蚁群优化算法及觅食行为模型研究
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摘要
蚁群优化是模拟蚁群在觅食过程中能获得巢穴到食物源间最短路径的机制而提出的启发式方法，其一经产生就成为求解复杂优化问题的重要方法。当前对蚁群优化领域的研究主要包括两个方向：一种是基于解空间概率函数的优化算法，算法通过确定状态转移概率、信息素更新方式对优化问题进行求解；一种是基于主体蚂蚁的基本行为规则而确定的演化模型，模型通过基于规则的行为演化仿真揭示蚁群觅食、聚类等行为的特点、结果及复杂性成因。本论文对蚁群优化的两个方向分别进行了深入研究，首先，基于复杂适应系统理论建立基于Agent的蚁群觅食演化模型，之后，对基于解空间概率函数的蚁群优化算法进行了分析和改进，最后，将本文所得模型和算法用于实际工程问题中，仿真结果验证了模型和算法的有效性和实用性。
主要研究内容包括以下几个方面：
（1）根据蚁群觅食行为的原理，利用复杂适应系统理论建立了基于Agent的蚁群觅食行为演化模型，并对模型及模型中几个重要参数进行仿真分析。在此基础上，提出基于参数自适应和加入新规则的蚁群觅食行为演化模型，模型通过新规则和新参数的加入，在寻找食物源的仿真中获得了更好的效果；
（2）针对基本蚁群算法容易出现早熟和停滞现象的缺点，提出了一种侧重数据处理和基于匀称度动态城市选择及信息素更新的改进算法，并证明了算法的收敛性，通过实验验证了算法在防止过早停滞和加速收敛上的优势；
（3）针对蚁群算法求解连续域优化问题的不足，在蚁群算法创始人Dorigo提出的基于实数优化的蚁群算法基础上，通过对算法参数的含义及算法收敛性的研究，提出了基于均匀参数选择和解的权值改进的扩展蚁群算法。仿真试验表明了该方法在求解连续空间优化问题的可行性和有效性；
（4）针对扩展蚁群算法的不足提出了三种融合算法，以提高算法的求解效率：提出了一种求解连续空间优化问题的量子扩展蚁群算法，算法使用量子比特的概率幅编码种群个体，通过量子非门实现变异；提出了一种基于云模型的遗传扩展蚁群算法，利用遗传算法获得扩展蚁群算法的初始解，同时，利用云模型理论自适应的调整扩展蚁群算法中的两个重要参数；提出了一种鱼群扩展蚁群算法，利用鱼群算法的追尾和聚群行为获得扩展蚁群算法的初始解，在扩展蚁群算法每次迭代中加入鱼群随机觅食行为。通过对多个多维连续函数的仿真实验，验证了三种改进算法在处理连续函数寻优问题上的优势；
（5）针对模糊神经控制器模糊规则以及控制器参数较难确定的问题，提出了两类基于扩展量子蚁群算法的模糊神经控制器。一类是利用量子扩展蚁群算法优化参数的正规化模糊神经控制器，在此基础上，通过对变论域伸缩因子和隶属度函数进行设计获得变论域模糊神经控制器。通过对两类控制器建立不同的输入变量和模糊规则对单级倒立摆系统分别进行仿真实验，在与其它控制器的对比中验证所设计的控制器具有更好的控制性能。
（6）根据蚁群觅食行为过程和机器人路径规划的相似性，将改进蚁群觅食行为模型和改进离散域蚁群算法用于复杂动静态环境下的机器人路径规划求解，确定了蚁群觅食模型和蚁群算法的适应性和有效性。
The ant colony optimization (ACO) is a heuristic method which is proposed bysimulating the mechanism that the ant colony can find out the shortest path betweenthe nest to a food source. The algorithm is being the important method to solve thecomplex optimization problem as soon as being proposed. Nowadays, researches onACO mainly include two fields: one is ACO based on probability function insolution space, which solves optimization problem by the determination of statetransition probability and regeneration pattern of pheromone; the other is the modelbased on basic ant’s behavior rule, which reveals the characteristics, results andcomplexity causes of the ant colony’ behavior, such as the foraging and clusteringetc, through the behavior evolution based on the rule. In this thesis, the two researchfields of ACO are deeply studied respectively. Firstly, by the use of the complexadaptive systems theory, the ant colony foraging behavior model based on Agent isestablished. Next, the analysis and improvement of ACO based on probabilityfunction in solution space is studied. Finally, the model and the algorithms are usedin actual engineering problem, and the simulation results verify the effective and th epracticality of the methods.
