基于改进NSGA-II的卫星在轨加注任务规划研究

doi:10.16182/j.issn1004731x.joss.25-1198

摘要/Abstract

摘要：

针对大规模场景下建模复杂度高及传统算法易陷入局部最优的难题，提出一种基于多叉树编码的改进NSGA-II求解框架。基于多叉树建模，将复杂的混合整数规划问题转化为多叉树构型优化问题，降低了约束处理难度并提升了解空间的搜索效率；设计多叉树交叉、变异算子和目标函数计算方法；引入大邻域搜索策略，通过“破坏-修复”机制有效平衡了算法的全局探索与局部开发能力。仿真结果表明：在不同规模场景下，改进算法在HV和IGD指标上均优于NSGA-II、MOEA/D和SPEA2等经典多目标进化算法。

关键词: 卫星, 在轨加注, 多叉树, LNS-NSGA-II, 任务规划

Abstract:

An improved NSGA-II solution framework based on multi-tree encoding is proposed to address the problems of high modeling complexity under large-scale scenarios and the tendency of traditional algorithms to fall into local optima. Based on multi-tree modeling, the complex mixed-integer programming problem is transformed into a multi-tree configuration optimization problem, thus reducing the constraint handling difficulty and improving the search efficiency of the solution space. Multi-tree crossover and mutation operators as well as the calculation method for objective functions are designed. A large neighborhood search (LNS) strategy is introduced, and the global exploration and local exploitation capabilities of the algorithm are balanced through a "destruction-repair" mechanism. Simulation results demonstrate that under scenarios of different scales, the improved algorithm outperforms classic multi-objective evolutionary algorithms including NSGA-II, MOEA/D and SPEA2 in terms of HV and IGD metrics.

Key words: satellite, on-orbit refueling, multi-tree, LNS-NSGA-II, mission planning

中图分类号:

TP391

李国政,王锐,路毅 . 基于改进NSGA-II的卫星在轨加注任务规划研究[J]. 系统仿真学报, 2026, 38(10): 3113-3125.

Li Guozheng,Wang Rui,Lu Yi . On-orbit Refueling Mission Planning of Satellites Based on Improved NSGA-II[J]. Journal of System Simulation, 2026, 38(10): 3113-3125.

图/表 29

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表1

多叉树编码优势理论分析

对比	序列编码	多叉树编码
解空间增长率	$O ((n!) k)$	$O (B n ⋅ n!)$
无效解比例	高	低
结构信息保留	无	完整
C1、C2访问唯一性	需要修复算子	树结构天然保证
C3往返次数	需要额外编码	子树数量直接表示
破坏操作	$O (n)$	$O (l o g n)$
修复操作	$O (n 2)$	$O (n l o g n)$
可行性检验	$O (n 2)$	$O (n)$

表1

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Fig. 12

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表 2

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表8

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参数	场景规模
参数	10	30	50	100
种群大小	50	100	150	200
迭代次数	50	100	150	150
交叉概率	0.9	0.9	0.9	0.9
变异概率	0.1	0.1	0.1	0.1
破坏精英个体比例	0.2	0.2	0.2	0.2

名称	相位/rad	燃料需求/kg	名称	相位/rad	燃料需求/kg
T1	0.16	227.89	T16	4.59	261.43
T2	1.4	155.01	T17	6.11	207.25
T3	4.25	247.29	T18	3.47	175.71
T4	0.55	278.44	T19	3.89	265.88
T5	0.19	184.38	T20	3.63	272.34
T6	3.18	143.73	T21	0.29	240.91
T7	1.25	105.31	T22	1.82	145.58
T8	3.42	229.98	T23	1.46	115.96
T9	3.7	144.09	T24	1.75	120.20
T10	0.04	261.89	T25	2.29	227.14
T11	4.39	261.16	T26	1.32	174.04
T12	0.98	168.05	T27	5.89	153.40
T13	2.11	291.44	T28	3.83	229.61
T14	0.61	118.55	T29	4.58	134.23
T15	3.79	269.50	T30	2.38	132.68