一种面向多Agent交互的博弈Nash均衡求解方法

现有的图型博弈Nash均衡求解方法基本是在离散化剖面空间中搜索求解，最终只能得到近似Nash均衡。针对现有求解方法存在的不足，把求解图型博弈的Nash均衡看作是连续策略空间中的函数优化问题，定义Agents在策略剖面中的效用偏离度之和为优化目标，其最优解就是博弈的Nash均衡。本文基于对实例的分析指出目标函数下降梯度的计算可归结为一组线性规划，进而提出一种求解图型博弈Nash均衡的新型梯度下降算法。算法分析及实验研究表明，对于多Agent交互模型中的相关问题，本文提出的方法可求解任意图结构图型博弈Nash均衡，对于大规模图型博弈也有较好的求解精度和求解效率。     

一种新的多目标优化策略机制及其应用

在博弈问题中很多学习机制只能使Agent收敛到Nash均衡解，不能很好地满足实际需要。将博弈问题转化为多目标优化问题，提出了一种新的多目标优化策略机制——保留受控策略机制，并将其应用到囚徒困境问题中得到比Nash均衡更有意义的Pareto最优解，在自博弈实验中取得了较高的满意度。实验结果表明,该策略机制求解Pareto最优解的有效性。     

多组对策系统非劣Nash策略的最优均衡解算法

多组对策系统中求解组与组之间的非劣Nash策略至关重要.如何针对一般问题解析求出非劣Nash策略还没有有效的方法.本文阐述了一种利用组与组之间的非劣反应集构造求解非劣Nash策略的迭代算法.为此首先引进多组对策系统组内部合作对策的最优均衡值和最优均衡解的概念,然后通过证明最优均衡解是组内部隐含某一权重向量的合作对策的非劣解,得到求解合作对策的单目标规划问题.进一步说明在组内部该问题的解不仅是非劣解而且对所有局中人都优于不合作时的Nash平衡策略.最后给出了验证该算法有效性的一个实际例子.     

基于粒子群算法的粗糙博弈模型与算法设计

连续博弈中至少存在一个混合策略Nash均衡,但是关于无限策略混合策略Nash均衡的解法,以及局中人的策略集或是效益函数是不确定性博弈均衡问题,国内外相关的研究成果还比较少。运用粒子群算法对目标函数没有严格要求,参数较少,编码简单的优势,创立了一种计算无限策略混合策略的近似算法;并在此基础上提出了粗糙博弈论的概念,以粗糙集和Vague集的理论为基础,发现了一种粗糙博弈论转化为经典博弈论的方法。无限策略混合策略Nash均衡的近似算法和粗糙博弈论的研究为策略集和效益函数不确定时的博弈问题提供了理论依据。算法示例结果表明,基于改进的粒子群算法的无限策略混合策略Nash均衡近似算法和粗糙博弈论的解法是有效可行的。     

基于自适应小生境粒子群算法的多重Nash均衡求解

针对n人非合作博弈多重Nash均衡求解问题,提出一种自适应小生境粒子群算法。该算法融合了序列小生境技术、粒子群优化算法的思想,并加入了变异算子和自动生成小生境半径机制,使得所有粒子尽可能分布到整个搜索空间的不同局部峰值区域,从而有效地求得博弈问题的多重Nash均衡。最后给出几个数值算例,计算结果表明所提出的算法具有较好的性能。     

面向突发事件的应急资源调度模型的构建和求解

针对突发事件发生后存在多个事故、应急资源有限的情况,提出了基于非合作博弈的应急资源调度模型和算法。在该调度模型中,各个事故点被视为博弈模型的局中人,可能的资源调度方案映射为策略集,将应急资源的调度问题转化为对非合作博弈调度模型的Nash均衡点求解问题,并对基本蚁群算法进行了改进,嵌入了遗传算法的交叉操作和变邻域搜索策略,将其应用于求解该博弈模型的Nash均衡解。最后通过算例测试验证了模型和算法的有效性和可行性。     

基于策略迭代算法的连续时间线性Markov跳变系统非零和微分反馈Nash控制

针对一类连续时间线性Markov跳变系统,本文提出了一种新的策略迭代算法用于求解系统的非零和微分反馈Nash控制问题.通过求解耦合的数值迭代解,以获得具有线性动力学特性和无限时域二次成本的双层非零和微分策略的Nash均衡解.在每一个策略层,采用策略迭代算法来计算与每一组给定的反馈控制策略相关联的最小无限时域值函数.然后,通过子系统分解将Markov跳变系统分解为N个并行的子系统,并将该算法应用于跳变系统.本文提出的策略迭代算法可以很容易求解非零和微分策略所对应的耦合代数Riccati方程,且对高维系统有效.最后通过仿真示例证明了本文设计方法的有效性和可行性.     

