标准粒子群算法的收敛性分析及改进研究

发布时间：2018-01-08 00:19

本文关键词：标准粒子群算法的收敛性分析及改进研究　出处：《渤海大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着人们在实际生活中遇到的优化问题越来越多,传统优化算法不能解决部分复杂的优化问题。因此一些新颖的启发式优化算法被提出,如遗传算法,模拟退火算法,引力搜索算法,蚁群算法等。这些算法基本都是模拟或揭示自然现象或过程而得到发展,其思想和内容涉及数学、物理学、生物进化、人工智能、神经科学和统计力学等方面。粒子群优化算法(Particle Swarm Optimization,PSO)就是其中一个,粒子群算法规则简单,可调参数少,容易实现,收敛速度快,且有很多措施可以避免陷入局部最优,在工程应用中比较广泛,根据粒子群算法优异的性能,本论文对该算法做了进一步的研究,主要工作如下:1、基于概率理论计算了标准粒子群算法中粒子的转移概率,通过其转移概率对PSO算法进行了收敛性分析,并证明了粒子群算法在一定条件下依概率1收敛。2、提出了一种新的改进粒子群优化(IPSO)算法,保证IPSO算法是依概率1收敛的。为了平衡IPSO算法的探索和开发能力,在IPSO算法中,我们提出了探索和开发算子。最后,IPSO算法测试了13个基准测试函数,并与其他算法进行比较。数值结果证实了IPSO算法在求解非线性函数中具有更好的性能。
[Abstract]:With more and more optimization problems people encounter in real life, the traditional optimization algorithm can not solve some complex optimization problems. Therefore, some novel heuristic optimization algorithms have been proposed, such as genetic algorithm, simulated annealing algorithm, gravitational search algorithm, ant colony algorithm. These algorithms are basically the simulation of natural phenomena or process to get the development of the thought and content involves mathematics, physics, biology, artificial intelligence, neural science and statistical mechanics. The particle swarm optimization algorithm (Particle Swarm Optimization, PSO) is one of the particle swarm algorithm has simple rules, less adjustable parameters, easy realization, fast convergence speed, and there are a lot of measures you can avoid falling into local optimum, is widely applied in engineering, according to the excellent performance of particle swarm algorithm, this thesis make a further research on the algorithm, the main work such as : 1, particle transfer probability of the standard particle swarm algorithm was calculated based on probability theory, through the transfer of probability convergence analysis of PSO algorithm, and proves that under certain conditions the particle swarm algorithm converges with probability 1.2, proposed a new improved particle swarm optimization (IPSO) algorithm, guarantee the IPSO algorithm is convergence with probability 1. In order to explore and develop the ability to balance the IPSO algorithm, the IPSO algorithm, we put forward the exploration and development of the operator. Finally, IPSO algorithm is tested on 13 benchmark functions, and compared with other algorithms. The numerical results show that the IPSO algorithm has better performance in solving nonlinear function.

【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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