基于混沌蚂蚁的群集协同求解算法及应用
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摘要
群集智能源于对社会性生物群集行为的研究,科学界的研究动机是分析生物群集通过个体之间的相互作用产生的涌现和自组织行为,工程应用领域的研究目的是构建由大量简单嵌入式设备构成的分布式自治系统,如无线自组织网络、机器人协作系统等。尽管群集智能在这两方面已经取得了大量的成果,但大部分研究集中在蚁群优化算法(Ant Colony Optimization,ACO)和粒子群算法(Particle Swarm Optimization,PSO)等随机型算法,且多关注这类算法的应用,而没有考虑群集内个体之间的信息协同交互方式以及研究尺度对算法求解效果的影响,也很少涉及群集智能的协同求解方法研究。
近年来,生物学家Cole对群居蚂蚁的研究中发现,蚂蚁个体的活动是混沌的,而整个蚁群则是一种周期性行为,并且学者Sole给出了蚂蚁个体行为的混沌映射表达式。蚂蚁群集智能体现在自发地分布式协调资源配置来协同完成任务的自组织行为,若从动力学的角度看,蚁群的自组织能力必然与蚂蚁个体的混沌行为存在着内在的联系,所以我们认为蚁群的周期性行为正是一个由混沌态到自组织态的转换过程。
因此,本论文从微观层内个体、微观层个体与宏观层群集之间的联系两个角度分析蚂蚁个体混沌行为与蚁群的自组织行为之间的关系,围绕如何构建蚂蚁群集协同求解算法进行研究,形成组合优化问题、高维函数优化问题、复杂分布式协同优化问题、动态分布式约束优化问题的协同求解方法,以深化和拓宽群集智能的研究。
本论文的主要研究工作如下：
(1)对当前相关研究工作进行了调查、分析与总结,指出需要进一步解决的问题。从混沌同步的角度,阐释了混沌蚂蚁群算法(Chaotic Ant Swarm,CAS)的协同机制；
(2)从微观层内个体之间信息交互方式的角度,构建了基于混沌蚂蚁群算法的组合优化问题协同求解算法。首先,提出了求解经典TSP的集中式算法(Chaotic Ant Swarm for the Traveling Salesman Problem,CAS-TSP),该算法在CAS的基础上引入连续空间到离散空间的映射、反向操作和交义操作,数值仿真实验表明该算法对标准测试问题库TSPLIB中实例是有效的；然后,提出了求解无线传感器网络分布式任务分配算法(Chaotic Ant Swarm for Decentralized Task Allocation,CAS-DTA),该算法的目标函数考虑了任务能耗和任务执行可靠性,任务分配的过程通过任务映射、通信路由分配和任务分配方案优化三个步骤获得,其中任务映射由蚂蚁的混沌行为产生,通信路由分配由蚂蚁的邻居选择方法确定,用A*算法实现,任务分配方案优化由蚁群的自组织能力实现；大量的仿真实验表明了CAS-DTA算法能有效地延长无线传感器网络生命期、节省能量消耗和均衡网络负载；
(3)从微观层内蚂蚁个体行为及其之间交互方式的角度,为减少协同个体之间交互的计算量和通信量,提出了扰动混沌蚂蚁群算法(Disturbance Chaotic Ant Swarm,DCAS)。由于混沌蚁群优化算法CAS求解高维优化问题存在计算复杂和搜索精度低的问题,DCAS算法通过建立新的蚂蚁最优位置更新方法、邻居选择形式和自适应扰动三个策略改进CAS算法,实现了对CAS算法的性能改善,并证明了DCAS算法的全局收敛性。通过两组测试函数,对DCAS算法的性能进行了高达1000维的大量仿真实验,测试结果表明DCAS算法对复杂的高维优化问题可行有效；
(4)从微观层个体相互作用与宏观层群集行为的联系角度,基于动态信息熵,提出了基于混沌蚂蚁的复杂分布式系统协同优化方法。在复杂系统理论指导下,分析复杂分布式系统中自主Agent的基本动力学特征,进而提出复杂分布式系统协同优化模型；在此基础上,借助混沌蚂蚁群算法的思想,建立基于混沌蚂蚁的复杂分布式系统协同优化算法(CAS based Collaborative Optimization,CAS-CO)。通过对复杂多Agent网络中基于位置的任务分配问题进行仿真实验,同时与已有算法的仿真结果比较,表明CAS-CO算法的可行性和有效性,说明了所提出模型的正确性和Agent的自主性在复杂分布式系统设计与构建中的重要性；
(5)从微观层个体行为与宏观层群集行为的决策关系角度,提出了一种群集自治的分布式协调算法(Decentralized Coordination Algorithm,DCA),能够有效协调群集个体并使它们的状态达到整体最优组态。DCA算法受单个蚂蚁的混沌行为和整个蚁群的自组织行为启发而设计,首先,将每个Agent看作一个非线性振子,表现单个蚂蚁的混沌行为；然后,借鉴蚁群的自组织行为建立自组织机制,并分析了DCA算法的收敛性；最后,采用群集节点的聚集、分散问题评估DCA算法的有效性,并与分布式梯度算法相比,仿真结果表明了DCA算法能使群集节点自治地达到最优组态。此外,采用DCA算法分布式协调机制,结合动态分布式约束优化问题,进一步提出了基于混沌蚂蚁的动态分布式约束优化问题协同求解算法(Chaotic Ant based Dynamic Distributed Constraint Optimization Problem,CA-DDCOP)。该算法首先根据单只蚂蚁的混沌行为,建立Agent的受控变量混沌选值策略,实现Exploration操作；然后模拟蚁群的自组织行为,构建Agent个体受其邻居和自组织能力的作用机制,实现Exploitation操作；最后基于玻尔兹曼分布建立群集宏观层对个体微观层的决策关系,实现Exploration与Exploitation操作协同求解。为评估CA-DDCOP算法性能,还将CA-DDCOP算法应用于多射频多信道(Multi-Radio Multi-Channel)无线Ad Hoc网络的信道分配。在信道分配中,网络节点需要根据它感知到的信道干扰情况,协调节点之间的信道分配组态,最大化其收益。相关的仿真实验表明了CA-DDCOP算法求解动态的信道分配问题是有效的。