基于免疫粒子群算法的非合作博弈Nash均衡问题求解*

针对N人非合作博弈Nash均衡求解问题,将免疫算法中抗体浓度抑制机制和免疫记忆功能引入基本粒子群算法,提出了一种求解博弈问题Nash均衡的免疫粒子群算法。该算法通过抗体浓度抑制机制和免疫记忆功能来保持种群的多样性,不仅保持了粒子群算法简单、易于实现的特点,而且增强了粒子群算法的全局寻优能力,加快了算法的速度。实验表明,提出的算法具有较好的性能,优于免疫算法和基本粒子群算法。     

带资源属性的负载均衡问题的算法设计磁

针对带有一对属性值（ai ,bi ）的n个agent分配m个资源问题,构建了该问题的博弈模型,给出了判断Nash均衡是否存在的充要条件,利用充要条件对Nash均衡的存在性进行分析和讨论,并且分析了Nash均衡与最优分配的关系。设计了求解最优分配的算法,并证明了算法是收敛的,证明过程显示该算法的收敛性与初始分配无关。     

Solving Nash equilibrium for N-persons' non-cooperative game based on immune particle swarm algorithm

针对N人非合作博弈Nash均衡求解问题,将免疫算法中抗体浓度抑制机制和免疫记忆功能引入基本粒子群算法,提出了一种求解博弈问题Nash均衡的免疫粒子群算法.该算法通过抗体浓度抑制机制和免疫记忆功能来保持种群的多样性,不仅保持了粒子群算法简单、易于实现的特点,而且增强了粒子群算法的全局寻优能力,加快了算法的速度.实验表明,提出的算法具有较好的性能,优于免疫算法和基本粒子群算法.     

基于矩阵图谱表达法的蛋白质序列的相似性分析

在DNA序列的混沌游走方法（CGR）及DNA序列的4线图谱表达方法（4-LGR）的基础上,提出了一种新型DNA序列的表达方法—矩阵图谱表达法（MGR）,并进一步,在DNA序列的上述三种表达式基础上,分别推广建立了基于经典HP模型的蛋白质序列的图谱表达法,对蛋白质序列的相似性进行了比较验证。研究表明：矩阵图谱表达方法不仅能够说明蛋白质序列间的相似性,而且与传统的方法相比,该方法更具有灵活性和变通性。     

基于两阶段迭代优化的空天观测资源协同任务规划方法

为提高空天观测资源协同观测能力,基于分而治之框架,提出一种两阶段迭代优化方法以解决空天观测资源协同任务规划问题.第1阶段,根据观测机会和冲突度构造适应度函数,基于适应度将任务分配到合适的子规划中心;第2阶段,子规划中心根据分配到的任务进行资源调度,得到各类观测资源的观测计划,并将资源观测方案和观测收益反馈给第1阶段.第1阶段再根据第2阶段的反馈结果,结合禁忌表策略,对任务分配方案进行迭代调整和更新,直到生成近似最优或满意的任务分配方案和资源观测方案.为验证所提出方法的有效性,开展大量仿真实验.实验结果表明,与最大权重最先分配算法、基于适应度的任务分配算法、基于资源优先度的任务分配算法相比,所提出方法在任务收益率方面提高了2.40%sim14.14%.研究成果可为空天观测资源传感网络的协同管控提供技术支持.     