Main research contents are as follows:
（1）According to the principle of the ant foraging behavior, an ant colonyforaging behavior model based on Agent is proposed by the use of the complexadaptive systems theory. Through simulating and analyzing several importantparameters in the model, the models based on adaptive parameters and added newbehavior rules are proposed respectively. And with the addition of the new behaviorrules and the new parameters, the better effective is obtained in the simulation offinding food source;
（2）To overcome the premature and stagnation phenomenon in basic ACOalgorithm, this paper proposes an improved ACO algorithm which emphasizes dataprocessing and bases on symmetry degree city selection and pheromoneregeneration, and proves the convergence of this algorithm. Finally, experimentalresults show that this algorithm can overcome the defects of premature andstagnation, and accelerate convergence;
（3）Due to the lack of ACO in solving optimization problem in continuespace, on this basis of extended ACO proposed by M. Dorigo, who is founder ofACO algorithm, this paper proposes an extended ACO based on uniform parameterselection and weighted improvement of solution by studying implication ofalgorithm parameter and convergence of extended ACO algorithm. Simulation experiments show that this algorithm has feasibility and efficiency in solvingoptimization problem in continue space;
（4）Aiming to the shortcomings of the extended ACO, this paper proposesthree hybrid algorithms of ACO. Firstly, an improved quantum extended ACO isproposed to solve continue optimization problem. This algorithm codes individualby using probability amplitude of quantum bit and fulfills mutation by quantum notgate. Secondly, this paper proposed a genetic extended ACO based on cloudy model.This algorithm obtains initial solution of extended ACO by GA and uses the cloudymodel to adjust the two parameters in extended ACO adaptively. Thirdly, this paperproposes an extended ACO based artificial fish swarm algorithm. This algorithmobtains initial solution of extended ACO by artificial fish-swarm algorithm andadds random foraging behavior of fish swarm in each iteration. Many multi-dimensions continue function simulation experiments show the advantages of thethree extended algorithms to solve optimization problem in continue space;
（5）As fuzzy rules and control parameters in fuzzy neural controller aredifficult to acquired, this paper puts forward two fuzzy neural network controllersbased on extended quantum ACO. One is the normal fuzzy neural networkcontroller of which the parameter is optimized by extended quantum ACO. On thebasis of the controller, through designing the variable universe contractionexpansion factor and membership function, the variable universe fuzzy neuralcontroller is proposed. Finally, using these two controller to the single levelinverted pendulum system respectively, and compare with other controllers,simulation results show that this controller has better control performance;
（6）According to the similarity between the process of ant colony foragingbehavior and the robot path planning, the improved ant colony foraging behaviormodel and modified discrete domain ant colony algorithm are used to the robot pathplanning in the static and dynamic complex environment, the experiment resultsverify the adaptability and the effectiveness of the methods.
主要研究内容包括以下几个方面：
（1）根据蚁群觅食行为的原理，利用复杂适应系统理论建立了基于Agent的蚁群觅食行为演化模型，并对模型及模型中几个重要参数进行仿真分析。在此基础上，提出基于参数自适应和加入新规则的蚁群觅食行为演化模型，模型通过新规则和新参数的加入，在寻找食物源的仿真中获得了更好的效果；
（2）针对基本蚁群算法容易出现早熟和停滞现象的缺点，提出了一种侧重数据处理和基于匀称度动态城市选择及信息素更新的改进算法，并证明了算法的收敛性，通过实验验证了算法在防止过早停滞和加速收敛上的优势；
（3）针对蚁群算法求解连续域优化问题的不足，在蚁群算法创始人Dorigo提出的基于实数优化的蚁群算法基础上，通过对算法参数的含义及算法收敛性的研究，提出了基于均匀参数选择和解的权值改进的扩展蚁群算法。仿真试验表明了该方法在求解连续空间优化问题的可行性和有效性；
（4）针对扩展蚁群算法的不足提出了三种融合算法，以提高算法的求解效率：提出了一种求解连续空间优化问题的量子扩展蚁群算法，算法使用量子比特的概率幅编码种群个体，通过量子非门实现变异；提出了一种基于云模型的遗传扩展蚁群算法，利用遗传算法获得扩展蚁群算法的初始解，同时，利用云模型理论自适应的调整扩展蚁群算法中的两个重要参数；提出了一种鱼群扩展蚁群算法，利用鱼群算法的追尾和聚群行为获得扩展蚁群算法的初始解，在扩展蚁群算法每次迭代中加入鱼群随机觅食行为。通过对多个多维连续函数的仿真实验，验证了三种改进算法在处理连续函数寻优问题上的优势；
（5）针对模糊神经控制器模糊规则以及控制器参数较难确定的问题，提出了两类基于扩展量子蚁群算法的模糊神经控制器。一类是利用量子扩展蚁群算法优化参数的正规化模糊神经控制器，在此基础上，通过对变论域伸缩因子和隶属度函数进行设计获得变论域模糊神经控制器。通过对两类控制器建立不同的输入变量和模糊规则对单级倒立摆系统分别进行仿真实验，在与其它控制器的对比中验证所设计的控制器具有更好的控制性能。
（6）根据蚁群觅食行为过程和机器人路径规划的相似性，将改进蚁群觅食行为模型和改进离散域蚁群算法用于复杂动静态环境下的机器人路径规划求解，确定了蚁群觅食模型和蚁群算法的适应性和有效性。
