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基于任务效用最大化的多雷达协同任务规划算法
doi: 10.12000/JR23013
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1 1 若要消除该假设，可通过将一个待执行任务q拆分成在同一个位置的多个子任务。例如：可将某项任务\begin{document}${\boldsymbol{\nu}}_{{\rm{Prop}}}^q=\left\{\left(x^{q}, y^{q}\right), \rho^{q}, t^{q}\right\} $\end{document} \begin{document}${\boldsymbol{\nu}}_{{\rm{Sub}}{\text{-}}{\rm{Prop}}}^1,{\boldsymbol{\nu}}_{{\rm{Sub}}{\text{-}}{\rm{Prop}}}^2,\cdots, {\boldsymbol{\nu}}_{{\rm{Sub}}{\text{-}}{\rm{Prop}}}^k $\end{document} \begin{document}${\boldsymbol{\nu}}_{{\rm{Sub}}{\text{-}}{\rm{Prop}}}^k =\{(x^q,y^q),\rho^q,t^k\} $\end{document} \begin{document}$\sum t^k =t^q$\end{document}
作者简介:
袁 野，博士，主要研究方向为多雷达协同探测、目标跟踪、雷达资源管控技术等
杨 剑，博士，副教授，主要研究方向为雷达信号处理、阵列信号处理、精确制导与对抗技术等
刘辛雨，博士生，主要研究方向为雷达通信一体化信号设计、雷达对抗波形设计等
易 伟，博士，教授，主要研究方向为低可观测目标检测跟踪、多雷达协同探测等
孔令讲，博士，教授，主要研究方向为新体制雷达、统计信号处理、优化理论和算法、雷达信号处理、非合作信号处理技术和自适应阵列信号处理等
通讯作者:
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摘要: 该文针对多雷达协同场景下的多任务实时规划问题，提出了一种基于任务效用最大化的多雷达协同在线任务规划模型。该模型以任务效用函数最大化为目标将多雷达协同任务分配建模成一个基于整数规划的多变量混合优化问题；随后提出了启发式穷举搜索算法和基于凸松弛的两步解耦算法，可在多项式时间内完成了该NP难优化问题的求解，且分别在优化性能和计算效率方面有所侧重。仿真实验表明，相比于可找到最优解的穷举搜索算法，该文提出算法可有效降低任务规划问题复杂度，提升问题求解效率，以满足在线任务分配的实时性要求。Abstract: A utility maximization-based multiradar online task planning algorithm aiming at the real-time multitask planning problem is proposed in this paper. Using the maximization of the task utility function as the objective, multiradar task planning is formulated as an integer programming-based mixed multivariable optimization problem. Then, two algorithms, namely heuristic greedy search and convex relaxation-based two-step decoupling are proposed to solve the resulting NP-hard optimization problem in polynomial time, respectively. Simulation experiments demonstrate that compared with the optimal exhaustive search algorithm, the proposed algorithms can effectively reduce the computing time or improve solution efficiency such that the real-time requirement of online task planning can be satisfied.
