534
15	NGUYEN B H , GERMAN R , TROVAO J , et al. Real-time energy management of battery/supercapacitor electric vehicles based on an adaptation of Pontryagin's minimum principle[J]. IEEE Trans.on Vehicular Technology, 2019, 68 (1): 203- 212. doi: 10.1109/TVT.2018.2881057
16	BI X , WANG C . A niche-elimination operation based NSGA-Ⅲ algorithm for many-objective optimization[J]. Applied Intelligence, 2018, 48 (1): 118- 141.
17	WU K , ZHANG D , CHEN Z , et al. Multi-type multi-objective imaging scheduling method based on improved NSGA-Ⅲ for satellite formation system[J]. Advances in Space Research, 2019, 63 (8): 2551- 2565. doi: 10.1016/j.asr.2019.01.006
18	NAMURA N , SHIMOYAMA K , OBAYASHI S . Expected improvement of penalty-based boundary intersection for expensive multiobjective optimization[J]. IEEE Trans.on Evolutionary Computation, 2018, 21 (6): 898- 913.
19	BADER J , ZIZLER E . HypE: an algorithm for fast hypervolume- based many-objective optimization[J]. Evolutionary Computation, 2011, 19 (1): 45- 76. doi: 10.1162/EVCO_a_00009

编号	a/km	e/(°)	i/(°)	ω/(°)	Ω/(°)	f/(°)
1	9 501	0.213	28.226	34.607	152.421	325.392
2	7 059	0.001	98.084	76.815	185.081	281.000
3	10 239	0.402	33.033	322.222	123.001	142.332
4	7 623	0.044	100.000	77.500	300.000	211.420
5	7 568	0.004	99.031	56.562	47.938	308.882
6	7 554	0.002	90.045	245.844	85.215	113.968
7	8 428	0.201	82.982	262.555	29.901	44.341
8	9 306	0.238	28.321	224.138	307.927	135.862

组号	M₁/(°)	M₂/(°)	M₃/(°)	M₄/(°)	M₅/(°)	M₆/(°)
1	(31.8, -172.8)	(25.3, -152.4)	(32.2, -148.3)	(23.5, -171.0)	(21.4, -160.2)	(28.9, -148.5)
2	(13.1, 151.8)	(15.6, 166.8)	(14.1, 156.8)	(24.9, 161.1)	(22.1, 178.6)	(18.6, 176.2)
3	(-28.9, -164.6)	(-17.6, -171.4)	(-22.8, -143.6)	(-28.9, -160.7)	(-20.2, -141.8)	(-31.2, -133.2)
4	(-28.8, 67.9)	(-19.3, 67.0)	(-29.5, 79.9)	(-55.3, 95.0)	(-38.8, 79.0)	(-41.9, 95.9)
5	(28.1, -51.4)	(20.5, -41.5)	(28.1, -31.3)	(21.4, -27.4)	(14.8, -31.5)	(9.3, -28.6)
6	(-2.5, -141.3)	(-8.6, -136.1)	(3.2, -133.4)	(-4.4, -134.3)	(-11.1, -126.3)	(-9.9, -131.9)

组号	f₁/s	f₂/s	f₃/(km/s)	f₄/(km/s)	f₅/(°)	f₆/(°)
1	5 300.002	4 932.732	7.211	7.904	78.973	88.442
	5 322.009	4 934.814	7.121	7.878	77.759	88.029
	5 311.231	4 932.732	7.211	7.904	78.973	88.442
	5 304.002	4 932.732	7.122	7.811	78.973	88.442
2	5 701.765	5 004.107	7.462	8.008	78.228	88.510
	5 705.007	5 100.325	7.322	7.799	77.760	88.449
	5 708.710	5 005.704	7.441	8.011	78.228	88.510
	5 701.765	5 004.107	7.462	8.008	78.228	88.510
3	5 523.995	5 192.329	7.305	7.882	79.265	89.020
	5 534.098	5 197.112	7.305	7.882	78.761	88.773
	5 523.995	5 192.329	7.305	7.882	79.265	89.020
	5 530.124	5 194.093	7.305	7.882	79.009	89.001
4	5 636.874	5 102.333	7.399	7.810	80.365	90.000
	5 646.578	5 110.220	7.402	7.996	79.227	90.000
	5 636.874	5 104.113	7.402	7.996	80.365	90.000
	5 644.556	5 110.270	7.312	7.791	80.223	90.000
5	5 498.708	4 807.864	7.667	8.276	82.301	89.578
	5 522.116	4 816.254	7.468	8.200	82.112	89.400
	5 500.712	4 809.554	7.433	8.101	82.211	89.578
	5 550.238	4 817.864	7.446	8.109	82.115	89.404
6	5 309.900	4 879.651	7.554	8.103	80.369	89.301
	5 311.460	4 888.113	7.454	8.022	80.223	89.009
	5 309.945	4 882.115	7.490	8.079	80.306	89.001
	5 309.900	4 879.651	7.554	8.103	80.369	89.301

组号	NSGA-Ⅲ-GKM	NSGA-Ⅲ	NSGA-Ⅲ-OSD	θ-NSGA-Ⅲ
1	5.442e-1	4.923e-1	5.110e-1	5.243e-1
	2.702e-1	2.055e-1	2.448e-1	2.503e-1
	9.001e-2	8.020e-2	9.199e-2	8.561e-2
2	5.667e-1	4.823e-1	5.310e-1	5.441e-1
	2.911e-1	2.155e-1	2.642e-1	2.898e-1
	1.209e-1	1.020e-1	1.135e-1	9.326e-2
3	5.198e-1	4.823e-1	5.111e-1	4.869e-1
	2.857e-1	2.433e-1	2.859e-1	2.577e-1
	1.108e-1	9.146e-2	1.239e-1	1.037e-1
4	6.045e-1	5.223e-1	5.718e-1	5.924e-1
	3.255e-1	2.451e-1	2.841e-1	2.805e-1
	1.541e-1	1.126e-1	1.433e-1	1.336e-1
5	5.484e-1	5.022e-1	5.419e-1	5.306e-1
	2.715e-1	2.351e-1	2.332e-1	2.599e-1
	1.067e-1	1.127e-1	9.172e-2	9.170e-2
6	6.990e-1	5.811e-1	6.311e-1	6.491e-1
	3.512e-1	2.455e-1	2.776e-1	3.660e-1
	1.600e-1	1.2208e-1	1.434e-1	2.165e-2

组号	NSGA-Ⅲ-GKM	NSGA-Ⅲ	NSGA-Ⅲ-OSD	θ-NSGA-Ⅲ
1	359.601	344.362	360.223	364.003
2	359.614	345.362	359.663	363.025
3	359.551	344.685	360.200	363.568
4	359.627	344.698	360.102	363.423
5	359.600	345.369	360.032	363.556
6	359.609	344.989	360.221	362.356