静态环境下改进粒子群算法研究

【作者】 张倩；

【导师】 刘衍民；

【作者基本信息】 贵州大学 ， 数学， 2023， 硕士

【摘要】 群智能算法在解决高维优化问题时表现出强大的适应性,其中粒子群算法(Particle Swarm Optimization,PSO)因全局搜索能力强、原理简单等特点受到广泛关注。但该算法的缺点同样明显,例如易陷入局部收敛。因此,为解决这一困境,本文对静态环境下的PSO算法进行改进,其内容如下:(1)对单目标优化情境下的PSO算法进行改进。由于此情境下的算法局部搜索能力不足,因此通过标记因子对陷入收敛状态的解进行记录,随后改变种群结构,并结合学习策略以提升算法的局部寻优能力。通过数值检验,上述措施可提升算法的求解性能。(2)对多目标优化情境下的PSO算法进行改进。该算法在此情境下跳出局部收敛的能力不足,且求解结果严重依赖于粒子的先验知识,因此需要进行存档分化,随后增加更新学习机制以加强对最优区域的搜索。通过数值检验,上述策略可提升粒子的多样性和求解精度。(3)尽管存档分化可提升粒子的多样性,但算法结果却严重依赖于存档分化过程中采取的策略。因此在上一段基础上需要应用多重存档存放优质粒子,随后采用高斯扰动的思想提升算法的解集质量。通过数值检验,上述策略可提升粒子分布性和解集收敛性。(4)为探究消除存档和种群规模的限制,是否会对算法的求解结果产生影响。首先对粒子进行聚类择优,其次采用自适应策略对种群规模进行扩充或缩减,以此达到取消存档和种群规模限制的目的。通过数值检验,采用上述策略在达到取消存档和种群规模限制的同时还可保证粒子分布性和收敛性。更多还原

【Abstract】 Swarm intelligence algorithms show strong adaptability in solving high dimensional optimization problems,among which Particle Swarm Optimization(PSO)has been widely concerned because of its strong global search ability and simple principle.However,it has an obvious disadvantage that it is easy to fall into local convergence.Therefore,in order to solve this dilemma,the PSO in the static environment is improved in this paper,and its contents are as follows:(1)The PSO under the single objective optimization is improved.Due to the lack of local search ability of PSO in this situation,the solutions that fall into the convergence state are recorded through marker factors,and then the population structure is changed,combined with learning strategies to improve the local search ability of the algorithm.Through numerical experiment,the above measures can improve the performance of PSO.(2)The PSO under the multi-objective optimization is improved.In this case,the algorithm has insufficient ability to jump out of local convergence,and the solution results are heavily dependent on the prior knowledge of particles.Therefore,archival differentiation is needed,and then update learning mechanism is added to enhance the search for the optimal region.Through numerical experiment,the above strategy can improve the diversity of particles and the solution accuracy of the algorithm.(3)Although archival differentiation can improve the diversity of particles,the algorithm results are heavily dependent on the strategies adopted during archival differentiation.Therefore,on the basis of the above paragraph,it is necessary to apply multiple archives to store high-quality particles,and then adopt the idea of Gaussian perturbation to improve the quality of the solution set of the algorithm.Through numerical experiment,the above strategy can improve the particle distribution and convergence.(4)In order to explore whether the elimination of restrictions on archiving and population size will affect the solution results of the algorithm.Firstly,particles are selected by clustering.Secondly,the adaptive strategy is used to expand or reduce the population size,so as to eliminate the archiving and population size restriction.Through numerical experiment,the above strategies can ensure the distribution and convergence of particles while eliminating the limitation of archiving and population size.更多还原