Mixed coordination mechanisms for scheduling games on hierarchical machines

In this paper, we study scheduling games under mixed coordination mechanisms on hierarchical machines. The two scheduling policies involved are ‐ and ‐, where ‐ (resp., ‐) policy sequences jobs in nondecreasing order of their hierarchies, and jobs of the same hierarchy in nonincreasing (resp., nondecreasing) order of their processing times. We first show the existence of a Nash equilibrium. Then we present the price of anarchy and the price of stability for the games with social costs of minimizing the makespan and maximizing the minimum machine load. All the bounds given in this paper are tight.     

Necessary optimality conditions in a nonsmooth control problem with variable structure

An optimal control problem with nonsmooth performance criterion described by a system of ordinary differential equations is considered. Necessary first-order optimality conditions are obtained.     

会计信息失真现象的博弈分析

在对现实进行合理假定的基础上建立了会计信息失真现象的有限完美信息动态博弈模型，并利用后退归纳法找到了五个满足不同条件的纳什均衡解。通过对均衡条件的分析，找出了导致会计信息失真的治理结构原因和法律制度因素，并提出了建设性的解决措施。     

A constructive approach to sequential Nash equilibria

We present a Coq-formalized proof that all non-cooperative, sequential games have a Nash equilibrium point. Our proof methodology follows the style advocated by LCF-style theorem provers, i.e., it is based on inductive definitions and is computational in nature. The proof (i) uses simple computational means, only, (ii) basically is by construction, and (iii) reaches a constructively stronger conclusion than informal efforts. We believe the development is a first as far as formalized game theory goes.     

分段线性材料桁架的位移灵敏度

本文推导了分段线性材料桁架结构的位移对截面积的灵敏度，并给出三杆桁架实例。指出了在材料性质发生突变处位移对截面积的灵敏度不连续、位移等值面不光滑：讨论了，采用准则法求解优化问题时的灵敏度计算和迭代公式，旨在指出文献中的错误。     

Some Notes on the Formal Properties of Bidirectional Optimality Theory

In this paper, we discuss some formal properties of the model ofbidirectional Optimality Theory that was developed inBlutner (2000). We investigate the conditions under whichbidirectional optimization is a well-defined notion, and we give aconceptually simpler reformulation of Blutner's definition. In thesecond part of the paper, we show that bidirectional optimization can bemodeled by means of finite state techniques. There we rely heavily onthe related work of Frank and Satta (1998) about unidirectionaloptimization.     

连续体结构的参数化水平集统一优化

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.     

On the sizing of a solar thermal electricity plant for multiple objectives using evolutionary optimization

Design, implementation and operation of solar thermal electricity plants are no more an academic task, rather they have become a necessity. In this paper, we work with power industries to formulate a multi-objective optimization model and attempt to solve the resulting problem using classical as well as evolutionary optimization techniques. On a set of four objectives having complex trade-offs, our proposed procedure first finds a set of trade-off solutions showing the entire range of optimal solutions. Thereafter, the evolutionary optimization procedure is combined with a multiple criterion decision making (MCDM) approach to focus on preferred regions of the trade-off frontier. Obtained solutions are compared with a classical generating method. Eventually, a decision-maker is involved in the process and a single preferred solution is obtained in a systematic manner. Starting with generating a wide spectrum of trade-off solutions to have a global understanding of feasible solutions, then concentrating on specific preferred regions for having a more detailed understanding of preferred solutions, and then zeroing on a single preferred solution with the help of a decision-maker demonstrates the use of multi-objective optimization and decision making methodologies in practice. As a by-product, useful properties among decision variables that are common to the obtained solutions are gathered as vital knowledge for the problem. The procedures used in this paper are ready to be used to other similar real-world problem solving tasks.     

证券市场中庄家与散户间的确定性微分博弈

基于确定性微分博弈理论,建立了一种庄家与散户间的连续时间的博弈模型.首先将所有散户作为一个整体与庄家进行博弈,以博弈双方持股率的动态关系作为动态系统方程,并以此构建了一个确定性微分博弈模型; 然后运用开环纳什均衡和反馈纳什均衡分别求解出满足共态函数的常微分方程组和满足价值函数的Issacs - Bellman偏微分方程,以此得到庄家与散户博弈的开环纳什均衡策略和反馈纳什均衡策略.该结果可为金融监管部门监管证券市场和证券市场投资者买卖股票提供参考.     

分布式预测控制在空气分馏塔中的应用

在大型空分控制系统中,集中式控制由于在线计算量大,对计算机的要求较高。采用分布式预测控制,把复杂系统的控制过程分散到各个子系统中去,降低了计算的复杂度,同时提高了系统的可靠性。建立了分馏塔的数学模型,并拆分成若干个子系统,利用纳什优化原理,获得了全局最优解。仿真结果表明,该算法取得了较好的控制效果。