基于模型知识融合的图神经网络多雷达协同任务调度算法

李浩情; 余点; 潘常春; 郁文贤; 李东瀛

doi:10.12000/JR24222

基于模型知识融合的图神经网络多雷达协同任务调度算法

DOI: 10.12000/JR24222

李浩情¹,
余点²,
潘常春^1, ,,
郁文贤^1, ,,
李东瀛¹

1.
上海交通大学电子信息与电气工程学院北斗导航与位置服务上海市重点实验室上海 200240
2.
上海交通大学巴黎卓越工程师学院上海 200240

基金项目: 上海市科学技术委员会项目(24Z511005506)

详细信息

作者简介:
李浩情，硕士生。主要研究方向为雷达任务调度算法，强化学习

余　点，本科生(本硕连读)。主要研究方向为图神经网络和强化学习

潘常春，副研究员。主要研究方向为ATR任务规划与调度，工业系统建模与优化

郁文贤，教授。主要研究方向为信号与信息处理、信息融合、目标识别、遥感与导航

李东瀛，副教授。主要研究方向为雷达探测、雷达环境感知、智能目标识别

通讯作者:
潘常春 pan_cc@sjtu.edu.cn

郁文贤 wxyu@sjtu.edu.cn

责任主编：易伟 Corresponding Editor: YI Wei
中图分类号: TN958.92; TP389.1
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- 文章访问数: 22
- HTML全文浏览量: 13
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-10
- 修回日期: 2025-01-16

Multiradar Collaborative Task Scheduling Algorithm Based on Graph Neural Networks with Model Knowledge

LI Haoqing¹,
YU Dian²,
PAN Changchun^{1
, ,},
YU Wenxian^{1
, ,},
LI Dongying¹

1.
Shanghai Key Laboratory of Navigation and Location based Services, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China
2.
Paris Elite Institute of Technology , Shanghai Jiao Tong University, Shanghai, 200240, China

Funds: Funding from the Shanghai Municipal Science and Technology Commission (24Z511005506)

More Information

Corresponding author: PAN Changchun, pan_cc@sjtu.edu.cn; YU Wenxian, wxyu@sjtu.edu.cn

摘要

摘要: 现代雷达的探测、跟踪、识别等任务场景越来越复杂。任务类型的多变性，雷达资源的稀缺性和任务执行时间窗口的严格要求，使得雷达任务调度成为一类强NP-Hard问题。然而，现有的调度算法在处理涉及复杂逻辑约束的多雷达协同调度问题时适应性不足，效率不高。因此，基于人工智能(AI)的调度算法正在成为研究热点，但是AI调度算法的效率与问题特征提取是否全面密切相关。如何能快速，全面的提取多雷达协同任务调度问题的共性特征，是提升这类AI调度算法效率的关键。因此，该文提出了基于模型知识融合的图神经网络(MKEGNN)调度算法。该算法首先将雷达任务协同调度问题建模为异构网络图模型，利用模型知识来优化GNN算法训练过程。算法创新在于：通过低复杂度的计算手段，获取模型的关键知识，进而优化GNN模型。在特征提取阶段，引入随机酉矩阵变换，利用任务异构图的随机拉普拉斯矩阵谱特征作为全局特征来强化图神经网络对共性特征的提取能力，弱化特定问题的个性化特征；在参数化决策阶段，利用由问题的引导解和经验解构成的上/下界结构知识从原理上减少决策空间大小，引导网络快速优化，加速决策学习过程的收敛。最后，进行了大量数据仿真实验。结果表明，相比目前的算法，MKEGNN算法对于所有任务集在稳定性和精度方面都有所提升，调度成功率性能提升3%～10%，加权调度成功率提升5%～15%。尤其当处理多雷达协同关系复杂的任务集时，任务调度成功率提升4%以上，算法稳定性和鲁棒性显著增强。
- 雷达任务调度 /
- 图神经网络 /
- 强化学习 /
- 模型知识 /
- 拉普拉斯矩阵 /
- 随机矩阵
Abstract: Modern radar systems face increasingly complex challenges in tasks such as detection, tracking, and identification. The diversity of task types, limited data resources, and strict execution time requirements make radar task scheduling a strongly NP-hard problem. However, existing scheduling algorithms struggle to efficiently handle multiradar collaborative tasks involving complex logical constraints. Therefore, Artificial Intelligence (AI)-based scheduling algorithms have gained significant attention. However, their efficiency is heavily dependent on effectively extracting the key features of the problem. The ability to quickly and comprehensively extract common features of multiradar scheduling problems is essential for improving the efficiency of such AI scheduling algorithms. Therefore, this paper proposes a Model Knowledge Enhanced Graph Neural Network (MKEGNN) scheduling algorithm. This method frames the radar task collaborative scheduling problem as a heterogeneous network graph, leveraging model knowledge to optimize the training process of the Graph Neural Network (GNN) algorithm. A key innovation of this algorithm is its capability to capture critical model knowledge using low-complexity calculations, which helps to further optimize the GNN model. During the feature extraction stage, the algorithm employs a random unitary matrix transformation. This approach utilizes the spectral features of the random Laplacian matrix from the task’s heterogeneous graph as global features, enhancing the GNN’s ability to extract shared problem features while downplaying individual characteristics. In the parameterized decision-making stage, the algorithm leverages the upper and lower bound knowledge derived from guiding and empirical solutions of the problem model. This strategy significantly reduces the decision space, enabling the network to optimize quickly and accelerating the learning process. Extensive simulation experiments confirm the effectiveness of the MKEGNN algorithm. Compared to existing approaches, it demonstrates improved stability and accuracy across all task sets, boosting the scheduling success rate by 3%～10% and the weighted success rate by 5%～15%. For particularly challenging task sets involving complex multiradar collaborations, the success rate improves by over 4%. The results highlight the algorithm’s stability and robustness.
- Radar task scheduling /
- Graph neural network /
- Reinforcement learning /
- Model knowledge /
- Laplace matrix /
- Random matrix

HTML全文

图 1 雷达任务结构

Figure 1. Structure of radar task

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图 2 任务调度示意

Figure 2. Schematic of task scheduling

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图 3 基于异构图网络的雷达任务调度问题描述

Figure 3. Description of the radar task scheduling problem based on heterogeneous graph networks

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图 4 基于模型知识融合的图神经网络框架

Figure 4. Framework for model knowledge embedded graph neural networks

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图 5 随机处理对任务集关系网络特征值分布的影响

Figure 5. The effect of stochastic processing on the distribution of eigenvalues of task-set relational networks

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图 6 不同参数任务数据集随机变换后的特征分布

Figure 6. Distribution of features after random transformation of datasets with different parameter tasks

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图 7 图神经网络结构图

Figure 7. Graph neural network structure

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图 8 10×3实例上的训练曲线

Figure 8. Training curves on instance 10×3

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图 9 平均相对调度评分

Figure 9. Average Relative Scheduling Score

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图 10 两种GNN模型对相同实例的成功调度结果甘特图对比

Figure 10. Comparison of successfully scheduling results gantt charts of two models on the same instance

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图 11 算法性能比较

Figure 11. Algorithm Performance Comparison

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图 12 1个实例调度50次，两种模型的调度结果

Figure 12. Scheduling results for both models on one instance

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表 1 基于任务节点的7维度特征嵌入

Table 1. 7-dimensional feature embedding based on task nodes

序号	特征维度	特征说明
1	任务状态$ {\rm{ST}}_{{i}} $	标识任务此前是否被调度过，已调度任务状态为$ {\rm{ST}}_{{i}}=1 $，否则为$ {\rm{ST}}_{{i}}=0 $。
2	处理时间$ {{p}}_{{i}} $	雷达资源执行任务所需时间，包括准备时间
3	时间裕度tr	任务的截止期$ {{d}}_{{i}} $与雷达最早可用时间$ {{t}}_{{a}}^{{{m}}_{{i}}} $之差，反映任务的紧急程度。
4	任务所关联雷达的未调度任务个数$ {{N}}_{{i}}^{{t}} $	$ {t} $时刻待处理任务队列中，与属于任务$ {i} $同属于雷达$ {{m}}_{{i}} $，且尚未调度的任务的个数。
5	权重值$ {{\varphi}}_{{i}} $	与任务优先级相关的权重值
6	入度弧个数$ {{E}}_{{i}} $	表示有向弧中指向任务$ {i} $的弧的个数
7	同步弧个数$ {{{\mathrm{Syn}}}}_{{i}} $	表示与任务$ {i} $同步任务的个数。

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表 2 不同参数任务数据集的全局特征

Table 2. Global characteristics of the dataset for different parameter tasks

参数	零特征值个数	最小非零特征值	谱半径	MSR
平均前置个数：1	9	0.7903	5.4809	2.3955
平均前置个数：2	0	0.0441	13.0964	7.9675
处理时间分布标准差：0	6	0.2592	4.9889	2.8304
处理时间分布标准差：2	6	0.5715	6.0868	1.9645

