粒子群优化算法研究及其在海底地形辅助导航中的应用
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摘要
海底地形辅助导航是水下潜器智能化航行的关键技术之一,其研究目的是利用存储在计算机中的数字地图,来对参考导航系统的漂移累积误差进行校正,从而达到精确的导航目的。匹配搜索算法是地形辅助导航的核心,传统地形辅助导航采用遍历的搜索方式进行匹配定位,该方式所带来的巨大计算量严重影响了导航效率,同时由于水下环境的特殊性,海底地形辅助导航相对于陆地环境更加复杂,因此对复杂的匹配搜索策略进行改进和优化是提高海底地形辅助导航效率的重要手段。
粒子群优化算法是20世纪90年代中期提出的一种群智能优化算法,其优越的全局寻优能力、简单的速度—位移模型以及特有的记忆功能引起了相关领域学者的广泛关注。目前粒子群优化算法已经是当今诸多领域的热点研究内容,并且在诸多问题上得到了成功应用,验证了其在复杂优化问题应用中的有效性。本文主要针对粒子群优化算法及其在海底地形辅助导航中的应用进行研究,论文主要研究工作如下:
1.从粒子群算法的理论基础入手,对其求解优化问题的统一框架和设计步骤进行分析,概述了粒子群算法的基本原理,并在此基础上对粒子群优化算法的收敛性进行分析证明。
2.从典型拓扑结构以及粒子之间的通信方式两方面研究了种群拓扑结构对粒子群算法性能的影响,在原始粒子群算法速度与位置更新公式的基础上,建立了表现粒子个体影响力的加权模型,并以地形辅助导航为应用背景,设计了更加合理的加权函数,仿真试验验证了该加权函数的有效性。提出了一种基于pso for pso思想的粒子群算法参数设置方法,将算法的参数选取问题转变为非线性优化问题,并使用粒子群算法本身对其进行寻优求解。仿真结果表明,该方法可以方便有效地实现对算法参数的优选。
3.针对粒子群算法在求解存在多局部极值的优化问题时存在早熟收敛的问题,提出了一种基于种群多样性的模糊粒子群算法。在对种群多样性进行分析的基础上,指出种群多样性的迅速下降是导致算法陷入早熟收敛的主因,提出通过引入变异操作来抑制种群多样性的衰减,并设计了动态调整变异率ρ_0和惯性权重w的模糊逻辑控制器FLC,实现对搜索过程的动态调整。对典型测试函数的求解结果表明,基于种群多样性的模糊粒子群算法是有效的,可以有效地降低算法陷入局部最优的危险性。
4.针对本质上连续的粒子群算法在离散空间的应用,提出了一种具有双子群结构的二进制离散粒子群优化算法。建立了双子群运动模型,并在此基础上设计了子群规模的动态变化规则,提出引入基于爬山思想的位置更新策略和伪变异策略以提高算法的收敛速度和全局寻优性能。分析了算法参数对算法性能的影响,给出了算法的整体流程。最后通过对两类测试函数的求解试验验证了算法的有效性。
5.针对基于粒子群优化的海底地形辅助导航的实现方法及关键技术进行了深入研究,分别以模糊粒子群算法和双子群粒子群算法为基础,设计了基于粒子群优化的海底地形辅助导航方法。仿真结果表明,该方法可以有效地解决海底地形辅助导航问题,在导航精度和稳定性上具有比传统地形辅助导航方法更大的优势。
The seabed terrain-aided navigation (STAN) is one of the key technologies in submarine automation and intelligent navigation. It revises the error of reference navigation system using digital map, and the main purpose is to make navigation more exact. The search algorithm is the core of STAN, traditional STAN algorithm uses ergodic search method, which brings too much calculation, and affects the navigation efficiency a lot. Furthermore, as the particularity of STAN, STAN is more complex than land environment. So the optimization of complex search strategy is the key method to improve efficiency of STAN.
Particle Swarm Optimization (PSO) is proposed in the end of the 20th century, it is simple in comcept, easy in implementation and few in parameters, so it has attracted much attention since proposed, and becomes a study hotspot in the world. Many successful applications verified the validity of PSO. This paper is mainly about PSO algorithm and its application in STAN systerm. The main content is as follows:
1. The theory and characterization of PSO is studied. First the artificial life and artificial life computation are studied. Then the unified framework and design steps for solving optimization problem are analysed. After summarize the basic theory of PSO, the comvergence of PSO is investigated in details.
2. The influence of swarm topology on PSO is studied in two aspects: typical swarm topology and communication style between two particles. A weighting model is established to represent the particle’s force, and a more reasonable weighting function is designed for the application of STAN. A parameter setting methods based on pso for pso thinking is proposed. The parameter selection problem is transformed into nonlinear optimization problem, and the PSO algorithm is selected to solve the problem.
3. As PSO has premature convergence problem when solving multi-modal problems, a fuzzy particle swarm optimization algorithm based on swarm diversity is proposed. After the swarm diversity is analysed, the rapid decline of the diversity is considered as the main reason for premature convergence. Mutation strategy is introduced to restrain the decline of diversity, and the fuzzy logic controller is designed for dynamical adjustment of mutation rateρ_0 and inertia weight w .
4. The PSO algorithm is essentially continuous, so its application in discrete domain is an important study aspect. A discrete PSO algorithm with two sub-swarms is proposed in the paper. First, the double sub-swarms movement model is established, and based on the movement model, the changing rules of sub-swarms’size is designed. At the same time, a position updating strategy based on the hill-climbing theory and pseudo mutation strategy are introduced into the algorithm to increase the convergence speed and global optimization performance. The influence of parameters is analysed, and the whole flow of the algorithm is designed.
