Fuzzy bilevel programming with multiple non-cooperative followers: model,algorithm and application

In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers’ inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.     

递阶优化问题理论及其算法研究与进展

递阶优化问题用来描述具有层次结构的决策问题,两级优化问题是最基本的递阶问题,又称为两层规划或静态Stackelberg问题。这里比较系统地介绍两级以及多级优化问题的模型以及其特征,并探讨了该领域有待研究的几个方向。     

A ${bm lambda}$-Cut and Goal-Programming-Based Algorithm for Fuzzy-Linear Multiple-Objective Bilevel Optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a ${lambda}$-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using ${lambda}$-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a ${lambda}$-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a ${lambda}$-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm.      

Accelerated Bayesian learning for decentralized two-armed bandit based decision making with applications to the Goore Game

The two-armed bandit problem is a classical optimization problem where a decision maker sequentially pulls one of two arms attached to a gambling machine, with each pull resulting in a random reward. The reward distributions are unknown, and thus, one must balance between exploiting existing knowledge about the arms, and obtaining new information. Bandit problems are particularly fascinating because a large class of real world problems, including routing, Quality of Service (QoS) control, game playing, and resource allocation, can be solved in a decentralized manner when modeled as a system of interacting gambling machines. Although computationally intractable in many cases, Bayesian methods provide a standard for optimal decision making. This paper proposes a novel scheme for decentralized decision making based on the Goore Game in which each decision maker is inherently Bayesian in nature, yet avoids computational intractability by relying simply on updating the hyper parameters of sibling conjugate priors, and on random sampling from these posteriors. We further report theoretical results on the variance of the random rewards experienced by each individual decision maker. Based on these theoretical results, each decision maker is able to accelerate its own learning by taking advantage of the increasingly more reliable feedback that is obtained as exploration gradually turns into exploitation in bandit problem based learning. Extensive experiments, involving QoS control in simulated wireless sensor networks, demonstrate that the accelerated learning allows us to combine the benefits of conservative learning, which is high accuracy, with the benefits of hurried learning, which is fast convergence. In this manner, our scheme outperforms recently proposed Goore Game solution schemes, where one has to trade off accuracy with speed. As an additional benefit, performance also becomes more stable. We thus believe that our methodology opens avenues for improved performance in a number of applications of bandit based decentralized decision making.     

Decentralized optimality conditions of stochastic differential decision problems via Girsanov’s measure transformation

In this paper, we apply two methods to derive necessary and sufficient decentralized optimality conditions for stochastic differential decision problems with multiple Decision Makers (DMs), which aim at optimizing a common pay-off, based on the notions of decentralized global optimality and decentralized person-by-person (PbP) optimality. Method 1: We utilize the stochastic maximum principle to derive necessary and sufficient conditions which consist of forward and backward Stochastic Differential Equations (SDEs), and conditional variational Hamiltonians, conditioned on the information structures of the DMs. The sufficient conditions for decentralized PbP optimality are local conditions, closely related to the necessary conditions for decentralized PbP optimality. However, under certain convexity condition on the Hamiltonian, and a global version of the sufficient conditions for decentralized PbP optimality, we show decentralized global optimality. Method 2: We utilize the value processes of decentralized PbP optimal policies, we relate them to solutions of backward SDEs, we identify sufficient conditions for decentralized PbP optimality, and we show these are precisely those derived via the maximum principle. For both methods, as usual, we utilize Girsanov’s theorem to transform the initial decentralized stochastic optimal decision problems, to equivalent decentralized stochastic optimal decision problems on a reference probability space, in which the controlled process and the information processes which generate part of the information structures of the DMs, are independent of any of the decisions.     

