群智能计算的广义统计场论及其应用

Swarm Intelligence (SI) is presently one of the most important research topics in both natural computation and complex system. For the main purpose of this project non-equilibrium Statistical Field Theory is generalized to the dynamic system of swarm intelligence in n-dimensional space by using interdisciplinary approaches. In pursuit of this goal, firstly, need to be defined several terms including ‘Swarm-Entropy Barrier’ and ‘Topological Potential’, which borrowed from the concepts of Evolutionary Physical, in order to study the statistical characteristics and the phases transformation of swarm behavior in swarm intelligent dynamical system, then we derive a new global convergence criteria of qualitative and quantitative of systems based on new terminologies in Field Theory. Secondly, for a specific swarm intelligent dynamics, eg. Particle Swarm Optimization or other methods, the formation mechanism, maintenance, evolution, and steady-state nature of coherent structures of the specific must be investigated under the different sensing surroundings, then further explorations for the network topology, controllability and stability and complexity of swarm behavior evolution of the systems and the relationship among them by integrating topological potential into accretive graph methods, it can be obtained the controllable parameter setting strategies for the global stable coherent structures of the swarm dynamics. Thirdly, with the studies of the self-organization and adaptive synchronization problems of swarm intelligent systems under delay conditions, it is obtained the parameter adjustment method, robust coordination control and consistency synchronization strategy which have meanings of evolutionary physics. And finally, we expect to primarily propose a novel adaptive algorithm that has globally sensing ability of the objective scene, as well as the generalized Statistical Field Theory for swarm intelligence can be established formally. At the same time the development of a swarm engineering simulation test platform would be bound to support the improvement of the overall performances of the swarm intelligent system and practical engineering applications of the swarm robotics experimentally and theoretically.

群智能是目前自然计算和复杂系统领域最重要的研究课题之一。将非平衡统计场理论推广到n-维空间的群智能动力系统，通过定义群动态系统的"群熵势垒"等演化物理量，研究统计场论中群智能动力系统的群行为统计特征和相变规律，导出基于群温度和群熵势垒的全局收敛性的定性和定量判别准则；研究不同感知环境下具体群智能系统的相干结构的形成机理、维持、演化及稳态性质；采用拓扑势和增长图方法探讨群动力系统网络拓扑与系统可控性、稳定性、群行为复杂性间的关系，得到群系统全局稳定相干结构的可控性条件与参数设置策略；研究群系统在不同延迟条件下的自组织和自适应同步问题，得出具有演化物理意义的参数调整方法、鲁棒的协调控制与一致性同步策略，提出具有目标场景全局感知能力的新型自适应性算法，形成系统的群智能计算的广义统计场理论论证，并开发群工程仿真测试平台，为改善群系统的综合性能和群智能机器人系统的实际工程应用提供实验和理论支撑。

(1)研究了群智能动力系统中群行为的统计特征和相变规律及其与群熵势垒的关系，针对具体群智能方法与系统(如ACO/PSO/GSO/FA等)的构造与群温度或群熵势垒描述的个体运动的随机微分方程，反映个体浓度瞬时涨落的概率密度函数(pdf)及群行为函数，研究不同感知环境(有限、全局、各向同性、各向异性、随机干扰、延迟等)下群智能系统中的相干结构的形成机理、维持、演化及稳态性质，以及相干结构与群行为的关系等，提出一种填充函数的全局优化、结合社交关系的复杂网络方法应用于图象标签推荐中。.(2)研究了群智能动力系统处于远离平衡的状态时，有限状态空间内的个体(particle/agent)通过局部感知或间接通信(stigmerg)相互协同，自发地产生时空有序的、相对稳定的相干结构，形成广义的统计场。从群居性生物的群体行为中群内个体间接通信stigmergy过程开始，为了形式化地建立群智能计算和统计场论间的推理。通过定义“群温度”和“个体浓度”、“群活性”、“群熵势垒”等演化物理量的场论意义，分析群智能动态系统中全局峰和局部峰与群熵势垒的关系。.(3)采用拓扑势为加权边表示网络节点的重要性，探讨群动力系统网络拓扑的增长图与系统可控性、稳定性、自组织复杂性间的关系，通过构造Lyapunov泛函和Barbalat引理进行稳定性分析，得到群系统全局稳定相干结构的可控性条件与参数设置策略；研究群行为的相变特征、动态网络中耦合振子的自组织和自适应同步方式，采用抑制耦合和自我调整策略，证明动态网络中不同延迟条件下的自组织和自适应同步控制方法和精度范围。.(4)还研究了VM映射中功耗感知的自适应PSO、基于信赖域方向引导搜索的调节种群多样性的粒子群算法、基于种群的梯度搜索策略的人工蜂群算法、变尺度混沌光强吸收系数调整策略的混沌萤火虫优化算法、智能自适应策略在不同尺度下提取遥感影像不同区域的边缘特征生成感知哈希序列等。