基于GIS的最优路径算法研究与实现
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摘要
最优路径规划是网络优化的基本科学问题之一,多年来产生了大量相关领域的研究成果,然而计算机网络与通信系统,基于GIS的智能交通系统、移动机器人、军事指挥系统等众多应用领域出现的新问题,对最优路径的研究又提出了新的任务和要求。论文在相关研究的基础上,以军工科研项目为主要需求,重点研究了作战背景下满足一定解算条件的单任务、多任务最优路径问题,最短路径的高效算法,多约束最优路径问题以及时变网络最优路径问题。
论文的研究成果主要包括:
(1)基于数字地图线状图元文件,构建了适于最优路径算法研究的道路网拓扑结构。
(2)设计并实现了作战背景下满足最短和最快解算原则的单任务、多任务最优路径辅助决策系统。针对多任务算法实现过程中出现的路段冲突,提出了同步法和异步法两种解决方案。原型系统试验显示上述算法有效可行。
(3)最短路径算法效率是战时辅助军事决策、应急救援等系统普遍关注和迫切需要解决的问题。论文针对项目地理信息系统平台中路网道路分布不均、道路不规则等特点,提出了两种最短路径的改进算法:比值系数τ分段取值的矩形限制搜索区域算法和带启发因子的直线优化A~*算法。上述两种改进算法稳定性好,且在路段搜索范围、算法的速度、资源消耗等方面较经典Dijkstra算法有较大改善。
(4)针对多弧权网络最优路径问题,提出了多约束最优路径问题的MCOP算法;将启发式思想引入多约束最优路径问题的研究,提出了多约束最优路径问题的A~*_MCOP算法。实例验证了上述算法的正确性以及A~*_MCOP算法的优越性。
(5)系统研究了FIFO网络、非FIFO网络最短时间路径的算法理论并给出相应的证明。所提出的非FIFO网络最短路径理论为解决非FIFO网络最短时间路径问题提供了新的途径。文中还对各种等待约束情况下的“前向”、“反向”最短时间路径算法进行了设计和总结。
对于最优路径算法研究这一具有很强应用背景的课题,本文从军工科研项目需求出发,通过对已有算法的总结及现存问题的分析,提出了一系列新的算法思想与算法理论。实际系统运行结果及算法实例表明文中所提出的最优路径算法的正确性和有效性。
Optimal path planning is one of the elementary scientific toptics in network optimization, which has produced a considerable amount of research results of the corresponding fields. However, new situations appearing in many burgeoning fields such as computer network and communication system, intelligent transportation systems based on GIS, mobile robot and military command system, bring forward new tasks and demands for the research of the optimal path problem. Mainly, to meet the demand of the scientific research project of army industry and based on the interrelated research, the follow problems are emphatically researched in this dissertation: optimal path problems of single-task and multitask under some computing conditions under the antagonism condition; high-efficiency algorithms in the shortest path problem; multi-constraint optimal path problem and the optimal path problem in time-dependent network.
Main contributions of the dissertation include:
(1) A topological structure of road network, which is based on the line-like elements file of digital map, is constructed for optimal path algorithm analysis.
(2) An aid decision-making system under the antagonism condition is designed and realized for shortest and fastest path computation of single-task and multitask. Considering the conflict in multitask path optimization, this paper proposes two kinds of resolving schemes: synchronization algorithm and asynchronism algorithm. Experiment on prototype system shows that aforementioned algorithms are reasonable and feasible.
(3) Algorithmic efficiency of the shortest path searching is problem which has brought wide attention and need to be resolved urgently in war paramilitary decision-making system, contingency succor system, etc. In this paper, two improved shortest path algorithms are proposed to adapt for asymmetry and abnormity of the road network of the item GIS platform: the restricted rectangle searching area algorithm with variational ratio coefficient r and the beeline optimizing A~* algorithm with heuristic gene. The two algorithms are all of high stability and achieve significantly higher computational performance in searching scope, computational efficiency and EMS memory over the classical Dijkstra's algorithm.
(4) Aimmed at the optimal path problem of the network which provided with multiple constraints on each link, a multi-constraint optimal path (MCOP) algorithm is proposed. Furthermore, by introducing heuristic idea into the research of MCOP problem, an exact A*_MCOP algorithm is designed. Experiments show the validity of the two algorithms and the superiority of A~*_MCOP algorithm.
(5) Theories of least time path algorithm in FIFO and non-FIFO network are studied and proved systematically. Thereinto, the research about non-FIFO network provides a new approach for least time path problem in non-FIFO network. The "forward" and "backward" least time path algorithms under various waiting constraints are designed and summarized also in this paper.
