基于信赖域的粒子群优化算法研究

发布时间：2017-12-26 19:28

本文关键词：基于信赖域的粒子群优化算法研究　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：由于粒子群优化算法具有易于理解与实现、收敛速度快、可调参数少、对适应度函数要求低以及较好的全局搜索能力等优点,它已经广泛地应用于科学研究和工程实践等领域。但是与其他随机优化技术一样,粒子群优化算法也存在自身的缺陷,搜索方向存在盲目性、后期收敛速度慢、容易失去种群多样性而陷入局部极优等。为了提高粒子群优化算法的寻优性能,适当的在随机搜索中引入确定性搜索可以提高算法的搜索效率。信赖域方法在一定条件下具有快速的局部收敛性和理想的总体收敛性,且具有稳定的数值性能。通过在粒子群优化算法中引入信赖域方法以引导粒子朝更优的方向搜索,不但能够保证局部收敛,加快收敛速率,还具有很高的确定性。同时,为了保持种群多样性,借鉴信赖域的思想和变异算子的优势,在粒子陷入局部极优的时候,实施基于信赖域技术的柯西变异,帮助粒子逃离局部最优,以提高算法的全局寻优性能。本文将基于信赖域的算法与粒子群优化算法结合起来以改善粒子群的搜索能力,提出了两类改进的混合粒子群优化算法,在保证有效的问题搜索空间的条件下,提高了搜索效率和精度。本文主要工作如下:(1)提出了一种基于信赖域的吸引排斥粒子群优化算法。该算法在ARPSO保持种群多样性的基础上,使用信赖域方法进行局部搜索,利用获得的潜在最优解来调整搜索方向,避免了盲目的重复搜索。相对于标准的粒子群算法及其他几种改进算法,实验表明,该算法在收敛精度和稳定性上取得了较好的效果,且需要更少的迭代次数。除此之外,本章还从理论上分析了新算法能够以更高的概率收敛到全局最优点。(2)基于社会阶级的思想和信赖域技术,提出了一种基于信赖域技术变异的随机重组分级粒子群优化算法。该算法根据现代社会阶级的思想将种群分为三个不同级别,较高的级别主要负责全局性勘探,期待发现最优解所在的区域,同时在中层阶级中引入基于信赖域技术的柯西变异,保证群体多样性避免陷入局部极优,导致“早熟”,丧失继续搜索的能力。最下层的粒子群接受上层粒子的领导,分群进行局部精细化搜索,加快收敛速率,提高收敛精度。相比于前面提出的改进算法,该算法不要求计算搜索方向,降低了计算的复杂度,并对目标函数没有解析性要求,实验结果表明,改进的粒子群优化算法明显优于标准粒子群算法及其相关改进。本文通过对粒子群优化算法原理的深入讨论与分析,引入确定性信赖域方法发现潜在的最优解方向,较好地避免粒子盲目重复的搜索以及借鉴社会阶级分工的思想,结合变异操作保证了整个种群的全局搜索性能和收敛能力。本文工作为基于混合搜索的粒子群优化算法的性能改进提供了新的思路。
[Abstract]:Particle swarm optimization (PSO) has been widely applied in scientific research and engineering practice because of its advantages of easy understanding and implementation, fast convergence speed, few adjustable parameters, low requirement for fitness function and better global search ability. However, like other stochastic optimization techniques, particle swarm optimization algorithm also has its own shortcomings, such as blindness in search direction, slow convergence in later stage, loss of population diversity and fall into local optimum. In order to improve the optimization performance of particle swarm optimization (PSO), a proper search in random search can improve the efficiency of the algorithm. The trust region method has fast local convergence and ideal overall convergence under certain conditions, and has stable numerical performance. By introducing trust region method into particle swarm optimization algorithm, we can guide particles to search in a better direction. It not only ensures local convergence, but also has high certainty rate. At the same time, in order to maintain the diversity of population, learn from the idea of trust region and the advantage of mutation operator, we implement the Cauchy mutation based on trust region technology when particles fall into local optimum, and help particles escape local optimum, so as to improve the global optimization performance of the algorithm. In this paper, the trust region algorithm and particle swarm optimization algorithm are combined to improve the search ability of particle swarm. Two improved hybrid particle swarm optimization algorithms are proposed. Under the condition of ensuring effective search space, the efficiency and accuracy of search are improved. The main work of this paper is as follows: (1) a kind of particle swarm optimization (PSO) algorithm based on trust region is proposed. Based on ARPSO maintaining population diversity, the algorithm uses local search based on trust region method, and adjusts search direction by using the potential optimal solution, avoiding blind repeated search. Compared with standard particle swarm optimization algorithm and several other improved algorithms, experiments show that the algorithm achieves better results in convergence accuracy and stability, and requires fewer iterations. In addition, this chapter also theoretically analyses that the new algorithm can converge to the global best advantage with higher probability. (2) based on the idea of social class and trust region technology, a random recombinant particle swarm optimization (PSO) algorithm based on trust region technology variation is proposed. The algorithm is based on modern social class thought of population can be divided into three different levels, the higher level is mainly responsible for the overall exploration, expecting to find the optimal solution region, while the middle class in the introduction of Cauchy mutation technology based on trust region, ensure diversity of the population to avoid falling into a local optimum, lead to "premature", the loss of the ability to search. The lower layer of particle group accepts the leadership of the upper layer particle, and divides the local fine search to speed up the convergence rate and improve the convergence precision. Compared with the improved algorithm proposed previously, the algorithm does not require the computation of search direction, reduces the computational complexity and does not require the resolution of the objective function. Experimental results show that the improved particle swarm optimization algorithm is superior to the standard particle swarm optimization algorithm and its related improvements. Based on the in-depth discussion and analysis of the principle of particle swarm optimization algorithm, we introduce deterministic trust region method to find the direction of potential optimal solution, can avoid blind duplicate search and particle reference social class division thought, combined with mutation operation to ensure global search ability and the convergence ability of the whole population. This work provides a new idea for the performance improvement of particle swarm optimization (PSO) based on mixed search.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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