A rough set-based incremental approach for learning knowledge in dynamic incomplete information systems

With the rapid growth of data sets nowadays, the object sets in an information system may evolve in time when new information arrives. In order to deal with the missing data and incomplete information in real decision problems, this paper presents a matrix based incremental approach in dynamic incomplete information systems. Three matrices (support matrix, accuracy matrix and coverage matrix) under four different extended relations (tolerance relation, similarity relation, limited tolerance relation and characteristic relation), are introduced to incomplete information systems for inducing knowledge dynamically. An illustration shows the procedure of the proposed method for knowledge updating. Extensive experimental evaluations on nine UCI datasets and a big dataset with millions of records validate the feasibility of our proposed approach.     

Parameter estimation using dynamic optimization in limited nutrient-consumer hybrid dynamical systems

A limited nutrient consumer hybrid system which exhibits rich dynamics such as stability, instability and oscillatory characteristics is considered. The parameters that strongly influence the behavior of the system are identified and are estimated using the techniques of dynamic optimization. Two independent bio-control mechanisms are introduced into the system when the basic system exhibits instability characteristics. Values of the parameters representing these mechanisms are estimated at which the system stabilizes. Examples and simulations illustrate the main results.     

Nonlinear dynamic systems design based on the optimization of the domain of attraction

In this paper an optimization-based methodology for the design of the operating equilibrium of a nonlinear dynamic system based on a measure of the extension of its domain of attraction is proposed. The approach consists in maximizing the radius of a ball in the state space contained in the region of negative definiteness of the time derivative of a quadratic Lyapunov function, using a two level optimization strategy.A deterministic global optimization problem is solved at the inner level to ensure proper estimation of the domain of attraction for each feasible realization of the design variables which are optimized at the outer level. In order to cope with the non-differentiable nature of the inner problem, a stochastic algorithm is applied to manipulate the design variables at the outer level.The methodology is applied to several examples to illustrate different aspects of the approach.     

Automatic clustering of business processes in business systems planning

In this paper, we apply the technique of hierarchical clustering to business processes identified in business systems planning (BSP) which is an important methodology in information systems planning. A measure based on notions of cohesion and coupling is proposed as a guidance in searching for optimal number of clusters of business processes. By optimality, we mean that the net cohesion is maximized and net coupling is minimized. Moreover, we show that optimal number of clusters occurs at level of 0.5 in the hierarchy of partitions.     

Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation

We propose a family of retrospective optimization (RO) algorithms for optimizing stochastic systems with both integer and continuous decision variables. The algorithms are continuous search procedures embedded in a RO framework using dynamic simplex interpolation (RODSI). By decreasing dimensions (corresponding to the continuous variables) of simplex, the retrospective solutions become closer to an optimizer of the objective function. We present convergence results of RODSI algorithms for stochastic “convex” systems. Numerical results show that a simple implementation of RODSI algorithms significantly outperforms some random search algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).     

Sensitivity analysis in dynamic optimization

To find the optimal control of chemical processes, Pontryagin's minimum principle can be used. In practice, however, one is not only interested in the optimal solution, which satisfies the restrictions on the control, the initial and terminal conditions, and the process parameters. It is also important to known how the optimal control and the minimum value of the objective function change, due to small variations in all the restrictions and the parameters. It is shown how to determine the effect of these variations directly from the optimal solution. This saves computer time, compared with the more traditional sensitivity analysis based on computing the optimal control for every single variation considered. The theory is applied to a chemical process.This paper is based on the author's doctoral study performed at Akzo Research Laboratories, Department of Applied Mathematics, Arnhem, Holland.     

Second-variation methods in dynamic optimization

An entire class of rapid-convergence algorithms, called second-variation methods, is developed for the solution of dynamic optimization problems. Several well-known numerical optimization techniques included in this class are developed from a unified point of view. The generalized Riccati transformation can be applied in conjunction with any second-variation method. This fact is demonstrated for the Newton-Raphson or quasilinearization technique.This work was supported by the National Research Council of Canada under Grant No. 67-3134 and is based on investigations described in more detail in Ref. 1.     

Adding intelligent assessment: a Java framework for integrating dynamic mathematical software components into interactive learning activities

Dynamic geometry constructions are commonly embedded into hypertext documents to create interactive exercises. In practice, this approach often constrains the possibilities of creating complex learning environments due to technical limitations. A Java-based framework for the development of interactive learning environments based on exploration laboratories containing dynamic geometry applets is presented. Dynamic geometry software (DGS) applets of different types can be integrated into the same laboratory and interact with each other. Within our framework, interactive exercises based on DGS constructions can be enriched with automated and semi-automated assessment algorithms. Students?? learning processes can be recorded using capture-and-replay software. Two sample learning environments based on the framework are presented.     

An approach to the solution of the vector optimization problem of dynamic systems

The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.Paper prepared during the author's visiting period at the Centro di Studio dei Sistemi di Controllo e Calcolo Automatici, Consiglio Nazionale delle Richerche, Roma, Italia; at Istituto di Mathematica Applicata; and at the Sezione Automatica, Informatica, e Sistemistica, Instituto di Elettronica, Facolta di Ingegneria, Universita di Firenze, Firenze, Italia.     