Swarm intelligence (SI) is derived from the studies of the biological collective behavior, the scientific motivation for studying SI is the analysis of emergent and self-organizing swarming behaviors with distributed interactions among individuals, and the engineering objective for studying SI is to build a distributed autonomous system consisting of a large number of simple embedded equipments, such as wireless ad hoc networks, robot collaboration system. Although a lot of results have been gotten in these two areas, most of them are on the stochastic algorithms including ant colony optimization (ACO) and particle swarm optimization (PSO). In particular, more attentions are paid to apply the above two stochastic algorithms. In previous studies, the effects of both collaborative interactions between the individuals and research scales are concerned to these stochastic algorithms; furthermore, collaborative swarm algorithms are rarely involved.
In recent years, a biologist named Cole investigated the behaviors of social ants, and discovered that the single ant shows chaotic activity pattern, while the whole ant colony exhibits a periodic behavior. Moreover, a famous scholar Sole gave a chaotic mapping expression of individual ant's behavior. As well known, the intelligence of ant colony lies in self-organizing behavior that the ants can cooperate to finish tasks one by one with the spontaneous distributed coordination for resources assignment. From the viewpoint of dynamics, it is evident that the self-organization ability of ant colony must have inherent relations with the chaotic behavior of individual ant. As a result, we believe that the periodic behavior is a process of transforming chaos to self-organization.
Therefore, we analyze the relations between the chaotic behaviors of individuals and the self-organizing behavior of ant colony from the aspects of the two scales including individual micro-level, individual micro-level and collective macro-level. Then we focus on how to establish some collaborative swarm algorithms for the combinatorial optimization problems, the high-dimensional function optimization problems, the complex distributed collaborative optimization problems, and the dynamic distributed constraint optimization problems so as to deepen and broaden the studies of SI.