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图 1 任务排列与任务分配概念解释
Figure 1. An illustration of the concepts for task arrangement and task scheduling
图 2 任务规划示意图(
$ N=2,\;Q=8 $ )Figure 2. Schematic diagram of the task scheduling with
$N = 2,{\text{ }}Q = 8$ 
图 5 3种算法下的多雷达-多任务分配结果
Figure 5. Multiradar-multitask scheduling results of the three algorithms
图 6 3种算法下的各雷达分得的任务执行顺序排序结果
Figure 6. The task execution order of each radar under the three algorithms
图 7 不同任务数量Q下3种算法得到的任务效用值
Figure 7. Task utility values of the three algorithms with different number of tasks Q
图 8 不同任务数量Q下3种算法运行时间
Figure 8. Runtime of the three algorithms with different number of tasks Q
图 9 不同探测构型下CRTSD算法任务分配结果
Figure 9. Task scheduling results of CRTSD algorithm with different radar configurations
图 10 不同任务优先级设置下CRTSD算法得到的任务效用值
Figure 10. Task utility values of CRTSD algorithm with different task priorities
1 穷举搜索算法
1. Exhaustive search algorithm
输入：雷达位置、雷达时间资源、任务位置、任务耗时 for ${\text{id}}{{\text{x}}_1} = 1:N$ for ${\text{id}}{{\text{x}}_2} = 1:N$ $ \ddots $ for ${\text{id}}{{\text{x}}_Q} = 1:N$ 完成任务-雷达节点分配：设置$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right.\left( {{\text{id}}{{\text{x}}_1},1} \right) = 1 $,
${\boldsymbol{U} }\left| {_\mathbb{Q} } \right.\left( { {\text{id} }{ {\text{x} }_2},2} \right) = 1,{\text{ } } \cdots$, ${\boldsymbol{U}}\left| {_\mathbb{Q}} \right.\left( {{\text{id}}{{\text{x}}_Q},Q} \right) = 1 $, $ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right. $其余
项为0；完成任务排序：根据上一步得到的$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right. $，对每个雷达分得
任务进行排列，并计算每次排列对应问题的目标函数值，选
出效用函数最大排列结果，记为$\phi \left( { {\text{id} }{ {\text{x} }_1},{\text{id} }{ {\text{x} }_2}, \cdots ,{\text{id} }{ {\text{x} }_Q} } \right)$；end ${\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}}$ end end 选出最大的$\phi \left( { {\text{id} }{ {\text{x} }_1}, {\text{id} }{ {\text{x} }_2}, \cdots ,{\text{id} }{ {\text{x} }_Q} } \right)$，其对应的任务分配方案即为
最优任务分配，记为：${\left\{ {\mathbb{Q},{\boldsymbol{U}}\left| {_\mathbb{Q}} \right.} \right\}^{{\text{OPT}}}}$；输出：任务分配方案${\left\{ {\mathbb{Q},{\boldsymbol{U}}\left| {_\mathbb{Q}} \right.} \right\}^{{\text{OPT}}}}$ 
下载: 导出CSV
2 离散化任务分配变量
2. Discretization of task scheduling variables
输入：问题求解得到的任务分配变量$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right. $ 初始化任务分配变量$ {{\boldsymbol{U}}^{{\text{opt}}}} $为$N \times Q$维零矩阵； for $i = 1:NQ$ 找出$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right. $中最大元素，记为$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right.\left( {q,n} \right) $； 判断若将$ {{\boldsymbol{U}}^{{\text{opt}}}}\left( {q,n} \right) $设置为1，并将$ {{\boldsymbol{U}}^{{\text{opt}}}} $代入式(15)后，是否
满足式(15)的所有约束；若满足，则设置$ {{\boldsymbol{U}}^{{\text{opt}}}}\left( {q,n} \right) = 1 $； 设置$ {\boldsymbol{U}}\left| {_\mathbb{Q}} \right.\left( {q,n} \right) = 0 $； end 输出：离散化的任务分配变量$ {{\boldsymbol{U}}^{{\text{opt}}}} $
下载: 导出CSV
3 启发式贪婪算法
3. Heuristic greedy search algorithm
输入：雷达位置、雷达时间资源、任务位置、任务耗时 设置$r_{\max }^q = 0{\text{ }}\left( {q = 1,2, \cdots ,Q} \right)$； for $q = 1:Q$ for $n = 1:N$ 计算任务q与雷达n的距离$r_n^q$； if $r_n^q > r_{\max }^q$ and $ {t_{n,\max }} > {t^q} $ 将任务q改为分配给节点n； 设置$ {t_{n,\max }} = {t_{n,\max }} - {t^q} $, $r_{\max }^q = r_n^q$； end end end for $n = 1:N$ 对雷达n分得的任务进行排序； end 输出：任务分配变量${ {\boldsymbol{U} }^{ {\text{opt} } } }$
下载: 导出CSV
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