基于混合搜索的含逻辑“与”“或”的RM优化算法

相对于标准约束优化问题,广义约束优化问题（或称析取优化问题）的等式或不等式约束条件中不仅包含逻辑“与”关系,还含有逻辑“或”关系.单调速率（RM）优化问题是广义约束优化问题的一个重要应用.目前RM优化问题已有的解法包括函数变换、混合整数规划、线性规划搜索等算法.随着任务数的增多,这些算法的求解时间较长.提出一种基于线性规划的深度广度混合搜索算法（LPHS）,将广义约束优化问题拆分成若干子问题,建立线性规划搜索树,合理选择搜索顺序,利用动态剪枝算法减小子问题的规模,最终求得最优解.实验结果表明,LPHS算法比其他方法有明显的效率提升.研究成果与计算机基础理论中的可满足性模理论的研究相结合,有助于提高可满足性模理论问题的求解效率,促进该理论在程序验证、符号执行等领域的进一步应用.     

单调速率及其扩展算法的可调度性判定

任务可调度性判定是实时系统调度理论研究的核心问题.单调速率(RM)算法是实时调度的重要算法,自其提出以来已被广泛研究.然而到目前为止,尚缺乏专题性的文章来系统而深入地探讨RM及其扩展算法的可调度性判定,以及各种现实条件和实现方式(包括任务调度的时间开销和任务同步问题等)对可调度性的影响.围绕RM算法下的可调度性判定问题,由浅入深,系统性地讨论各种不同假设和实现方式对可调度性的影响,具体为下述3大类问题：（1）理想的RM算法下的可调度性判定的CPU利用率最小上界最小及可调度的充分必要条件;（2）考虑调度时间开销情况下的可调度性判定条件;（3）优先级反转协议及其对可调度性的影响.给除了具体实例来叙述上述问题,并从算法复杂度和可检测率两方面比较各种算法的优劣。     

采用二元CSP引擎求解RTL数据通路的可满足性

针对寄存器传输级(RTL)验证和测试过程中非常重要的数据通路可满足性求解问题,提出一种基于二元约束满足问题(CSP)的求解方法,包括数据通路提取、二元CSP建模和搜索求解3个步骤.数据通路提取通过对接口布尔变量和某些字变量赋值,为各个数据通路器件建立环境;二元CSP建模则根据该环境和各个数据通路器件的功能,将数据通路的可满足性问题转化为二元CSP描述;该二元CSP问题的描述被送入到二元CSP引擎,并采用冲突引导的回跳搜索策略进行求解,获得有解的例证或无解的判定.实验结果表明,即使在没有采取很多优化策略的条件下,该方法仍有较好的性能,并优于基于线性规划(LP)的求解方法.     

一种改进的RM可调度性判定算法

固定优先级任务可调度性判定是实时系统调度理论研究的核心问题之一.目前已有的各种判定方法可归结为两大类:多项式时间调度判定和确切性判定.多项式时间调度判定通常采用调度充分条件来进行,为此,许多理想条件下基于RM(rate monotonic)调度算法的CPU利用率最小上界被提了出来.确切性判定利用RM调度的充要条件,保证任何任务集均可被判定,并且判定结果是确切的.但是由于时间复杂度较差,确切性判定方法难以实现在线分析.提出了一种改进的RM可调度性判定方法(improved schedulability test algorithm,简称ISTA).首先介绍了任务调度空间这一概念,并提出了二叉树表示,然后进一步提出了相关的剪枝理论.在此基础上,研究了任务之间可调度性的相关性及其对判定任务集可调度性的影响,提出并证明了相关的定理.最后基于提出的定理,给出了一种改进的伪多项式时间可调度性判定算法,并与已有的判定方法进行了比较.仿真结果表明,该算法平均性能作为任务集内任务个数的函数具有显著提高.     