5. According to the deep research of way and key technologies of STAN, the seabed terrain-aided navigation algorithm based on the Particle Swarm Optimization is proposed. Based on the anylysis of particularity of STAN, the determination methods of searching space and matching sequence is given, and the hausdorff distance which has strong anti-interference ability is chosen to be the similarity measure. The matching search policy based on PSO is designed to increase the efficiency of matching search.
粒子群优化算法是20世纪90年代中期提出的一种群智能优化算法,其优越的全局寻优能力、简单的速度—位移模型以及特有的记忆功能引起了相关领域学者的广泛关注。目前粒子群优化算法已经是当今诸多领域的热点研究内容,并且在诸多问题上得到了成功应用,验证了其在复杂优化问题应用中的有效性。本文主要针对粒子群优化算法及其在海底地形辅助导航中的应用进行研究,论文主要研究工作如下:
1.从粒子群算法的理论基础入手,对其求解优化问题的统一框架和设计步骤进行分析,概述了粒子群算法的基本原理,并在此基础上对粒子群优化算法的收敛性进行分析证明。
2.从典型拓扑结构以及粒子之间的通信方式两方面研究了种群拓扑结构对粒子群算法性能的影响,在原始粒子群算法速度与位置更新公式的基础上,建立了表现粒子个体影响力的加权模型,并以地形辅助导航为应用背景,设计了更加合理的加权函数,仿真试验验证了该加权函数的有效性。提出了一种基于pso for pso思想的粒子群算法参数设置方法,将算法的参数选取问题转变为非线性优化问题,并使用粒子群算法本身对其进行寻优求解。仿真结果表明,该方法可以方便有效地实现对算法参数的优选。
3.针对粒子群算法在求解存在多局部极值的优化问题时存在早熟收敛的问题,提出了一种基于种群多样性的模糊粒子群算法。在对种群多样性进行分析的基础上,指出种群多样性的迅速下降是导致算法陷入早熟收敛的主因,提出通过引入变异操作来抑制种群多样性的衰减,并设计了动态调整变异率ρ_0和惯性权重w的模糊逻辑控制器FLC,实现对搜索过程的动态调整。对典型测试函数的求解结果表明,基于种群多样性的模糊粒子群算法是有效的,可以有效地降低算法陷入局部最优的危险性。
4.针对本质上连续的粒子群算法在离散空间的应用,提出了一种具有双子群结构的二进制离散粒子群优化算法。建立了双子群运动模型,并在此基础上设计了子群规模的动态变化规则,提出引入基于爬山思想的位置更新策略和伪变异策略以提高算法的收敛速度和全局寻优性能。分析了算法参数对算法性能的影响,给出了算法的整体流程。最后通过对两类测试函数的求解试验验证了算法的有效性。
5.针对基于粒子群优化的海底地形辅助导航的实现方法及关键技术进行了深入研究,分别以模糊粒子群算法和双子群粒子群算法为基础,设计了基于粒子群优化的海底地形辅助导航方法。仿真结果表明,该方法可以有效地解决海底地形辅助导航问题,在导航精度和稳定性上具有比传统地形辅助导航方法更大的优势。
The seabed terrain-aided navigation (STAN) is one of the key technologies in submarine automation and intelligent navigation. It revises the error of reference navigation system using digital map, and the main purpose is to make navigation more exact. The search algorithm is the core of STAN, traditional STAN algorithm uses ergodic search method, which brings too much calculation, and affects the navigation efficiency a lot. Furthermore, as the particularity of STAN, STAN is more complex than land environment. So the optimization of complex search strategy is the key method to improve efficiency of STAN.
Particle Swarm Optimization (PSO) is proposed in the end of the 20th century, it is simple in comcept, easy in implementation and few in parameters, so it has attracted much attention since proposed, and becomes a study hotspot in the world. Many successful applications verified the validity of PSO. This paper is mainly about PSO algorithm and its application in STAN systerm. The main content is as follows:
1. The theory and characterization of PSO is studied. First the artificial life and artificial life computation are studied. Then the unified framework and design steps for solving optimization problem are analysed. After summarize the basic theory of PSO, the comvergence of PSO is investigated in details.
2. The influence of swarm topology on PSO is studied in two aspects: typical swarm topology and communication style between two particles. A weighting model is established to represent the particle’s force, and a more reasonable weighting function is designed for the application of STAN. A parameter setting methods based on pso for pso thinking is proposed. The parameter selection problem is transformed into nonlinear optimization problem, and the PSO algorithm is selected to solve the problem.
3. As PSO has premature convergence problem when solving multi-modal problems, a fuzzy particle swarm optimization algorithm based on swarm diversity is proposed. After the swarm diversity is analysed, the rapid decline of the diversity is considered as the main reason for premature convergence. Mutation strategy is introduced to restrain the decline of diversity, and the fuzzy logic controller is designed for dynamical adjustment of mutation rateρ_0 and inertia weight w .
4. The PSO algorithm is essentially continuous, so its application in discrete domain is an important study aspect. A discrete PSO algorithm with two sub-swarms is proposed in the paper. First, the double sub-swarms movement model is established, and based on the movement model, the changing rules of sub-swarms’size is designed. At the same time, a position updating strategy based on the hill-climbing theory and pseudo mutation strategy are introduced into the algorithm to increase the convergence speed and global optimization performance. The influence of parameters is analysed, and the whole flow of the algorithm is designed.
5. According to the deep research of way and key technologies of STAN, the seabed terrain-aided navigation algorithm based on the Particle Swarm Optimization is proposed. Based on the anylysis of particularity of STAN, the determination methods of searching space and matching sequence is given, and the hausdorff distance which has strong anti-interference ability is chosen to be the similarity measure. The matching search policy based on PSO is designed to increase the efficiency of matching search.
引文
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