The ant colony optimization (ACO) is a heuristic method which is proposed bysimulating the mechanism that the ant colony can find out the shortest path betweenthe nest to a food source. The algorithm is being the important method to solve thecomplex optimization problem as soon as being proposed. Nowadays, researches onACO mainly include two fields: one is ACO based on probability function insolution space, which solves optimization problem by the determination of statetransition probability and regeneration pattern of pheromone; the other is the modelbased on basic ant’s behavior rule, which reveals the characteristics, results andcomplexity causes of the ant colony’ behavior, such as the foraging and clusteringetc, through the behavior evolution based on the rule. In this thesis, the two researchfields of ACO are deeply studied respectively. Firstly, by the use of the complexadaptive systems theory, the ant colony foraging behavior model based on Agent isestablished. Next, the analysis and improvement of ACO based on probabilityfunction in solution space is studied. Finally, the model and the algorithms are usedin actual engineering problem, and the simulation results verify the effective and th epracticality of the methods.
Main research contents are as follows:
（1）According to the principle of the ant foraging behavior, an ant colonyforaging behavior model based on Agent is proposed by the use of the complexadaptive systems theory. Through simulating and analyzing several importantparameters in the model, the models based on adaptive parameters and added newbehavior rules are proposed respectively. And with the addition of the new behaviorrules and the new parameters, the better effective is obtained in the simulation offinding food source;
（2）To overcome the premature and stagnation phenomenon in basic ACOalgorithm, this paper proposes an improved ACO algorithm which emphasizes dataprocessing and bases on symmetry degree city selection and pheromoneregeneration, and proves the convergence of this algorithm. Finally, experimentalresults show that this algorithm can overcome the defects of premature andstagnation, and accelerate convergence;
（3）Due to the lack of ACO in solving optimization problem in continuespace, on this basis of extended ACO proposed by M. Dorigo, who is founder ofACO algorithm, this paper proposes an extended ACO based on uniform parameterselection and weighted improvement of solution by studying implication ofalgorithm parameter and convergence of extended ACO algorithm. Simulation experiments show that this algorithm has feasibility and efficiency in solvingoptimization problem in continue space;
（4）Aiming to the shortcomings of the extended ACO, this paper proposesthree hybrid algorithms of ACO. Firstly, an improved quantum extended ACO isproposed to solve continue optimization problem. This algorithm codes individualby using probability amplitude of quantum bit and fulfills mutation by quantum notgate. Secondly, this paper proposed a genetic extended ACO based on cloudy model.This algorithm obtains initial solution of extended ACO by GA and uses the cloudymodel to adjust the two parameters in extended ACO adaptively. Thirdly, this paperproposes an extended ACO based artificial fish swarm algorithm. This algorithmobtains initial solution of extended ACO by artificial fish-swarm algorithm andadds random foraging behavior of fish swarm in each iteration. Many multi-dimensions continue function simulation experiments show the advantages of thethree extended algorithms to solve optimization problem in continue space;
（5）As fuzzy rules and control parameters in fuzzy neural controller aredifficult to acquired, this paper puts forward two fuzzy neural network controllersbased on extended quantum ACO. One is the normal fuzzy neural networkcontroller of which the parameter is optimized by extended quantum ACO. On thebasis of the controller, through designing the variable universe contractionexpansion factor and membership function, the variable universe fuzzy neuralcontroller is proposed. Finally, using these two controller to the single levelinverted pendulum system respectively, and compare with other controllers,simulation results show that this controller has better control performance;
（6）According to the similarity between the process of ant colony foragingbehavior and the robot path planning, the improved ant colony foraging behaviormodel and modified discrete domain ant colony algorithm are used to the robot pathplanning in the static and dynamic complex environment, the experiment resultsverify the adaptability and the effectiveness of the methods.
引文
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