改进的以SMT为基础的实时系统限界模型检测

基于SAT的限界模型检测在处理实时系统时具有很高的复杂度.SMT求解器在计算可满足性的同时,还能处理算术和其他可判定性理论.在对实时系统进行检测时,用SMT求解器代替SAT求解器,系统里的时钟就可以用整型或实型变量表示,时钟约束则可以直接表示成线性算术表达式,从而使整个检测过程更加高效.带时间参数的计算树逻辑(timed computation tree logic,简称TCTL)被用来描述实时系统里的性质.同时,还对检测方法作了相应的改进.     

改进的以SMT为基础的实时系统限界模型检测

基于SAT的限界模型检测在处理实时系统时具有很高的复杂度.SMT求解器在计算可满足性的同时,还能处理算术和其他可判定性理论.在对实时系统进行检测时,用SMT求解器代替SAT求解器,系统里的时钟就可以用整型或实型变量表示,时钟约束则可以直接表示成线性算术表达式,从而使整个检测过程更加高效.带时间参数的计算树逻辑(timed computation tree logic,简称TCTL)被用来描述实时系统里的性质.同时,还对检测方法作了相应的改进.     

一种可行的DMS可调度性分析

固定优先级任务的可调度性判定是实时系统调度理论研究的核心问题之一。提出了一种可行的DMS(Deadline Monotonic Scheduling,简称DMS)可调度性判定方法—确切性判定方法(precised schedulability test algorithm简称PSTA),利用DMS调度的充要条件,保证任何任务集均可被判定,并且判定结果是确切的。首先给出了DMS调度模型,介绍了可调度性判定的基本思想,然后通过实验提出并验证了PSTA相关的结论。     

基于逻辑"或"约束优化的实时系统设计

标准约束优化问题的等式或不等式约束之间是逻辑"与"关系,目前已经有很多高效、收敛的优化算法.但是,在实际应用中有很多更一般的约束优化问题,其等式或不等式约束之间不仅包含逻辑"与"关系,而且还包含逻辑"或"关系,现有的针对标准约束优化问题的各种算法不再适用.给出一种新的数学变换方法,把具有逻辑"或"关系的不等式约束转换为一组具有逻辑"与"关系的不等式,并应用到实时单调速率调度算法的可调度性判定充要条件中,把实时系统设计表示成混合布尔型整数规划问题,利用经典的分支定界法求解.实验部分指出了各种方法的优缺点.     

基于可满足性模理论的多处理机通信延迟优化任务调度方法

在一组相同处理器上调度带有通信延迟的任务图以实现其最短的执行时间,这在并行计算的调度理论和实践中具有重要的意义。针对具有通信延迟的任务图调度问题,提出一种基于可满足性模理论（SMT）的改进SMT方法。首先,将处理器映射约束和任务执行顺序等约束条件进行编码,将任务图调度问题转化为SMT问题;然后,调用SMT求解器对可行解空间进行搜索,以确定问题最优解。在约束编码阶段,使用整型变量表示任务和处理器的映射关系,从而降低处理器约束编码的复杂程度;在求解器调用阶段,通过添加独立任务的约束条件减小求解器的搜索空间,进一步提升最优解的查找效率。实验结果表明,与原始SMT方法相比,改进SMT方法在20 s和1 min超时实验中的平均求解时间分别减少了65.9%与53.8%,并且在处理器数量较多时取得了更大的效率优势。改进的SMT方法可以有效求解带通信延迟的任务图调度问题,尤其适用于处理器数量较多的调度场景。     

多处理器EPDFPfair算法的可调度性判定

针对多处理器实时调度中的最早伪时限优先(EPDF)Pfair算法,分析了EPDF算法在M个处理器平台上的可调度利用率约束,根据基于利用率的充分可调度性判定,提出了一种改进的可调度性判定方法。这种方法可以得到更多的可调度任务集,从而使得满足判定的强实时系统和使用tie-breaking规则困难的动态任务系统的调度有较小的开销。实验结果表明,改进的可调度性判定方法增加了判为可调度的任务集数量,具有较好的性能。     

A new linearization method for generalized linear multiplicative programming

This paper presents a deterministic global optimization algorithm for solving generalized linear multiplicative programming (GLMP). In this algorithm, a new linearization method is proposed, which applies more information of the function of (GLMP) than some other methods. By using this new linearization technique, the initial nonconvex problem is reduced to a sequence of linear programming problems. A deleting rule is presented to improve the convergence speed of this algorithm. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of this algorithm.     