The main works of the present dissertation are as follows:
(1) At the beginning of our studies, we conduct a survey, analysis and summary on the current researches, and point out some problems to be further resolved in this dissertation. Moreover, we elaborate the collaborative mechanisms of chaotic ant swarm (CAS) from chaos synchronization;
(2) In this dissertation, we construct two collaborative swarm algorithms for the combinatorial optimization problems based on CAS from the perspective of the information interactions between the individuals. Firstly, we propose a centralized algorithm for the classical TSP (CAS-TSP). The CAS-TSP is developed by introducing a mapping from a continuous space to a discrete space, a reverse operator and a crossover operator into the CAS. Computer simulations demonstrate that the CAS-TSP is capable of generating optimal solution to some instances of TSPLIB. Secondly, we present a decentralized task allocation algorithm in wireless sensor networks based on chaotic ant swarm (CAS-DTA). The objective function of this algorithm is established according to the energy consumption and reliability of the entire task execution. The optimal solution can be achieved through task mapping, communication routing and task allocation selection by means of the framework of chaotic ant swarm. Task mapping is carried out with ant chaotic behaviors, communication routing is established with neighbor selection method and searched with A*algorithm, while task allocation selection is implemented with the self-organization capability of ant colony. Experimental results show the superiority of our algorithm in terms of both load balancing and lifetime of wireless sensor networks;
(3) In this dissertation, we present a disturbance chaotic ant swarm (DCAS) from the perspective of the individual ant's behavior and the interactions between individuals in order to reduce the amount of computation and communication. To resolve the problems of high computational complexity and low solution accuracy existing in CAS, DCAS is achieved by introducing three strategies, a new method of updating ant's best position, a neighbor selection method and a self-adaptive disturbance strategy, into CAS. The global convergence of DCAS algorithm is also proved. Extensive computational simulations and comparisons are carried out to validate the performance of DCAS on two sets of benchmark functions with up to1000dimensions. The results show clearly that DCAS is feasible as well as effective;
(4) In this dissertation, we propose a collaborative optimization method (CAS-CO) based on CAS and information entropy for complex distributed systems (CDS) from the perspective of the micro-level of the individual interactions and the macro-level of the collective behavior. The basic dynamic characteristics of CDS are analyzed under the guide of system complexity, and a model of collaborative optimization of CDS is formulated; on these bases, CAS-CO is established based on the ideas of CAS; To verify the validity of the proposed model and algorithm, a locality-based task allocation in complex networked multi-agent system is resolved by CAS-CO, and the comparison results of the proposed algorithm and the existing ones show that the CAS-CO algorithm is feasible and effective, and then illuminate that the proposed model is correct and the autonomy of an agent is of importance for the design and modeling of CDS;
(5) In this dissertation, we propose a decentralized coordination algorithm of autonomous swarm from the perspective of the decision-making relations between the micro-level of individuals and the macro-level of a global swarm, which can efficiently coordinate the autonomous swarm to the optimal solution. Our algorithm is inspired by the chaotic behavior of a single ant and the self-organizing behavior of the whole ant colony. To construct this algorithm, we firstly assume that each agent is a nonlinear oscillator presenting the chaotic behavior of a single ant. Then we establish a self-organization mechanism according to the self-organization behavior of the whole ant colony. Moreover, we analyze the convergence of the proposed algorithm. Finally we experimentally evaluate the performance of our algorithm with the clustering and dispersion operations of a swarm. Comparison results of the proposed algorithm and the gradient-type one are also presented to illustrate the effectiveness of the proposed scheme in approximately global optimization for swarms. In addition, we apply the distributed coordination mechanism of DCA, combine with the dynamic distributed constraint optimization problem, and further propose a chaotic ant based algorithm for dynamic distributed constraint optimization problem, named CA-DDCOP. To construct the CA-DDCOP algorithm, we firstly establish a value selecting strategy for the controlled variable of an agent based on chaotic behavior of a single ant to achieve the exploration operation; secondly, we develop a mechanism that an agent is subjected to its neighbors and self-organization ability according to self-organizing behavior of ant colony to achieve exploitation operation; Finally, we devise the decision-making relations between the individual micro-level and the collective macro-level based on the Boltzmann distribution so as to achieve the collaboration of two operations, exploration and exploitation. In order to investigate the performance of the CA-DDCOP algorithm, we apply the CA-DDCOP algorithm to multi-radio multi-channel channel allocation in ad hoc networks. The network nodes communicate with their neighbors, and coordinate their channel configuration according to their channel interference-aware so as to maximize their online rewards. Simulation results show that the CA-DDCOP algorithm can solve the dynamic channel allocation problem effectively.
