【作者】 王艳；

【导师】 王秋萍；

【作者基本信息】 西安理工大学 ， 数学， 2018， 硕士

【摘要】 群智能优化算法是模拟生物群体智能行为设计的随机优化算法,具有良好的搜索能力和寻优能力,易于实现,实用性强,参数少,流程简单。然而,许多非连续的组合优化问题亟待解决,迫切需要对连续性萤火虫算法进行离散化改进研究。本文主要工作如下:1.基于惯性权重对数递减的萤火虫算法针对萤火虫算法收敛速度慢的不足,提出了一种基于惯性权重对数递减的萤火虫算法。首先,实验说明惯性权重对萤火虫算法对种群多样性的影响。然后,引入对数调整因子,不同的对数调整因子确保算法搜索的成功率。最后,选取四种典型函数分别进行给定迭代次数和给定精度的仿真测试。实验结果表明,改进的算法在收敛速度和收敛精度方面有明显的改进。2.基于改进萤火虫算法求解旅行商问题鉴于TSP问题是古老的组合优化难题,而萤火虫算法在求解函数优化问题中表现出优良的性能,因此,利用改进的萤火虫算法求解TSP问题。首先,在分析了旅行商问题的特点后,采用整数编码的方式来表示萤火虫的位置。然后,在标准萤火虫算法的位置更新过程中引入了对数递减的惯性权重来影响萤火虫的迭代过程,同时结合了遗传算法中的选择,交叉,变异以及进化逆转操作来提高每一次迭代中种群多样性及种群搜索能力,并将改进的算法解决TSP问题。最后,通过MATLAB仿真实验表明改进的算法在求解TSP问题时具有更好收敛速度和优化效果。3.改进的萤火虫算法在k-means聚类中的应用为了克服萤火虫算法容易陷入局部最优解的缺点,提出改进的萤火虫算法。通过引入随机权重和布谷鸟算法中的Levy飞行策略增强种群的多样性,也平衡了算法的全局搜索能力和局部搜索能力。将改进的算法应用在k-means聚类中,通过UCI标准数据库进行仿真实验,结果表明,改进的算法能有效提高算法的收敛精度,改善萤火虫算法的寻优能力。同时改进的FA在一定程度上解决了k-means聚类算法对初始值敏感且受异常数据影响的问题,验证了改进算法的可行性。更多还原

【Abstract】 Swarm intelligence optimization algorithms belong to stochastic optimization algorithm by simulating the behavior of biological swarm intelligence,which have good search capabilities optimization abilities,and easy to implement,which are flexible and practical,less parameters and simple process.However,there are many discrete combination optimization problems that need to be solved in practical application,so it is urgent to improve the traditional FA.The main work of this article is as follows:1.Firefly algorithm based on the inertia weight logarithmic decreasingIn the light of the problems of slow convergence rate and falling into the local optimization easily for the firefly algorithm,the algorithm which based on the inertia weight logarithmic decreasing is proposed.Firstly,experiment shows the influence of inertia weight on population diversity of firefly algorithm,and then the logarithmic adjustment factor is introduced.Changes of logarithmic adjustment factor ensure the success rate.Finally,the simulation experiments for four kinds of typical function in the given number of iterations and precision.The test results show that the strategy can improve the algorithm’s global convergence and convergence speed easily.2.Solving Traveling Salesman Problem Based on Improved Firefly AlgorithmIn view of traveling salesman problem(TSP)is an oldest combinatorial optimization problem,Firefly Algorithm(FA)shows great performance to complicated function optimization.Hence,in this paper,we used FA to solve TSP.Firstly,after the characteristics of TSP is analyzed,then the method of integer encoding is adopted to set the position of fireflies.Then,the logarithmic adjustment factor is introduced on the standard of firefly algorithm.Meanwhile,we combine with crossover,mutation and reverse operation in genetic algorithm(GA)to improve the population for each iteration of the population diversity and search ability,and it is applied to solve TSP.Finally,the numerical experiments shows that the proposed algorithm has faster convergence speed and optimization effectively.3.An Improved Firefly Algorithm and Its Application in Solving k-means clustering algorithmFor the problems of easily relapsing into local optimum in Firefly Algorithm(FA),an improved Firefly Algorithm is proposed.By introducing random weights and Levy flight strategy in cuckoo algorithm,we can enhance the diversity of population,so that both the global and local search ability of the algorithm balanced.The improved algorithm is used for k-means algorithm.We conducted experiments test on several groups of UCI data,the results show that the proposed algorithm has a higher accuracy and a better optimization ability.At the same time,the improved firefly algorithm solves the problem that k-means clustering algorithm is sensitive to initial values and is affected by abnormal data to some extent,which proves the feasibility of the improved algorithm.更多还原