Problem solving in architectural design

This thesis is presented in two parts. The first part is an attempt to set out a framework of factors influencing the problem solving stage of the architectural design process. The discussion covers the nature of architectural problems and some of the main ways in which they differ from other types of design problems. The structure of constraints that both the problem and the architect impose upon solutions are seen as of great importance in defining the type of design problem solving situation. The problem solver, or architect, is then studied. The literature of the psychology of thinking is surveyed for relevant work . All of the traditional schools of psychology are found wanting in terms of providing a comprehensive theory of thinking. Various types of thinking are examined, particularly structural and productive thought, for their relevance to design problem solving. Finally some reported common traits of architects are briefly reviewed. The second section is a report of u~o main experiments which model some aspects of architectural design problem solving. The first experiment examines the way in which architects come to understand the structure of their problems. The performances of first and final year architectural students are compared with those of postgraduate science students and sixth form pupils. On the whole these groups show significantly different results and also different cognitive strategies. The second experiment poses design problems which involve both subjective and objective criteria, and examines the way in which final year architectural students are able to relate the different types of constraint produced. In the final section the significance of all the results is suggested. Some educational and methodological implications are discussed and some further experiments and investigations are proposed.

A systems and cybernetic perspective on complex problem solving

This thesis is concerned with Organisational Problem Solving. The work reflects the complexities of organisational problem situations and the eclectic approach that has been necessary to gain an understanding of the processes involved. The thesis is structured into three main parts. Part I describes the author's understanding of problems and suitable approaches. Chapter 2 identifies the Transcendental Realist (TR) view of science (Harre 1970, Bhaskar 1975) as the best general framework for identifying suitable approaches to complex organisational problems. Chapter 3 discusses the relationship between Checkland's methodology (1972) and TR. The need to generate iconic (explanatory) models of the problem situation is identified and the ability of viable system modelling to supplement the modelling stage of the methodology is explored in Chapter 4. Chapter 5 builds further on the methodology to produce an original iconic model of the methodological process. The model characterises the mechanisms of organisational problem situations as well as desirable procedural steps. The Weltanschauungen (W's) or "world views" of key actors is recognised as central to the mechanisms involved. Part II describes the experience which prompted the theoretical investigation. Chapter 6 describes the first year of the project. The success of this stage is attributed to the predominance of a single W. Chapter 7 describes the changes in the organisation which made the remaining phase of the project difficult. These difficulties are attributed to a failure to recognise the importance of differing W's. Part III revisits the theoretical and organisational issues. Chapter 8 identifies a range of techniques embodying W's which are compatible with .the framework of Part I and which might usefully supplement it. Chapter 9 characterises possible W's in the sponsoring organisation. Throughout the work, an attempt 1s made to reflect the process as well as the product of the author's leaving.

Minority influence and optimal problem-solving

An analogous thinking task was used to test Nemeth's Convergent–Divergent theory of majority and minority influence. Participants read a (base) problem and one of three solutions (one of which is considered the ‘best' solution). They then generated solutions to a second (target) problem which shared similar structural features to the first problem. Due to the similarities between problems, the solution given to the first problem can be used as an analogy in solving the second. In contrast to Nemeth's theory, when the solution to the base problem was endorsed by a numerical majority there was not an increase in analogy-transfer in solving the target problem. However, in support of Nemeth's theory, when the base solution was supported by a numerical minority then the participants were more likely to generate the ‘best' solution to the target problem regardless of which base solution they were given. Copyright © 1999 John Wiley & Sons, Ltd.

Towards a web-based progressive handwriting recognition environment for mathematical problem solving

The emergence of pen-based mobile devices such as PDAs and tablet PCs provides a new way to input mathematical expressions to computer by using handwriting which is much more natural and efficient for entering mathematics. This paper proposes a web-based handwriting mathematics system, called WebMath, for supporting mathematical problem solving. The proposed WebMath system is based on client-server architecture. It comprises four major components: a standard web server, handwriting mathematical expression editor, computation engine and web browser with Ajax-based communicator. The handwriting mathematical expression editor adopts a progressive recognition approach for dynamic recognition of handwritten mathematical expressions. The computation engine supports mathematical functions such as algebraic simplification and factorization, and integration and differentiation. The web browser provides a user-friendly interface for accessing the system using advanced Ajax-based communication. In this paper, we describe the different components of the WebMath system and its performance analysis.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Algorithms for solving large random graphs

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Application of a problem-solving methodology to software usability

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An iterative procedure for solving a Cauchy problem for second order elliptic equations

An iterative method for reconstruction of solutions to second order elliptic equations by Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the elliptic operator and its adjoint. The convergence proof of this method in a weighted L2 space is included. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An Effective Method for Constructing Data Structures Solving an Array Maintenance Problem

In this paper a constructive method of data structures solving an array maintenance problem is offered. These data structures are defined in terms of a family of digraphs which have previously been defined, representing solutions for this problem. We present as well a prototype of the method in Haskell.

Solving a Direct Marketing Problem by Three Types of ARTMAP Neural Networks

An important task for a direct mailing company is to detect potential customers in order to avoid unnecessary and unwanted mailing. This paper describes a non-linear method to predict profiles of potential customers using dARTMAP, ARTMAP-IC, and Fuzzy ARTMAP neural networks. The paper discusses advantages of the proposed approaches over similar techniques based on MLP neural networks.

An UML Project of a Task-Oriented Environment for Teaching Algorithms

This paper continues the author’s team research on development, implementation, and experimentation of a task-oriented environment for teaching and learning algorithms. This environment is a part of a large-scale environment for course teaching in different domains. The paper deals only with the UML project of the teaching team’s side of the environment.. The implementation of the project ideas is demonstrated on a WINDOWS-based environment’s prototype.

Classification of Global Illumination Algorithms

This article describes and classifies various approaches for solving the global illumination problem. The classification aims to show the similarities between different types of algorithms. We introduce the concept of Light Manager, as a central element and mediator between illumination algorithms in a heterogeneous environment of a graphical system. We present results and analysis of the implementation of the described ideas.