离散时间最优控制—–评论动态规划

阐述离散时间最优控制的特点.对比3种求解离散时间最优控制的解法,即:1)用非线性规划求解离散时间最优控制;2)用无约束优化求解离散时间最优控制;3)动态规划及其数值解.1)和2)都适用于多维静态优化,计算效率较高,是高级方法.在名义上,3)为动态优化.实际上,3)为一维分段无约束静态优化,计算效率较低,是初级方法.本文并用数字实例进一步阐明动态规划及其数值解在求解方面较差,故动态规划及其数值解已失去实用价值.在求解离散时间最优控制问题方面,无法与非线性规划求解相匹敌.     

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.     

An adaptive nonmonotone truncated Newton method for optimal control of a class of parabolic distributed parameter systems

A black-box method using the finite elements, the Crank–Nicolson and a nonmonotone truncated Newton (TN) method is presented for solving optimal control problems (OCPs) governed by partial differential equations (PDEs). The proposed method finds the optimal control of a class of linear and nonlinear parabolic distributed parameter systems with a quadratic cost functional. To this end, the piecewise linear finite elements method and the well-known Crank–Nicolson method are used for discretizing in space and in time, respectively. Afterwards, regarding the implicit function theorem (IFT), the optimal control problem is transformed into an unconstrained nonlinear optimization problem. Considering that in a gradient-based method for solving optimal control problems, the evaluations of gradients and Hessians of the cost functional is important, hence, an adjoint technique is used to evaluate them effectively. In addition, to make a globalization strategy, we first introduce an adaptive nonmonotone strategy which properly controls the degree of nonmonotonicity and then incorporate it into an inexact Armijo-type line search approach to construct a more relaxed line search procedure. Finally, the obtained unconstrained nonlinear optimization problem is solved by utilizing the proposed nonmonotone truncated Newton method. Results gained from the new offered method compared with existing methods show that the new method is promising.     

Joint optimization for area traffic control and network flow

A joint optimization problem for solving area traffic control and network flow is investigated. A bilevel programming is used to formulate this joint optimization problem where the network flow following Wardrop's principles can be obtained by solving traffic assignment problems. In this paper, we present a solution approach for jointly optimizing the area traffic control and network flow on the basis of a newly presented algorithm for concurrent flow (Comput. Oper. Res. (2004) in press). We propose three kinds of formulations for this joint optimization problem and present a gradient-based method to effectively solve this problem via a mixture of locally optimal search and global search heuristic where a near global optimum may be found. Numerical comparisons are made for the values of performance index achieved by the joint optimization problem with system optimal flow and those did by equilibrium flow at various sets of initial signal settings. Substantially good results have demonstrated the robustness of the proposed algorithm in solving both system optimal and user equilibrium flow for the joint optimization problem at large-scale networks.     

基于单纯形法和局部枚举解混合整数线性规划问题

提出了一种基于单纯形法和局部枚举求解整数线性规划问题的新方法。它通过单纯形法得到松弛问题的最优解并确定变量以及目标函数取值范围,然后基于目标函数,进行局部枚举,从而得到其整数线性规划问题的最优解,与现有方法比较,新解法简单,计算量少,尤其是对于大规模整数线性规划问题,计算量少体现地更明显。     

A DC programming approach for planning a multisensor multizone search for a target

In this paper, we consider a well-known problem in the general area of search theory: planning a multisensor in multizone search so as to maximize the probability of detection of a target under a given resource effort to be shared. We propose a new optimization model that is a nonlinear mixed 0–1 programming problem. This problem is then reformulated as a DC (Difference of Convex) functions program via an exact penalty technique. DC programming and DCA (DC algorithm) have been investigated for solving the resulting DC program. Numerical experiments demonstrate the efficiency and the superiority of the proposed algorithm in comparison with the existing method.