基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

Evaluation of singular integrals for anisotropic elastic boundary element analysis

To improve the numerical evaluation of weakly singular integrals appearing in the boundary element method, a logarithmic Gaussian quadrature formula is usually suggested in the literature. In this formula the singular function is expressed in terms of the distance between source point and field point, which is a real variable. When an anisotropic elastic solid is considered, most of the existing fundamental solutions are written in terms of complex variables. When the problems with holes, cracks, inclusions, or interfaces are considered, to suit for the shape of the boundaries usually a mapping function is introduced and then the solutions are expressed in terms of mapped complex variables. To deal with the trouble induced by the complex variables, in this study through proper change of variables we develop a simple way to improve the evaluation of weakly singular integrals, especially for the problems of anisotropic elastic solids containing holes, cracks, inclusions, or interfaces. By simple matrix expansion, the proposed method is extended to the problems with piezoelectric or magneto-electro-elastic solids. By using the dual reciprocity method, the proposed method employed for the elastostatic fundamental solution can also be applied to the elastodynamic analysis.     

Enriched workflow modelling and Stochastic Branch-and-Bound

Workflow systems provide means and techniques for modelling, designing, performing and controlling repetitive (business) processes. The quality of commercial workflow systems is usually determined to a large extent by their versatility and multi-purpose application. One of the current trends in improving workflow systems lies in enriching modelling methods and techniques in order to enlarge design alternatives.The need for such advanced methods is particularly apparent in those fields in which the process duration can be determined only vaguely, but whose completion schedules are at the same time strictly enforced by a highly competitive market by means of fines and penalties. The risk of an overrun has to be weighed against the expected costs and benefits of certain measures reducing turn-around time and their combinations. Because they can help to avoid such penalties—or, at least, keep any potential losses low by identifying critical subprocesses and evaluate appropriate measures—modelling and evaluation techniques are becoming essential features of workflow systems.Methodologically, we use Stochastic Branch-and-Bound as a technique for finding “optimal” bundles of measures. A numerical study shows the benefits of this meta-approach by means of five stepwise-developed decision scenarios requiring rich modelling. Petri nets as a modelling tool and Stochastic Branch-and-Bound as an optimization technique determine for multi-mode resource constrained workflows of varying complexity an optimal workforce strategy with respect to the number of workers and their qualification.     

HIV dynamics: Modeling,data analysis,and optimal treatment protocols

We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented.