Comparison of some AI and statistical classification methods for a marketing case

Recent progress in data processing technology has made the accumulation and systematic organization of large volumes of data a routine activity. As a result of these developments, there is an increasing need for data-based or data-driven methods of model development. This paper describes data-driven classification methods and shows that the automatic development and refinement of decision support models is now possible when the machine is given a large (or sometimes even a small) amount of observations that express instances of a certain task domain. The classifier obtained may be used to build a decision support system, to refine or update an existing system and to understand or improve a decision-making process. The described AI classification methods are compared with statistical classification methods for a marketing application. They can act as a basis for data-driven decision support systems that have two basic components: an automated knowledge module and an advice module or, in different terms, an automated knowledge acquisition/retrieval module and a knowledge processing module. When these modules are integrated or linked, a decision support system can be created which enables an organization to make better-quality decisions, with reduced variance, probably using fewer people.     

A model for decision problems with continuous time parameter

The concept of statistical decision theory concerning sequential observations is generalized to decision problems, which are based upon a continuous stochastic process.

In this model decision functions are introduced, consisting of a stopping time and a terminal decision rule. A method of discretization shows the connections between the discrete sequential and the continuous model. Concerning Bayes problems we find, that under certain assumptions the decision problem can be viewed as an optimal stopping problem with continuous time parameter.     

On the optimal design of tandem queueing systems with finite buffers

We consider tandem queueing systems that can be formulated as a continuous-time Markov chain, and investigate how to maximize the throughput when the queue capacities are limited. We consider various constrained optimization problems where the decision variables are of one or more of the following types: (1) expected service times, (2) queue capacities, and (3) the number of servers at the respective stations. After surveying our previous studies of this kind, we open up consideration of three new problems by presenting some numerical results that should give some insight into the general form of the optimal design.     

Design and implementation of an optimization-based decision support system generator

Decision makers today need to be able to rapidly find good solutions to increasingly complex problems. Optimization-based decision support systems (OBDSSs) can help decision makers to meet this challenge. Building such systems, however, is expensive and time consuming.In this paper we present the design of an OBDSS generator that greatly automates the development process by integrating a model specification with a database, a solver, and a graphical user interface (GUI). The generator automatically creates the database for storing the instantiating data, the GUI, and the solver interface. With this generator, an OR/MS analyst can build an OBDSS faster and more efficiently than using traditional tools. The resulting OBDSSs can be used by decision makers with little knowledge of the underlying OR/MS technology. We also discuss our experience using the generator to develop production planning and truck dispatching OBDSSs for several firms in the context of a three-year R&D project.     

数学机械化进展综述（迎接ICM2002特约文章）

本文介绍数学机械化理论,构造性代数几何,构造性微分代数几何,构造性实代数几何,方程求解,与几何自动推理的主要进展及其若干领域的应用,我们还提出了一些待解决的问题。     

A Descriptive Approach to Multiple-Criteria Decision Making

Certain concepts from multivariate statistical analysis are applied to problems in multiple-criteria decision making. The aim of this approach is to identify basic relationships and conflicts between the available decision alternatives and between criteria. If these aspects can be clearly identified and conveyed to the responsible decision maker, he may well be in a position to make an intelligent selection of a course of action, without the need for formal utility analysis, computation of Pareto optimal sets, etc. Two appropriate multivariate statistical techniques are introduced to illustrate the approach, and each technique is applied to two sample problems.     

Combinatorial systems defined over one- and two-letter alphabets

In this paper we shall investigate some families of decision problems associated with a number of combinatorial systems whose alphabets are restricted to one and two letters. Our purpose is to try to gain a better understanding of the boundaries between classes of combinatorial systems whose decision problems are solvable and those whose decision problems are of any prescribed r.e. many-one degree of unsolvability. We show that, for one-letter alphabets, the decision problems considered here for semi-Thue systems, Thue systems, Post normal systems, Markov algorithms and Post correspondence classes are each solvable. In contrast, for two-letter alphabets, each such family of decision problems represents every r.e. many-one degree of unsolvability.     

Usage of 3D geometry descriptions and transformation techniques in log bucking and curve sawing

Detailed three dimensional models are nowadays frequently used in cross-cutting (bucking) tree stems into logs and in breakdown processes of logs into boards and flitches. Such models require increasingly sophisticated optimization models to assist planners (or automated decision support systems) in decision making. In this paper we develop two techniques that are linked to each other. The first is concerned with establishing high quality analytic approximations of full trees that are needed in full stem bucking applications. One important aspect is that inaccuracies due to measurement error can be reduced. The second is a transformation technique that makes it possible to apply curve sawing on logs in a standard straight sawing system. Numerical results based on real data are presented that support the usefulness of the techniques.     

Developments in linear and integer programming

In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies.     

Clifford 代数,几何计算和几何推理

Clifford代数是一种深深根植于几何学之中的代数系统,被它的创始人称为几何代数．历史上,E．Cartan,R．Brauer,H．Weyl,C．Chevalley等数学大师都曾研究和应用过Clifford代数,对它的发展起了重要作用．近年来,Clifford代数在微分几何、理论物理、经典分析等方面取得了辉煌的成就,是现代理论数学和物理的一个核心工具,并在现代科技的各个领域,如机器人学、信号处理、计算机视觉、计算生物学、量子计算等方面有广泛的应用．本文主要介绍Clifford代数在几何计算和几何推理中的应用．作为一种优秀的描述和计算几何问题的代数语言,Clifford代数对于几何体,几何关系和几何变换有不依赖于坐标的、易于计算的多种表示,因而应用它进行几何自动推理,不仅使困难定理的证明往往变得极为简单,而且能够解决一些著名的公开问题,目前在国际上,几何自动推理已经成为Clifford代数的一个重要应用领域。     

Probabilistic decision graphs for optimization under uncertainty

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions. The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper.     

Probabilistic decision graphs for optimization under uncertainty

This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the methods for solving influence diagrams can scale rather badly in the length of the decision sequence, we present a couple of approaches for calculating approximate solutions. The modeling scope of the influence diagram is limited to so-called symmetric decision problems. This limitation has motivated the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement the frameworks described in the paper.     

Statistical approximations for recourse constrained stochastic programs

The two stage stochastic program with recourse is known to have numerous applications in financial planning, energy modeling, telecommunications systems etc. Notwithstanding its applicability, the two stage stochastic program is limited in its ability to incorporate a decision maker's attitudes towards risk. In this paper we present an extension via the inclusion of a recourse constraint. This results in a convex integrated chance constraint (ICC), which inherits the convexity properties of two stage programs. However, it also inherits some of the difficulties associated with the evaluation of recourse functions. This motivates our study of conditions that may be applicable to algorithms using statistical approximations of such ICC. We present a set of sufficient conditions that these approximations may satisfy in order to assure convergence. Our conditions are satisfied by a wide range of statistical approximations, and we demonstrate that these approximations can be generated within standard algorithmic procedures.This work was supported in part by Grant No. NSF-DDM-9114352 from the National Science Foundation.     

多Agent自动谈判情感决策模型研究

在基于多Agent的自动谈判中,谈判Agent往往采取一个相对固定的策略,使得Agent对动态变化的谈判环境缺乏适应性。根据情感理论的研究成果,本文提出建立情感决策模型来提高Agent的智能程度和适应性。在对谈判Agent情感决策过程进行分析后,建立了一般情况下的情感产生模型和决策模型,并通过在单属性自动谈判环境下,运用具体的情感决策模型和实际数据进行试验,实证了数据模型的有效性。本文的研究成果,可以应用到各种形式的基于多Agent的自动谈判中。     

Modeling recreational systems using optimization techniques and information technologies

Due to intrinsic complexity and sophistication of decision problems in tourism and recreation, respective decision making processes can not be implemented without making use of modern computer technologies and operations research approaches. In this paper, we review research works on modeling recreational systems.     

An extensive-form analysis for comparing fuzzy information systems by means of the worth and quietness of information

Statistical decision problems deal with the choice among several actions, whose consequences depend upon the state of nature, and this choice is usually made on the basis of the outcome of an experiment selected from a collection of experiments whose probability measures depend upon the state. The selection criteria among the experiments are generally based on some measures of the information contained in each experiment about that true state.In this paper we suggest a new selection criterion among the experiments associated with a statistical decision problem, when the experimental outcomes cannot be exactly perceived by the decision maker, but rather the available information from each experimental outcome can be regarded as an element in a fuzzy information system (as defined by Tanaka, Okuda and Asai).In a previous paper we have proposed a method for comparing fuzzy information systems on the basis of the maximization of the ‘oworth of information of a fuzzy park information system’ (Tanaka et al). When the application of such a method leads to indifference between two fuzzy information systems, this indifference can be avoided by applying the criterion in this paper.This selection criterion is an extensive-form analysis which is based on two measures of the information contained in a fuzzy information system about the true state: the ‘worth of information of a fuzzy information system’ and the ‘expected quietness of information of a fuzzy information system’.The suitability of the criterion stated above is corroborated by studying its main properties and contrasting this procedure with other ones making use of different measures of information.     

Identification of distributed systems and the theory of the regularization

The identification problems, i.e., the problems of finding unknown parameters in distributed systems from the observations are very important in modern control theory. The solutions of these identification problems can be obtained by solving the equations of the first kind. However, the solutions are often unstable. In other words, they are not continuously dependent on the data. The regularization or Tihonov's regularization is known as one of the stabilizing algorithms to solve these non well-posed problems. In this paper is studied the regularization method for identification of distributed systems. Several approximation theorems are proved to solve the equations of the first kind. Then, identification problems are reduced to the minimization of quadratic cost functionals by virtue of these theorems. On the other hand, it is known that the statistical methods for identification such as the maximum likelihood lead to the minimization problems of certain quadratic functionals. Comparing these quadratic cost functionals, the relations between the regularization and the statistical methods are discussed. Further, numerical examples are given to show the effectiveness of this method.     

复合凸优化的快速邻近点算法

在大数据时代,随着数据采集手段的不断提升,大规模复合凸优化问题大量的出现在包括统计数据分析,机器与统计学习以及信号与图像处理等应用中.本文针对大规模复合凸优化问题介绍了一类快速邻近点算法.在易计算的近似准则和较弱的平稳性条件下,本文给出了该算法的全局收敛与局部渐近超线性收敛结果.同时,我们设计了基于对偶原理的半光滑牛顿法来高效稳定求解邻近点算法所涉及的重要子问题.最后,本文还讨论了如何通过深入挖掘并利用复合凸优化问题中由非光滑正则函数所诱导的非光滑二阶信息来极大减少半光滑牛顿算法中求解牛顿线性系统所需的工作量,从而进一步加速邻近点算法.     

Algorithms for solving discrete optimal control problems with infinite time horizon and determining minimal mean cost cycles in a directed graph as decision support tool

Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon for such systems are formulated. We introduce a certain graph-theoretic structure to model the transitions of the dynamical system. Algorithms for finding the optimal stationary control parameters are presented. Furthermore, we determine the optimal mean cost cycles. This approach can be used as a decision support strategy within such a class of problems; especially so-called multilayered decision problems which occur within environmental emission trading procedures can be modelled by such an approach.