联盟收益不确定下合作博弈的多目标粒子群扩展算法求解

在传统的合作博弈求解中,通常假设联盟收益确定或者局中人对联盟收益取值意见一致.现实中,联盟收益往往不确定,局中人对联盟收益取值意见不一致,且联盟分配方案的达成通常是局中人基于个体理性与判断进行多轮谈判,互相影响、相互妥协、最终趋同的结果.针对这种情况,本文首先对联盟收益不确定时局中人的收益进行描述,建立合作博弈的扩展模型,再考虑局中人的理性互动与策略博弈,借鉴群智能的建模思想和求解思路,利用多目标粒子群扩展算法对模型进行求解.本文对于联盟收益不确定时合作博弈的求解提供了新的思路与方法.     

基于时隙ALOHA协议的数据传输二人随机博弈模型

在一个给定的拓扑网络中研究关于数据传输的二人随机博弈模型.两个局中人（源节点）试图通过一个公共节点向目的节点传输随机数据包,这些数据包被分为重要的数据包和不重要的数据包两类,假设每个局中人都有一个用于存储数据包的有限容量的缓冲器.通过构造数据传输的成本分摊和奖励体系,把这种动态的冲突控制过程建模为具有有限状态集合的随机博弈,研究局中人在这种随机博弈模型下的非合作以及合作行为.在非合作情形下,给出纳什均衡的求解算法;在合作情形下,选择Shapley值作为局中人支付总和的分配方案,并讨论其子博弈一致性,提出使得Shapley值为子博弈一致的分配补偿程序.     

基于时隙ALOHA协议的数据传输二人随机博弈模型

在一个给定的拓扑网络中研究关于数据传输的二人随机博弈模型.两个局中人(源节点)试图通过一个公共节点向目的节点传输随机数据包,这些数据包被分为重要的数据包和不重要的数据包两类,假设每个局中人都有一个用于存储数据包的有限容量的缓冲器.通过构造数据传输的成本分摊和奖励体系,把这种动态的冲突控制过程建模为具有有限状态集合的随机博弈,研究局中人在这种随机博弈模型下的非合作以及合作行为.在非合作情形下,给出纳什均衡的求解算法;在合作情形下,选择Shapley值作为局中人支付总和的分配方案,并讨论其子博弈一致性,提出使得Shapley值为子博弈一致的分配补偿程序.     

带风险偏好的区间支付交流结构合作博弈及平均树解北大核心CSCD

针对具有区间支付的限制结盟合作博弈,考虑现实局中人的不同偏好信息,通过引入风险偏好均值,提出了具有风险偏好的区间支付交流结构合作博弈及其平均树解.通过公理化体系对此解的存在性进行了证明,并将此分配方法应用到供应链纵向研发合作企业收益分配的实例中,表明该方法的有效性和可行性.此研究同时考虑了合作结盟的限制约束性和局中人的风险态度差异性,不仅能有效刻画现实结盟情境,且利于分配收益函数的求解.     

带风险偏好的区间支付交流结构合作博弈及平均树解

针对具有区间支付的限制结盟合作博弈,考虑现实局中人的不同偏好信息,通过引入风险偏好均值,提出了具有风险偏好的区间支付交流结构合作博弈及其平均树解.通过公理化体系对此解的存在性进行了证明,并将此分配方法应用到供应链纵向研发合作企业收益分配的实例中,表明该方法的有效性和可行性.此研究同时考虑了合作结盟的限制约束性和局中人的风险态度差异性,不仅能有效刻画现实结盟情境,且利于分配收益函数的求解.     