近年来,生物学家Cole对群居蚂蚁的研究中发现,蚂蚁个体的活动是混沌的,而整个蚁群则是一种周期性行为,并且学者Sole给出了蚂蚁个体行为的混沌映射表达式。蚂蚁群集智能体现在自发地分布式协调资源配置来协同完成任务的自组织行为,若从动力学的角度看,蚁群的自组织能力必然与蚂蚁个体的混沌行为存在着内在的联系,所以我们认为蚁群的周期性行为正是一个由混沌态到自组织态的转换过程。
因此,本论文从微观层内个体、微观层个体与宏观层群集之间的联系两个角度分析蚂蚁个体混沌行为与蚁群的自组织行为之间的关系,围绕如何构建蚂蚁群集协同求解算法进行研究,形成组合优化问题、高维函数优化问题、复杂分布式协同优化问题、动态分布式约束优化问题的协同求解方法,以深化和拓宽群集智能的研究。
本论文的主要研究工作如下：
(1)对当前相关研究工作进行了调查、分析与总结,指出需要进一步解决的问题。从混沌同步的角度,阐释了混沌蚂蚁群算法(Chaotic Ant Swarm,CAS)的协同机制；
(2)从微观层内个体之间信息交互方式的角度,构建了基于混沌蚂蚁群算法的组合优化问题协同求解算法。首先,提出了求解经典TSP的集中式算法(Chaotic Ant Swarm for the Traveling Salesman Problem,CAS-TSP),该算法在CAS的基础上引入连续空间到离散空间的映射、反向操作和交义操作,数值仿真实验表明该算法对标准测试问题库TSPLIB中实例是有效的；然后,提出了求解无线传感器网络分布式任务分配算法(Chaotic Ant Swarm for Decentralized Task Allocation,CAS-DTA),该算法的目标函数考虑了任务能耗和任务执行可靠性,任务分配的过程通过任务映射、通信路由分配和任务分配方案优化三个步骤获得,其中任务映射由蚂蚁的混沌行为产生,通信路由分配由蚂蚁的邻居选择方法确定,用A*算法实现,任务分配方案优化由蚁群的自组织能力实现；大量的仿真实验表明了CAS-DTA算法能有效地延长无线传感器网络生命期、节省能量消耗和均衡网络负载；
(3)从微观层内蚂蚁个体行为及其之间交互方式的角度,为减少协同个体之间交互的计算量和通信量,提出了扰动混沌蚂蚁群算法(Disturbance Chaotic Ant Swarm,DCAS)。由于混沌蚁群优化算法CAS求解高维优化问题存在计算复杂和搜索精度低的问题,DCAS算法通过建立新的蚂蚁最优位置更新方法、邻居选择形式和自适应扰动三个策略改进CAS算法,实现了对CAS算法的性能改善,并证明了DCAS算法的全局收敛性。通过两组测试函数,对DCAS算法的性能进行了高达1000维的大量仿真实验,测试结果表明DCAS算法对复杂的高维优化问题可行有效；
(4)从微观层个体相互作用与宏观层群集行为的联系角度,基于动态信息熵,提出了基于混沌蚂蚁的复杂分布式系统协同优化方法。在复杂系统理论指导下,分析复杂分布式系统中自主Agent的基本动力学特征,进而提出复杂分布式系统协同优化模型；在此基础上,借助混沌蚂蚁群算法的思想,建立基于混沌蚂蚁的复杂分布式系统协同优化算法(CAS based Collaborative Optimization,CAS-CO)。通过对复杂多Agent网络中基于位置的任务分配问题进行仿真实验,同时与已有算法的仿真结果比较,表明CAS-CO算法的可行性和有效性,说明了所提出模型的正确性和Agent的自主性在复杂分布式系统设计与构建中的重要性；
(5)从微观层个体行为与宏观层群集行为的决策关系角度,提出了一种群集自治的分布式协调算法(Decentralized Coordination Algorithm,DCA),能够有效协调群集个体并使它们的状态达到整体最优组态。DCA算法受单个蚂蚁的混沌行为和整个蚁群的自组织行为启发而设计,首先,将每个Agent看作一个非线性振子,表现单个蚂蚁的混沌行为；然后,借鉴蚁群的自组织行为建立自组织机制,并分析了DCA算法的收敛性；最后,采用群集节点的聚集、分散问题评估DCA算法的有效性,并与分布式梯度算法相比,仿真结果表明了DCA算法能使群集节点自治地达到最优组态。此外,采用DCA算法分布式协调机制,结合动态分布式约束优化问题,进一步提出了基于混沌蚂蚁的动态分布式约束优化问题协同求解算法(Chaotic Ant based Dynamic Distributed Constraint Optimization Problem,CA-DDCOP)。该算法首先根据单只蚂蚁的混沌行为,建立Agent的受控变量混沌选值策略,实现Exploration操作；然后模拟蚁群的自组织行为,构建Agent个体受其邻居和自组织能力的作用机制,实现Exploitation操作；最后基于玻尔兹曼分布建立群集宏观层对个体微观层的决策关系,实现Exploration与Exploitation操作协同求解。为评估CA-DDCOP算法性能,还将CA-DDCOP算法应用于多射频多信道(Multi-Radio Multi-Channel)无线Ad Hoc网络的信道分配。在信道分配中,网络节点需要根据它感知到的信道干扰情况,协调节点之间的信道分配组态,最大化其收益。相关的仿真实验表明了CA-DDCOP算法求解动态的信道分配问题是有效的。