Based on the analysis and summarization of existing algorithms, this paper proposes a series of new optimal path algorithm ideas and algorithm theories with practicability as the goal. The algorithms for path optimization are experimentslly proved accurate and effective.
论文的研究成果主要包括:
(1)基于数字地图线状图元文件,构建了适于最优路径算法研究的道路网拓扑结构。
(2)设计并实现了作战背景下满足最短和最快解算原则的单任务、多任务最优路径辅助决策系统。针对多任务算法实现过程中出现的路段冲突,提出了同步法和异步法两种解决方案。原型系统试验显示上述算法有效可行。
(3)最短路径算法效率是战时辅助军事决策、应急救援等系统普遍关注和迫切需要解决的问题。论文针对项目地理信息系统平台中路网道路分布不均、道路不规则等特点,提出了两种最短路径的改进算法:比值系数τ分段取值的矩形限制搜索区域算法和带启发因子的直线优化A~*算法。上述两种改进算法稳定性好,且在路段搜索范围、算法的速度、资源消耗等方面较经典Dijkstra算法有较大改善。
(4)针对多弧权网络最优路径问题,提出了多约束最优路径问题的MCOP算法;将启发式思想引入多约束最优路径问题的研究,提出了多约束最优路径问题的A~*_MCOP算法。实例验证了上述算法的正确性以及A~*_MCOP算法的优越性。
(5)系统研究了FIFO网络、非FIFO网络最短时间路径的算法理论并给出相应的证明。所提出的非FIFO网络最短路径理论为解决非FIFO网络最短时间路径问题提供了新的途径。文中还对各种等待约束情况下的“前向”、“反向”最短时间路径算法进行了设计和总结。
对于最优路径算法研究这一具有很强应用背景的课题,本文从军工科研项目需求出发,通过对已有算法的总结及现存问题的分析,提出了一系列新的算法思想与算法理论。实际系统运行结果及算法实例表明文中所提出的最优路径算法的正确性和有效性。
Optimal path planning is one of the elementary scientific toptics in network optimization, which has produced a considerable amount of research results of the corresponding fields. However, new situations appearing in many burgeoning fields such as computer network and communication system, intelligent transportation systems based on GIS, mobile robot and military command system, bring forward new tasks and demands for the research of the optimal path problem. Mainly, to meet the demand of the scientific research project of army industry and based on the interrelated research, the follow problems are emphatically researched in this dissertation: optimal path problems of single-task and multitask under some computing conditions under the antagonism condition; high-efficiency algorithms in the shortest path problem; multi-constraint optimal path problem and the optimal path problem in time-dependent network.
Main contributions of the dissertation include:
(1) A topological structure of road network, which is based on the line-like elements file of digital map, is constructed for optimal path algorithm analysis.
(2) An aid decision-making system under the antagonism condition is designed and realized for shortest and fastest path computation of single-task and multitask. Considering the conflict in multitask path optimization, this paper proposes two kinds of resolving schemes: synchronization algorithm and asynchronism algorithm. Experiment on prototype system shows that aforementioned algorithms are reasonable and feasible.
(3) Algorithmic efficiency of the shortest path searching is problem which has brought wide attention and need to be resolved urgently in war paramilitary decision-making system, contingency succor system, etc. In this paper, two improved shortest path algorithms are proposed to adapt for asymmetry and abnormity of the road network of the item GIS platform: the restricted rectangle searching area algorithm with variational ratio coefficient r and the beeline optimizing A~* algorithm with heuristic gene. The two algorithms are all of high stability and achieve significantly higher computational performance in searching scope, computational efficiency and EMS memory over the classical Dijkstra's algorithm.
(4) Aimmed at the optimal path problem of the network which provided with multiple constraints on each link, a multi-constraint optimal path (MCOP) algorithm is proposed. Furthermore, by introducing heuristic idea into the research of MCOP problem, an exact A*_MCOP algorithm is designed. Experiments show the validity of the two algorithms and the superiority of A~*_MCOP algorithm.
(5) Theories of least time path algorithm in FIFO and non-FIFO network are studied and proved systematically. Thereinto, the research about non-FIFO network provides a new approach for least time path problem in non-FIFO network. The "forward" and "backward" least time path algorithms under various waiting constraints are designed and summarized also in this paper.
Based on the analysis and summarization of existing algorithms, this paper proposes a series of new optimal path algorithm ideas and algorithm theories with practicability as the goal. The algorithms for path optimization are experimentslly proved accurate and effective.
引文
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