基于NK模型的复杂系统中的组织结构分析

企业规模的扩大和环境的剧烈变化正在使企业的组织结构和经营活动越来越复杂。从企业动态演化的角度来看。组织结构不仅仅是一个静态和比较分析的概念,更是一个以提高企业绩效为目的、在长期内赢得竞争优势的过程。组织结构从决策权力分配的特征考虑可以分为集权模式和分权模式。通过一个绩效景观模拟模型可以观察到,当企业的决策问题结构"可分解"时,永久分权的组织模式能够给企业带来快速发展的能力,在短期和长期内都能实现较高的绩效。当决策结构"不可分解"时,一种先分权再集权的整合模式在长期内可以使企业达到最佳绩效,但是企业必须承受前期分权模式带来的绩效损失。在决策结构"不可分解"的情况下,只要允许企业分权游走足够长的时间,企业的绩效总能超过永久集权模式的游走,并且复杂性的增加并没有明显削弱整合模式相对集权模式提升绩效的能力。     

再制造率随机的闭环供应链产品差别定价策略

考虑闭环供应链的差别定价问题, 制造商回收废旧产品, 并生产新产品和再制造产品, 再制造率随机. 采用Stackelberg 博弈方法, 研究集中决策和分散决策下相应产品的最优定价, 给出供应链各成员的最优利润. 结果表明:若制造商对产品延迟定价, 则集中决策下回收价格高于分散决策, 而销售价格均低于分散决策; 当零售商的保守利润不低于一定值时, 集中决策下总利润不低于分散决策, 制造商可以采用改进的两部定价契约协调供应链.

     

非部分嵌套信息结构的LQG动态队决策问题的可解性（II）*

本文讨论非嵌套信息结构的递阶队决策问题和控制均享信息结构的LQG分散控制问题,文中首先证明这两类问题的信息结构都是“部分控制嵌入”的,进而给出最优策略(或控制)存在的充要条件和当此条件成立时最优策略(或控制)的表达式。     

基于分布式优化的协同干扰任务分配研究

为保证目标区域干扰覆盖和最小能量消耗的优化目标,建立协同干扰任务分配模型。在分布式协同优化框架下,将集中式任务分配问题,转换为各个虚任务区内小规模的分布式优化问题,采用分解-协调优化模式和启发式遗传算法相结合的方法,实现对各个子区域优化问题的二次迭代求解。仿真结果表明,分布式协同优化方法能够有效降低协同干扰任务分配问题的求解规模,避免“维数灾”,具有可行性。     

供应链动态合作广告策略

研究产品信誉受广告投入水平影响的供应链合作广告问题,建立具有广告投入水平抑制作用的产品信誉动态模型.通过哈密顿-雅可比-贝尔曼方程分别得到制造商和零售商在分散决策和集中决策下的最优广告策略以及在分散决策下制造商的最优合作广告参与率,比较发现,集中决策下制造商和零售商的最优广告投入水平高于分散决策下的相应值.设计了双边补贴策略来协调供应链.数值仿真实验验证了所得结论的正确性.     

On decentralized estimation and control with application to freeway ramp metering

This paper presents an approach to the suboptimal design of time invariant, infinite time horizon, L-Q-G regulator in which decision making and state estimation are decentralized into "local" subsystems. For a prespecified information pattern (set of admissible intercommunications) the problem of finding a best linear control law and state estimator is converted to a parameter optimization which can be solved off line. A modified Davidon-Fletcher-Powell algorithm is used to obtain numerical solutions to the static optimization. A design is illustrated by means of a 12 state freeway corridor ramp metering problem; behavior of centralized and decentralized designs in a nonlinear macroscopic simulation of the freeway are provided.     

滞后效应影响下低碳供应链减排投入与零售定价

考虑减排投资效果滞后效应的影响,构建低碳供应链纵向合作减排微分博弈模型.运用微分对策理论,得到分散式决策和集中式决策下低碳供应链的最优减排努力投入、宣传努力投入和零售定价策略,以及分散式决策下制造商的合作减排支付比例,并对不同决策机制下供应链成员的均衡策略进行比较分析.研究发现:集中式决策下,制造商减排努力投入和零售商宣传努力投入均高于分散式决策下的相应值;滞后时间存在一个阈值,只有滞后时间低于该阈值时,集中式决策才能提升整个供应链系统的经济绩效.     

动态背景下考虑顾客退货影响的供应链协调问题

在考虑店铺辅助服务降低顾客退货率的基础上,构建微分博弈模型并研究供应链的店铺辅助策略和供应链的协调问题.首先,利用微分对策理论,给出集中和分散两种决策模式下定价和店铺辅助的最优策略,并对两种决策模式下最优策略进行比较分析;然后,为了提升分散决策下供应链的利润,设计二部收费制契约,实现动态背景下供应链的协调;最后,通过数值算例分析店铺辅助努力和店铺辅助水平效率对供应链最优解及协调的影响.研究发现:集中决策下店铺辅助努力高于分散决策下的相应值,具有较高的店铺服务水平,但两种决策结构下的价格高低依赖于系统参数;契约的协调能力会随着店铺辅助努力或服务水平效率的增加而变强.     