Swarm intelligence (SI) is derived from the studies of the biological collective behavior, the scientific motivation for studying SI is the analysis of emergent and self-organizing swarming behaviors with distributed interactions among individuals, and the engineering objective for studying SI is to build a distributed autonomous system consisting of a large number of simple embedded equipments, such as wireless ad hoc networks, robot collaboration system. Although a lot of results have been gotten in these two areas, most of them are on the stochastic algorithms including ant colony optimization (ACO) and particle swarm optimization (PSO). In particular, more attentions are paid to apply the above two stochastic algorithms. In previous studies, the effects of both collaborative interactions between the individuals and research scales are concerned to these stochastic algorithms; furthermore, collaborative swarm algorithms are rarely involved.
In recent years, a biologist named Cole investigated the behaviors of social ants, and discovered that the single ant shows chaotic activity pattern, while the whole ant colony exhibits a periodic behavior. Moreover, a famous scholar Sole gave a chaotic mapping expression of individual ant's behavior. As well known, the intelligence of ant colony lies in self-organizing behavior that the ants can cooperate to finish tasks one by one with the spontaneous distributed coordination for resources assignment. From the viewpoint of dynamics, it is evident that the self-organization ability of ant colony must have inherent relations with the chaotic behavior of individual ant. As a result, we believe that the periodic behavior is a process of transforming chaos to self-organization.
Therefore, we analyze the relations between the chaotic behaviors of individuals and the self-organizing behavior of ant colony from the aspects of the two scales including individual micro-level, individual micro-level and collective macro-level. Then we focus on how to establish some collaborative swarm algorithms for the combinatorial optimization problems, the high-dimensional function optimization problems, the complex distributed collaborative optimization problems, and the dynamic distributed constraint optimization problems so as to deepen and broaden the studies of SI.
