几类优化问题的人工蜂群算法

发布时间：2018-03-27 15:02

本文选题：人工蜂群算法　切入点：群智能算法　出处：《西安电子科技大学》2016年博士论文

【摘要】：优化问题无处不有,而且各个领域提出的优化问题越来越复杂,许多传统的优化算法在一些复杂的优化问题面前变得无能为力.因此,人们不断寻找新的求解方法.仿生智能优化算法的出现,使得这些复杂优化问题的求解变为现实.由于该方法一般不需要目标函数和约束条件的任何先验信息,能较好适应复杂优化问题的求解,具有并行计算的特点,同时具有很好的鲁棒性,仿生智能优化算法一出现就引起了广大科研人员的关注,被应用于旅行商问题、神经网络训练、图像处理等问题.2005年提出的人工蜂群算法就是一种仿生智能优化算法,已成功应用于众多研究领域.但人工蜂群算法与以往的智能优化算法一样,也存在种群探索能力与开发能力之间不平衡的问题,算法的探索能力强大,但开发能力不足,易于陷入局部最优,收敛速度慢等,且其数学理论基础也十分薄弱.本文针对人工蜂群算法的缺点,提出了几种改进的人工蜂群算法,成功应用于函数优化问题,约束函数优化问题和非负线性最小二乘问题.同时通过引入随机过程中的鞅理论证明了人工蜂群算法的几乎处处必然强收敛性.本文的主要研究工作如下：1、证明了人工蜂群算法的收敛性.已有的人工蜂群算法收敛性分析是基于算法的遍历性分析,在概率收敛意义下考虑的.这种收敛性分析不确保算法在有限步内收敛到问题的全局最优解.本文尝试运用鞅论研究人工蜂群算法的几乎必然强收敛性,证明了人工蜂群算法确保能以概率1在有限步内达到全局最优解.这一结论为拓宽人工蜂群算法的应用范围奠定理论基础,并为人工蜂群算法的改进及收敛性研究提供了新的理论工具.2、提出了一种全局优化问题的混合人工蜂群算法.该算法通过引入正交初始化方法,使初始种群分布更加均匀,提高了算法的搜索效率,同时对原始算法雇佣蜂和跟随蜂的搜索方程添加随机扰动项,扩大了算法的搜素范围,利用benchmark函数测试所提算法的有效性,实验结果、收敛曲线图和箱型图表明算法能快速收敛到全局最优解.3、提出了一种求解函数优化问题的改进人工蜂群算法.该算法受差分进化算法的启发,对雇佣蜂和跟随蜂提出了两种新的搜索方程,利用p概率控制两个方程的使用,同时引入正交初始化方法,利用benchmark函数测试改进人工蜂群算法的性能,实验结果表明,所提算法比一些改进人工蜂群算法和其他智能优化算法更有效.4、提出了一种求解非负最小二乘问题的人工蜂群算法.该算法受粒子群算法和差分进化算法的启发,提出两种改进的搜索方程,在算法执行过程中不在区分雇佣蜂和跟随蜂的区别,将其统一为一种蜜蜂,利用p概率控制两个搜索方程的使用,通过测试函数确定参数p值,同时引入正交初始化,利用benchmark测试函数和非负最小二乘问题的实例测试,表明所提出的算法比其他改进算法和其他智能优化算法收敛速度更快,解的精度更高.5、提出了一种全局优化问题的混沌人工蜂群算法,并将该算法应用于非负线性最小二乘问题.为了克服人工蜂群算法的不足,算法中使用反学习初始化作为种群初始化方法.为了进一步改进算法的性能,均衡算法的探索能力和开发能力,为新算法设计了新的搜索机制.另外,在算法中加入混沌局部搜索机制,使得算法在最优解周围进行局部搜索.利用benchmark测试函数和非负最小二乘问题的实例测试,表明所提出的算法比其他改进算法和其他智能优化算法收敛速度更快,解的精度更高.6、针对约束函数优化问题,提出了一种算法投资组合的人工蜂群算法.该算法基于自适应约束处理进化策略和Deb选择策略下的人工蜂群算法,原有的处理约束函数优化问题的方法大部分是把算法的运行时间全部投入到一种算法或者是约束技术上去,该算法投资组合把算法的运行时间分配到不同的算法和约束处理技术上,避免了算法运行的风险,同时在算法中设计一个迁移阶段,用来反应算法之间的信息交流与共享,benchmark函数实验结果表明该算法比其他算法在求解约束优化问题时拥有更高的成功率,更有效.
[Abstract]:Optimization problems exist everywhere, and all areas of the proposed optimization problems become more and more complex, many traditional optimization algorithms become incapable of action in the face of complex optimization problems. Therefore, people are constantly looking for a new solution. The bionic intelligent optimization algorithm, which solve the complex optimization problem into reality. Because any prior the method generally does not require the objective function and constraint conditions, can better adapt to solve complex optimization problems, with the characteristics of parallel computing, and has good robustness, bionic intelligent optimization algorithm has attracted the attention of many researchers, is applied to the traveling salesman problem, neural network, artificial bee colony the algorithm of image processing problems such as.2005 put forward is a kind of bionic intelligent optimization algorithm, has been successfully applied in many research fields. But the artificial bee colony algorithm The intelligent optimization algorithm, also exist between population exploration ability and development ability imbalance, explore algorithm ability strong, but development ability is insufficient, easy to fall into local optimum, the slow speed of convergence, and the mathematical theory foundation is also very weak. Aiming at the disadvantages of artificial bee colony algorithm, artificial bee colony algorithm is put forward several improved and successfully applied to the problem of function optimization, constrained optimization problem and non negative linear least squares problem. At the same time that the artificial bee colony algorithm almost sure convergence of everywhere through the martingale theory into the stochastic process. The main research work of this paper are as follows: 1. The convergence of the artificial bee colony algorithm analysis. Artificial bee colony algorithm convergence analysis existing ergodic algorithm based on consideration in the sense of probabilistic convergence. Convergence analysis of this algorithm does not ensure in Co. Step in the convergence to the global optimal solution of the problem. This paper attempts to use the almost sure convergence of martingale theory of artificial bee colony algorithm, artificial bee colony algorithm to ensure that with probability 1 in finite steps to reach the global optimal