Optimal shape design of an electrostatic comb drive inmicroelectromechanical systems

Polynomial driving-force comb drives are synthesized using numerical simulation. The electrode shapes are obtained using the indirect boundary element method. Variable-gap comb drives that produce combinations of linear, quadratic, and cubic driving-force profiles are synthesized. This inverse problem is solved by an optimization procedure. Sensitivity analysis is carried out by the direct differentiation approach (DDA) in order to compute design sensitivity coefficients (DSCs) of force profiles with respect to parameters that define the shapes of the fingers of a comb drive. The DSCs are then used to drive iterative optimization procedures. Designs of variable-gap comb drives with linear, quadratic, and cubic driving force profiles are presented in this paper     

A generic algorithm for computing optimal ergonomic postures during working in an industrial environment

The present study tries to decrease the risk of work-related musculoskeletal disorders for industry workers by proposing a generic algorithm that recommends an optimal ergonomic posture for accomplishing tasks in an industrial environment. In the case of a dangerous ergonomic pose, the optimization algorithm starts by heuristically changing it to a more ergonomic one. Each recommended posture's feasibility is tested with an inverse kinematic method that can predict the worker's behavior for accomplishing a task. This iterative optimization procedure continues until the optimal ergonomic pose for the worker is achieved. The algorithm's validity is tested in thirteen cases, people with different gender (50 percent male, 50 percent female) aged between 20 and 35, and different height and body morphologies. According to studies, there is a connection between musculoskeletal disorders and the wrong posture for accomplishing tasks in industries. We suggest an optimization algorithm that can indicate the worker the optimal ergonomic pose by considering task constraints in real-time.     

Optimal redundancy resolution of a kinematically redundant manipulator for a cyclic task

This article proposes a method for the global optimization of redundancy over the whole task period in a kinematically redundant manipulator. The necessary conditions based on the calculus of variations for integral-type criteria result in a second-order differential equation. For a cyclic task, the boundary conditions for conservative joint motions are discussed. Then, we reformulate a two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method based on the iterative optimization for providing a globally optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of redundancy, we only search parameter values in the parameterized space using the configuration error between the initial and final time. We show through numerical examples that multiple nonhomotopic extremal solutions satisfying periodic boundary conditions exist according to initial joint velocities for the same initial configuration. Finally, we discuss an algorithm for topological liftings of the paths and demonstrate the generality of the proposed method by considering the dynamics of a manipulator.     

Clustering high dimensional data: A graph-based relaxed optimization approach

There is no doubt that clustering is one of the most studied data mining tasks. Nevertheless, it remains a challenging problem to solve despite the many proposed clustering approaches. Graph-based approaches solve the clustering task as a global optimization problem, while many other works are based on local methods. In this paper, we propose a novel graph-based algorithm “GBR” that relaxes some well-defined method even as improving the accuracy whilst keeping it simple. The primary motivation of our relaxation of the objective is to allow the reformulated objective to find well distributed cluster indicators for complicated data instances. This relaxation results in an analytical solution that avoids the approximated iterative methods that have been adopted in many other graph-based approaches. The experiments on synthetic and real data sets show that our relaxation accomplishes excellent clustering results. Our key contributions are: (1) we provide an analytical solution to solve the global clustering task as opposed to approximated iterative approaches; (2) a very simple implementation using existing optimization packages; (3) an algorithm with relatively less computation time over the number of data instances to cluster than other well defined methods in the literature.     

P2P流媒体系统覆盖网局部优化研究

P2P流媒体系统覆盖网优化对系统性能有重要影响.现有的优化策略主要从全局角度进行描述,而实际情况中节点仅拥有系统部分节点的信息.为分析局部优化问题,本文首先基于博弈论模型提出一种无协作局部优化策略(Non-CooperationLocal Optimization,NCLO)对流媒体系统进行分析;在此基础上,提出一种协作局部优化策略(Cooperation Local Optimization,CLO),该策略通过交换邻居节点信息,采用投标的方式选择邻居节点,在已知局部信息的情况下调整邻居关系对覆盖网进行优化.实验表明,基于协作的局部优化策略能达到较好的优化效果.     

Double-loop-iterative-tracking-algorithm-based direct coordination for hierarchical steady-state control of interconnected systems

An alternative hierarchical optimization algorithm obtained by combining a double-loop iterative strategy with an efficient coordination task is proposed. The new algorithm derived from the tracking method (Sidaoui et al. 1989, 1991) is applicable to non-convex problems and has the advantage of giving a better rate of convergence. Simulation results are given and compared with the original algorithm, indicating the superiority of the new approach for the example considered.