The main works of the present dissertation are as follows:
(1) At the beginning of our studies, we conduct a survey, analysis and summary on the current researches, and point out some problems to be further resolved in this dissertation. Moreover, we elaborate the collaborative mechanisms of chaotic ant swarm (CAS) from chaos synchronization;
(2) In this dissertation, we construct two collaborative swarm algorithms for the combinatorial optimization problems based on CAS from the perspective of the information interactions between the individuals. Firstly, we propose a centralized algorithm for the classical TSP (CAS-TSP). The CAS-TSP is developed by introducing a mapping from a continuous space to a discrete space, a reverse operator and a crossover operator into the CAS. Computer simulations demonstrate that the CAS-TSP is capable of generating optimal solution to some instances of TSPLIB. Secondly, we present a decentralized task allocation algorithm in wireless sensor networks based on chaotic ant swarm (CAS-DTA). The objective function of this algorithm is established according to the energy consumption and reliability of the entire task execution. The optimal solution can be achieved through task mapping, communication routing and task allocation selection by means of the framework of chaotic ant swarm. Task mapping is carried out with ant chaotic behaviors, communication routing is established with neighbor selection method and searched with A*algorithm, while task allocation selection is implemented with the self-organization capability of ant colony. Experimental results show the superiority of our algorithm in terms of both load balancing and lifetime of wireless sensor networks;
(3) In this dissertation, we present a disturbance chaotic ant swarm (DCAS) from the perspective of the individual ant's behavior and the interactions between individuals in order to reduce the amount of computation and communication. To resolve the problems of high computational complexity and low solution accuracy existing in CAS, DCAS is achieved by introducing three strategies, a new method of updating ant's best position, a neighbor selection method and a self-adaptive disturbance strategy, into CAS. The global convergence of DCAS algorithm is also proved. Extensive computational simulations and comparisons are carried out to validate the performance of DCAS on two sets of benchmark functions with up to1000dimensions. The results show clearly that DCAS is feasible as well as effective;
(4) In this dissertation, we propose a collaborative optimization method (CAS-CO) based on CAS and information entropy for complex distributed systems (CDS) from the perspective of the micro-level of the individual interactions and the macro-level of the collective behavior. The basic dynamic characteristics of CDS are analyzed under the guide of system complexity, and a model of collaborative optimization of CDS is formulated; on these bases, CAS-CO is established based on the ideas of CAS; To verify the validity of the proposed model and algorithm, a locality-based task allocation in complex networked multi-agent system is resolved by CAS-CO, and the comparison results of the proposed algorithm and the existing ones show that the CAS-CO algorithm is feasible and effective, and then illuminate that the proposed model is correct and the autonomy of an agent is of importance for the design and modeling of CDS;
(5) In this dissertation, we propose a decentralized coordination algorithm of autonomous swarm from the perspective of the decision-making relations between the micro-level of individuals and the macro-level of a global swarm, which can efficiently coordinate the autonomous swarm to the optimal solution. Our algorithm is inspired by the chaotic behavior of a single ant and the self-organizing behavior of the whole ant colony. To construct this algorithm, we firstly assume that each agent is a nonlinear oscillator presenting the chaotic behavior of a single ant. Then we establish a self-organization mechanism according to the self-organization behavior of the whole ant colony. Moreover, we analyze the convergence of the proposed algorithm. Finally we experimentally evaluate the performance of our algorithm with the clustering and dispersion operations of a swarm. Comparison results of the proposed algorithm and the gradient-type one are also presented to illustrate the effectiveness of the proposed scheme in approximately global optimization for swarms. In addition, we apply the distributed coordination mechanism of DCA, combine with the dynamic distributed constraint optimization problem, and further propose a chaotic ant based algorithm for dynamic distributed constraint optimization problem, named CA-DDCOP. To construct the CA-DDCOP algorithm, we firstly establish a value selecting strategy for the controlled variable of an agent based on chaotic behavior of a single ant to achieve the exploration operation; secondly, we develop a mechanism that an agent is subjected to its neighbors and self-organization ability according to self-organizing behavior of ant colony to achieve exploitation operation; Finally, we devise the decision-making relations between the individual micro-level and the collective macro-level based on the Boltzmann distribution so as to achieve the collaboration of two operations, exploration and exploitation. In order to investigate the performance of the CA-DDCOP algorithm, we apply the CA-DDCOP algorithm to multi-radio multi-channel channel allocation in ad hoc networks. The network nodes communicate with their neighbors, and coordinate their channel configuration according to their channel interference-aware so as to maximize their online rewards. Simulation results show that the CA-DDCOP algorithm can solve the dynamic channel allocation problem effectively.
引文
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