Equivalent stochastic control problems

A decentralized stochastic control problem is called static if the observations available for any one decision do not depend on the other decisions. Otherwise it is called dynamic. We consider only problems with a finite number of decisions. A notion of equivalence between problems, suitable for complexity analysis, is defined. It turns out that a large class of dynamic problems can be reduced to equivalent static problems. The class includes all sequential discrete variable problems and some of the most studied continuous variable problems.     

Weapon-target assignment in unreliable peer-to-peer architecture based on adapted artificial bee colony algorithm

It is of great significance for headquarters in warfare to address the weapon-target assignment(WTA)problem with distributed computing nodes to attack targets simultaneously from different weapon units.However,the computing nodes on the battlefield are vulnerable to be attacked and the communication environment is usually unreliable.To solve the WTA problems in unreliable environments,this paper proposes a scheme based on decentralized peer-to-peer architecture and adapted artificial bee colony(ABC)optimization algorithm.In the decentralized architecture,the peer computing node is distributed to each weapon units and the packet loss rate is used to simulate the unreliable communication environment.The decisions made in each peer node will be merged into the decision set to carry out the optimal decision in the decentralized system by adapted ABC algorithm.The experimental results demonstrate that the decentralized peer-to-peer architecture perform an extraordinary role in the unreliable communication environment.The proposed scheme preforms outstanding results of enemy residual value(ERV)with the packet loss rate in the range from 0 to 0.9.     

An approach to decentralized control of large scale systems using aggregation methods

A two-level decentralized control structure is formulated for large scale interconnected subsystems controlled byNdecision makers. Chained aggregation is used to decompose the overall team problem with a decentralized information structure into (N + 1) subproblems: one low order team problem with a centralized information structure andNdecentralized optimal control problems. Accordingly, the control of each decision maker is decomposed into three components: a decoupling control which induces aggregation, a local control which controls the subsystem dynamics, and an aggregate control which controls the dynamics of the interconnection variables. The robustness of this composite control with respect to perturbations in the system dynamics and the cost functional is established.     

Some properties of optimal thresholds in decentralized detection

A decentralized Bayesian hypothesis testing problem is considered. It is analytically demonstrated that for the known signal in the Gaussian noise binary hypothesis problem, when there are two sensors with statistically independent identically distributed Gaussian observations (conditioned on the true hypothesis), there is no loss in optimality in using the same decision rule at both sensors. Also, a multiple hypothesis problem is considered; some structure is analytically established for an optimal set of decision rules     

A scattering framework for decentralized estimation problems

In this paper we develop a comprehensive framework for the study of decentralized estimation problems. This approach imbeds a decentralized estimation problem into an equivalent scattering problem, and makes use of the super-position principle to relate local and centralized estimates. Some decentralized filtering and smoothing algorithms are obtained for a simple estimation structure consisting of a central processor and of two local processors. The case when the local processors exchange some information is considered, as well as the case when the local state-space models differ from the central model.     

多目标分散决策的目标规划模型和玻尔兹曼机解法

研究建立了分散组织结构下多目标分散决策的目标规划模型，根据随机神经网络──玻尔兹曼机的基本原理，提出了求解该问题的一种新方法。示例的仿真结果表明该方法是非常有效的。     

Decentralized multi-objective bilevel decision making with fuzzy demands

Decisions in a decentralized organization often involve two levels. The leader at the upper level attempts to optimize his/her objective but is affected by the follower; the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. When model a real-world bilevel decision problem, it also may involve fuzzy demands which appear either in the parameters of objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously in achieving a solution. This study addresses both fuzzy demands and multi-objective issues and propose a fuzzy multi-objective bilevel programming model. It then develops an approximation branch-and-bound algorithm to solve multi-objective bilevel decision problems with fuzzy demands. Finally, two case-based examples further illustrate the proposed model and algorithm.