solution. This conclusion lays the theoretical foundation for broaden the scope of application of artificial bee colony algorithm, and provides the theory of new tools for.2 modified artificial bee colony algorithm and convergence analysis, this paper presents a global optimization problem of hybrid artificial bee colony algorithm. The algorithm by introducing the orthogonal initialization method, the initial population distribution is more uniform, improve the search efficiency of the algorithm, the original algorithm employed bees and bee follow search add random equation disturbance, expand the scope of search algorithm, the proposed algorithm is effective, using benchmark function test results, convergence curves and box plots show that the algorithm can fast charge Convergence to the global optimal solution of.3, puts forward a solving function optimization problem improved artificial bee colony algorithm. The algorithm by differential evolutionary algorithm inspired, the employed bees and the following bee put forward two new search using P probability equation, using two equations of control, while the introduction of orthogonal initialization method, performance improved artificial bee colony algorithm using benchmark function test, the experimental results show that the proposed algorithm is better than the improved artificial bee colony algorithm and other intelligent optimization algorithm is more effective in.4, the paper puts forward a new method of non negative least squares problem. The algorithm of artificial bee colony algorithm by particle swarm algorithm and heuristic algorithm, puts forward two kinds of improved search equation in the process does not distinguish between the employed bees and wasps will follow the implementation of the algorithm, the uniform as a bee, using P probability using two search control equation, through the test function The parameter p value, while the introduction of orthogonal initialization, using benchmark test function and non negative least squares problem instance test show that the proposed algorithm is faster than the other algorithm and other intelligent optimization algorithm convergence speed, the precision is higher.5, this paper proposes an optimization problem of the chaotic artificial bee colony algorithm, and the algorithm is applied to non negative linear least squares problem. In order to overcome the shortcomings of the artificial bee colony algorithm, using inverse learning as the method of initialization initialization algorithm. In order to further improve the performance of the algorithm, exploration ability and exploitation ability equalization algorithm, the design of the new search mechanism for the new algorithm. In addition, with chaotic local search mechanism in the algorithm in the algorithm the optimal solution around the local search. By using the benchmark test function and non negative least squares problem instances show that the proposed test The algorithm is faster than the other algorithm and other intelligent optimization algorithm convergence speed, the precision is higher for.6, a constrained optimization problem, artificial bee colony algorithm is put forward an algorithm of portfolio. The algorithm of adaptive constraint handling artificial bee colony algorithm evolutionary strategy and Deb selection strategy based on the method of constrained function optimization problems the original is the most of the running time of the algorithm into an algorithm or constraint up, the algorithm of portfolio allocation algorithm to the running time of algorithm and constraint handling technique on different, to avoid the risk of running the algorithm, while the design of a transfer stage in the algorithm, for the reaction between algorithm the information exchange and sharing, benchmark function experimental results show that the algorithm is better than other algorithms in solving constrained optimization problems with higher success rate, more Effect.

【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP18

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