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表 3 任务实例生成

Table 3. Task instance generation

大小	优先级	处理时间	截止期	前置任务个数	同步任务个数
10×3	U(1, 5 )	U(1 , 5)	U(8 , 30)	U(0, 3)	U(0, 2)
20×3	U(1, 5 )	U(1 , 5)	U(8 , 30)	U(0, 3)	U(0, 2)
20×10	U(1, 5 )	U(1 , 5)	U(12 , 40)	U(0, 3)	U(0, 2)
30×5	U(1, 5 )	U(1 , 5)	U(12 , 40)	U(0, 3)	U(0, 2)
注：U(a, b)表示在区间[a, b]上的随机分布。

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表 4 不同规模数据训练模型的测试结果(成功率)

Table 4. Test results (success rate) of models trained with datasets of different sizes

测试集规模	10×3	20×3	20×10	30×5
10×3训练模型	96.10%	83.35%	97.90%	84.40%
20×3训练模型	94.60%	80.50%	96.75%	80.63%
20×10训练模型	95.10%	80.50%	96.95%	80.57%
30×5训练模型	93.40%	80.30%	96.45%	81.03%

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表 5 任务参数

Table 5. Task parameters

类别	类型	数量	驻留时长	截止期
跟踪确认TC	6	10	9	250
高精度跟踪HPT	5	10	8	250
精度跟踪PT	4	15	6	100
普通跟踪NT	3	15	4	100
高优先级搜索HS	2	20	2	100
低优先级搜索LS	1	20	1	100

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表 6 结果对比

Table 6. Comparison of results

方法	成功率	加权成功率	平均任务调度耗时(s)
MKEGNN	86.17	85.67	0.773
GNN	81.91	82.98	0.703
BBM	79.79	79.18	0.726
GTW	75.53	80.89	0.570
Score	76.6	78.16	0.012
注：平均任务调度耗时=计算耗时/调度成功任务个数。

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表 7 测试集实例生成

Table 7. Test instance generation

实例	任务数	雷达数	优先级	处理时间	截止期	前置任务个数	同步任务个数
Case1	20	3	U(1, 5)	U(1, 5)	U(8, 30)	U(0, 1)	U(0, 2)
Case2	20	3	U(1, 5)	U(1, 5)	U(8, 30)	U(0, 3)	U(0, 2)
Case3	30	5	U(1, 5)	U(1, 5)	U(12, 40)	U(0, 1)	U(0, 2)
Case4	30	5	U(1, 5)	U(1, 5)	U(12, 40)	U(0, 3)	U(0, 2)
Case5	60	5	U(1, 5)	U(1, 5)	U(16, 60)	U(0, 1)	U(0, 2)
Case6	60	5	U(1, 5)	U(1, 5)	U(16, 60)	U(0, 3)	U(0, 2)
注：U(a, b )表示在区间[a, b]上的随机分布。

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表 8 任务调度成功率(%)

Table 8. Success ratio of scheduling(%)

实例	MKEGNN	GNN	BBM	GTW	Score	FIFO	LPT	EDF
Case1	80.5	70.5	72.5	67.0	65.5	63.0	59.5	71.0
Case2	58.5	53.0	52.5	48.0	48.5	48.5	42.5	50.5
Case3	90.3	81.6	78.6	79.0	77.6	72.3	70.7	81.0
Case4	52.0	49.7	45.7	52.0	48.0	45.3	47.3	46.0
Case5	85.7	85.6	70.2	80.2	72.7	66.5	63.3	77.8
Case6	45.0	44.2	40.8	42.0	40.0	39.4	39.5	40.8

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表 9 任务加权调度成功率(%)

Table 9. Weighted success ratio of scheduling(%)

实例	MKEGNN	GNN	BBM	GTW	Score	FIFO	LPT	EDF
Case1	81.9	69.9	71.2	68.5	63.9	61.1	58.2	70.8
Case2	61.3	54.7	55.2	50.4	50.9	50.7	44.9	53.0
Case3	90.8	80.9	79.4	80.0	78.4	72.6	70.6	81.0
Case4	52.7	50.1	44.8	52.5	47.8	44.4	47.1	46.0
Case5	86.2	81.0	70.0	82.2	74.0	65.5	63.7	78.1
Case6	46.6	44.0	42.5	43.8	41.0	41.2	41.1	42.9

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表 10 各优先级任务调度成功率(%)

Table 10. Success ratio of scheduling of different priority(%)

优先级	MKEGNN	GNN	BBM	GTW	Score	FIFO	LPT	EDF
5	88.8	66.6	88.8	88.8	88.8	66.7	55.6	77.8
4	100	100	83.3	83.3	83.3	83.3	100	100
3	100	50.0	50.0	50.0	75.0	25.0	75.0	75.0
2	80.0	60.0	60.0	40.0	60.0	80.0	80.0	60.0
1	83.3	83.3	83.3	100	83.3	50.0	50.0	83.3

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