Satisfactory solutions approach to parameter optimization of dynamic systems with vector performance index

A novel approach to parameter optimization of large dynamic systems using vector performance index is described. The approach entails characterizing and determining a set of satisfactory solutions to the multiobjective optimization problem. The satisfactory solutions are defined with respect to a prespecified and satisfactory set of bounds on the indices. A theoretical basis is provided to obtain a compact and connected set of satisfactory solutions in the parameter space. Compactness and connectedness are essential requirements, since they assure a range of values for the parameters. An expedient numerical technique for determining the range of satisfactory values for the parameters is illustrated with an example. The satisfactory solutions approach provides a basis for designing a system with multiple requirements when all of them cannot be formulated in the framework of a composite vector index problem.This work constitutes part of the first author's doctoral dissertation in the Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, Chicago, Illinois. It was supported in part by the National Science Foundation, Grant No. ENG-76-09930. The first author is indebted to Drs. A. C. Raptis and T. P. Mulcahey of Argonne National Laboratory for their support and encouragement.     

Complementarity systems in optimization

Complementarity systems consist of ordinary differential equations coupled to complementarity conditions. They form a class of nonsmooth dynamical systems that is of use in mechanical and electrical engineering as well as in optimization and in other fields. The paper illustrates how complementarity systems arise in mathematical programming by means of a number of examples of various nature. This is followed by a brief survey of the results that are available concerning existence, uniqueness, and generation of solutions. The emphasis in this paper is on linear complementarity systems.     

Interior variations in dynamic optimization problems

In this article, the author examines the properties of interior variations and indicates how to use them in order to formulate the necessary condition of optimality for problems of dynamic optimization, in particular, problems of variational calculus and of optimal control. For optimal control problems, an optimization technique based on interior variations and polynomial approximations is suggested and then illustrated by an explanatory example.     

Scaling knowledge: how does knowledge accrue in systems?

This paper addresses the important and somewhat contentious matter of how knowledge accrues in a system. The matter has at its heart the establishment of a scaling function for knowledge (as distinct from the scaling used for information) which is related to the density of the knowledge structure at any point in the system. We commence with a discussion of whether it is possible at all to scale knowledge, dispensing with any concepts of knowledge as a simple finite resource and making a distinction between the establishment of a metric and the act of measurement itself. First, we draw on the Shannon–Weaver (H) measure to establish how knowledge can be seen as contributing to the partitioning of message sets under the H-measure. This establishes how knowledge contributes to the quantity of information held within a system when viewed as a meta-structure for that information. Second, we build on the idea of knowledge as an endemic property of a structure of interconnections between concepts. We observe that knowledge content can be dense both in structures that are highly interconnected deploying a modest number of concepts and in those where the interconnections are more sparse but where the number of concepts deployed is high. A scaling function exhibiting appropriate properties is then proposed. It can be seen that the scaling associated with knowledge as meta-information and the scaling deriving from the interconnectivity point of view are connected. This scaling function is particularly useful in three ways. Firstly, it outlines the properties of knowledge itself which can be used as criteria for future knowledge-based research. Its application in practice creates the ability to identify areas of knowledge concentration within a system. Finally, this identification of knowledge ‘hotspots’ can be used to direct the investment of resources for the management of knowledge and it provides an indication of the appropriate approach for the management of this knowledge. We make some observations on the limitations of the approach, on its potential as a basis for managerial action (particularly in Knowledge Management) and on its relevance and applicability to OR practice (particularly in respect of systems approaches to knowledge mapping). Lastly, we offer a view on the likely line of research which may result from this work.     

RETRACTED ARTICLE: Blockchain-based intelligent contract for factoring business in supply chains

Factoring business, an important aspect in the supply chain finance field, has significant potential in adopting blockchain-based intelligent contract technology. Based on the existing theories of factoring business in supply chains, this paper conducts a coupling analysis between blockchain technology and supply chain factoring business. Specifically, we propose the application scenarios of blockchain-based intelligent contract technology in the supply chain factoring business from three aspects: the division and transfer of creditors’ rights certificate, the factoring financing of upstream suppliers, and the due payment of core enterprises, and elaborate their implementation processes. Furthermore, from a game theoretical perspective, we analyze the mechanism of the key technology implementation of the intelligent contract to verify whether the nodes on the blockchains will follow the relevant protocols to automatically execute them. Finally, we conduct a three-way game analysis of the supply chain factor financing process and obtain an equilibrium solution based on the principle of utility maximization, which highlights the optimization effect of the intelligent contract technology on the decision-making behavior of individual entities in the supply chain.

     

Chaos in discrete learning systems

Departing from the customary view of the sigmoid thresholding functions as smooth nonlinearities introduced into multilayer perceptron networks to enable continuously differentiable gradient descents toward optimal solutions minimizing some error norm, here a different more fundamental point of view is advanced: the intrinsic local dynamics of the network become that of the quadratic map of the chaos theory. This new insight aids understanding of important supervised learning algorithms such as the widely used Backpropagation scheme.     

Fluctuations in one-dimensional dynamic systems

We consider one-dimensional dynamic systems with random fluctuations that are encountered in applications, analyze solutions, and investigate the stability of stationary points. Translated fromDinamicheskie Sistemy. Vol. 12, pp. 96–100, 1993.     

Bifurcations in gradient dynamic systems

Bifurcations of phase portraits are investigated in typical three- and four-parameter families of gradient vector fields. A complete topological classification is developed for the three-parameter case. It includes two bifurcations that are missing from the list of Thom's elementary catastrophes.Translated from Itogi Nauki i Tekhniki, Seriya Sovermennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 33, pp. 113–155, 1988.