考虑边流量有限的网络路径博弈问题研究

考虑每条边有流量约束的网络路径博弈问题, 根据收益函数单调递增的特点分析其内在零和性质, 并建模为存在公共边的路径博弈模型。在寻找均衡解的过程中, 首先考虑非合作的情形, 在局中人风险中性的假设下, 给出了求Nash均衡流量分配的标号法并证明该均衡分配的唯一性。接着进一步考虑局中人合作的可能性, 给出模型求得所有局中人的整体最大收益, 并基于纳什谈判模型给出目标函数为凸函数的数学模型确定唯一收益分配方案。事实上, 该方案是对剩余价值的平均分配。最后给出一个算例, 验证本文理论和方法的可行性。关键词:流量约束; 均衡流量; 网络路径博弈; 收益分配     

基于Selectope解集和局中人最大满意度的合作对策解的研究

针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

最短路博弈群体单调分配方案构造

群体单调分配方案(Population Monotonic Allocation Scheme, 后简称PMAS)是合作博弈的一类分配机制。在合作博弈中, PMAS为每一个子博弈提供一个满足群体单调性的核中的分配方案, 从而保证大联盟的动态稳定性。本文主要贡献为利用线性规划与对偶理论构造与求解一类基于最短路问题的合作博弈(最短路博弈)的PMAS。我们首先借助对偶理论, 利用组合方法为最短路博弈构造了一个基于平均分摊思想的PMAS。然后借鉴计算核仁的Maschler方案, 将PMAS的存在性问题转化为一个指数规模的线性规划的求解问题, 并通过巧妙的求解得到了与之前组合方法相同的最短路博弈的PMAS。     

具有模糊目标的多目标双矩阵对策集结与求解

针对不确定性多冲突环境,建立了多个具有模糊目标的多目标双矩阵对策的综合集结模型.在假定局中人各模糊目标的隶属函数为线性函数的情形下,基于总体模糊目标的可达度,给出了纳什均衡解的定义,并应用粒子群优化算法对集结模型求解.最后,给出一个军事例子说明了模型的实用有效性和粒子群优化算法求解的高效性.     

超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

基于PSO-AFSA混合算法的模糊投资组合问题的研究

针对模糊不确定的证券市场,用可能性均值、下可能性方差和协方差分别替换了投资组合模型中概率均值、方差和协方差,构建了双目标均值-方差投资组合模型。然后采用线性加权法将双目标模型转化为单目标模型,进而提出了一个PSO-AFSA混合算法对其求解。该混合算法中,将粒子群算法搜索的结果作为人工鱼群算法初始鱼群,进一步搜索,这样能有效的避免粒子群算法陷入局部最优。同时,将人工鱼群中的最好位置反馈到粒子群算法的速度更新公式中,指引粒子运动,加快算法收敛。最后,进行实例分析,结果表明:PSO-AFSA混合算法是有效的,混合算法搜索到的全局最优值好于基本粒子群算法搜索到的全局最优值。     

An evolutionary game based particle swarm optimization algorithm

Particle swarm optimization (PSO) is an evolutionary algorithm used extensively. This paper presented a new particle swarm optimizer based on evolutionary game (EGPSO). We map particles’ finding optimal solution in PSO algorithm to players’ pursuing maximum utility by choosing strategies in evolutionary games, using replicator dynamics to model the behavior of particles. And in order to overcome premature convergence a multi-start technique was introduced. Experimental results show that EGPSO can overcome premature convergence and has great performance of convergence property over traditional PSO.     

A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design

Multi-objective particle swarm optimization (MOPSO) is an optimization technique inspired by bird flocking, which has been steadily gaining attention from the research community because of its high convergence speed. On the other hand, in the face of increasing complexity and dimensionality of today’s application coupled with its tendency of premature convergence due to the high convergence speeds, there is a need to improve the efficiency and effectiveness of MOPSO. In this paper a competitive and cooperative co-evolutionary approach is adapted for multi-objective particle swarm optimization algorithm design, which appears to have considerable potential for solving complex optimization problems by explicitly modeling the co-evolution of competing and cooperating species. The competitive and cooperative co-evolution model helps to produce the reasonable problem decompositions by exploiting any correlation, interdependency between components of the problem. The proposed competitive and cooperative co-evolutionary multi-objective particle swarm optimization algorithm (CCPSO) is validated through comparisons with existing state-of-the-art multi-objective algorithms using established benchmarks and metrics. Simulation results demonstrated that CCPSO shows competitive, if not better, performance as compared to the other algorithms.     

A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem

We propose a novel cooperative swarm intelligence algorithm to solve multi-objective discrete optimization problems (MODP). Our algorithm combines a firefly algorithm (FA) and a particle swarm optimization (PSO). Basically, we address three main points: the effect of FA and PSO cooperation on the exploration of the search space, the discretization of the two algorithms using a transfer function, and finally, the use of the epsilon dominance relation to manage the size of the external archive and to guarantee the convergence and the diversity of Pareto optimal solutions.We compared the results of our algorithm with the results of five well-known meta-heuristics on nine multi-objective knapsack problem benchmarks. The experiments show clearly the ability of our algorithm to provide a better spread of solutions with a better convergence behavior.     

政府促进银行实施绿色信贷的多目标优化策略研究

传统的绿色信贷研究中存在着模型简单、非动态参数以及只能获取纳什均衡点的局限性。为改善这些局限性,研究了一种基于数据驱动多目标优化算法的政府促进银行实施绿色信贷的策略计算方法。首先针对绿色信贷的最优策略求解问题建立数据驱动的多目标优化算法框架,再基于历史数据建立算法框架中的最优策略马可夫状态转移模型,最后使用多目标粒子群优化算法对政府和银行的长远总收益进行最优策略求解。与传统的基于近似模型及博弈论的方法不同,本文提出的方法可以获得历史数据中的经验,从而制定出具有更加长远收益的策略,避免了传统方法中的“短视”现象。分析结果表明,绿色信贷的收益不会在短时间内显现,因此政府在做决策时,必须根据绿色信贷收益的回报周期作出长远的判断。     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了粒子种群在进化过程中的多样性与收敛性这一矛盾,使得算法的全局探索与局部开发得到有效平衡.利用经典的基准测试函数和平面冗余机械臂逆运动学问题的求解来验证提出算法的有效性,试验结果表明:与其他算法相比,HMPSO算法具有更快的收敛速度、更高的收敛精度、更强的收敛稳定性以及更低的计算成本.     

A hybrid simplex search and particle swarm optimization for unconstrained optimization

This paper proposes the hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder–Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification

The hybrid algorithm that combined particle swarm optimization with simulated annealing behavior (SA-PSO) is proposed in this paper. The SA-PSO algorithm takes both of the advantages of good solution quality in simulated annealing and fast searching ability in particle swarm optimization. As stochastic optimization algorithms are sensitive to their parameters, proper procedure for parameters selection is introduced in this paper to improve solution quality. To verify the usability and effectiveness of the proposed algorithm, simulations are performed using 20 different mathematical optimization functions with different dimensions. The comparative works have also been conducted among different algorithms under the criteria of quality of the solution, the efficiency of searching for the solution and the convergence characteristics. According to the results, the SA-PSO could have higher efficiency, better quality and faster convergence speed than compared algorithms.     

A dynamic global and local combined particle swarm optimization algorithm

Particle swarm optimization (PSO) algorithm has been developing rapidly and many results have been reported. PSO algorithm has shown some important advantages by providing high speed of convergence in specific problems, but it has a tendency to get stuck in a near optimal solution and one may find it difficult to improve solution accuracy by fine tuning. This paper presents a dynamic global and local combined particle swarm optimization (DGLCPSO) algorithm to improve the performance of original PSO, in which all particles dynamically share the best information of the local particle, global particle and group particles. It is tested with a set of eight benchmark functions with different dimensions and compared with original PSO. Experimental results indicate that the DGLCPSO algorithm improves the search performance on the benchmark functions significantly, and shows the effectiveness of the algorithm to solve optimization problems.