Decision-making algorithms in geometric modelling

Many of the applications of geometric modelling are concerned with the computation of well-defined properties of the model. The applications which have received less attention are those which address questions to which there is no unique answer. This thesis describes such an application: the automatic production of a dimensioned engineering drawing. One distinctive feature of this operation is the requirement for sophisticated decision-making algorithms at each stage in the processing of the geometric model. Hence, the thesis is focussed upon the design, development and implementation of such algorithms. Various techniques for geometric modelling are briefly examined and then details are given of the modelling package that was developed for this project, The principles of orthographic projection and dimensioning are treated and some published work on the theory of dimensioning is examined. A new theoretical approach to dimensioning is presented and discussed. The existing body of knowledge on decision-making is sampled and the author then shows how methods which were originally developed for management decisions may be adapted to serve the purposes of this project. The remainder of the thesis is devoted to reports on the development of decision-making algorithms for orthographic view selection, sectioning and crosshatching, the preparation of orthographic views with essential hidden detail, and two approaches to the actual insertion of dimension lines and text. The thesis concludes that the theories of decision-making can be applied to work of this kind. It may be possible to generate computer solutions that are closer to the optimum than some man-made dimensioning schemes. Further work on important details is required before a commercially acceptable package could be produced.

Computer aided geometric design of form-rolls for NC manufacture

Conventional methods of form-roll design and manufacture for Cold Roll-Forming of thin-walled metal sections have been entirely manual, time consuming and prone to errors, resulting in inefficiency and high production costs. With the use of computers, lead time can be significantly improved, particularly for those aspects involving routine but tedious human decisions and actions. This thesis describes the development of computer aided tools for producing form-roll designs for NC manufacture in the CAD/CAM environment. The work was undertaken to modernise the existing activity of a company manufacturing thin-walled sections. The investigated areas of the activity, including the design and drafting of the finished section, the flower patterns, the 10 to 1 templates, and the rolls complete with pinch-difference surfaces, side-rolls and extension-contours, have been successfully computerised by software development . Data generated by the developed software can be further processed for roll manufacturing using NC lathes. The software has been specially designed for portability to facilitate its implementation on different computers. The Opening-Radii method of forming was introduced as a subsitute to the conventional method for better forming. Most of the essential aspects in roll design have been successfully incorporated in the software. With computerisation, extensive standardisation in existing roll design practices and the use of more reliable and scientifically-based methods have been achieved. Satisfactory and beneficial results have also been obtained by the company in using the software through a terminal linked to the University by a GPO line. Both lead time and productivity in roll design and manufacture have been significantly improved. It is therefore concluded that computerisation in the design of form-rolls for automation by software development is viable. The work also demonstrated the promising nature of the CAD/CAM approach.

The geometric correction and registration of airborne line-scanned imagery for temporal thermal studies

This thesis begins by providing a review of techniques for interpreting the thermal response at the earth's surface acquired using remote sensing technology. Historic limitations in the precision with which imagery acquired from airborne platforms can be geometrically corrected and co-registered has meant that relatively little work has been carried out examining the diurnal variation of surface temperature over wide regions. Although emerging remote sensing systems provide the potential to register temporal image data within satisfactory levels of accuracy, this technology is still not widely available and does not address the issue of historic data sets which cannot be rectified using conventional parametric approaches. In overcoming these problems, the second part of this thesis describes the development of an alternative approach for rectifying airborne line-scanned imagery. The underlying assumption that scan lines within the imagery are straight greatly reduces the number of ground control points required to describe the image geometry. Furthermore, the use of pattern matching procedures to identify geometric disparities between raw line-scanned imagery and corresponding aerial photography enables the correction procedure to be almost fully automated. By reconstructing the raw image data on a truly line-by-line basis, it is possible to register the airborne line-scanned imagery to the aerial photography with an average accuracy of better than one pixel. Providing corresponding aerial photography is available, this approach can be applied in the absence of platform altitude information allowing multi-temporal data sets to be corrected and registered.

Using min-sum loopy belief propagation for decentralised supply chain formation

Modern business trends such as agile manufacturing and virtual corporations require high levels of flexibility and responsiveness to consumer demand, and require the ability to quickly and efficiently select trading partners. Automated computational techniques for supply chain formation have the potential to provide significant advantages in terms of speed and efficiency over the traditional manual approach to partner selection. Automated supply chain formation is the process of determining the participants within a supply chain and the terms of the exchanges made between these participants. In this thesis we present an automated technique for supply chain formation based upon the min-sum loopy belief propagation algorithm (LBP). LBP is a decentralised and distributed message-passing algorithm which allows participants to share their beliefs about the optimal structure of the supply chain based upon their costs, capabilities and requirements. We propose a novel framework for the application of LBP to the existing state-of-the-art case of the decentralised supply chain formation problem, and extend this framework to allow for application to further novel and established problem cases. Specifically, the contributions made by this thesis are: • A novel framework to allow for the application of LBP to the decentralised supply chain formation scenario investigated using the current state-of-the-art approach. Our experimental analysis indicates that LBP is able to match or outperform this approach for the vast majority of problem instances tested. • A new solution goal for supply chain formation in which economically motivated producers aim to maximise their profits by intelligently altering their profit margins. We propose a rational pricing strategy that allows producers to earn significantly greater profits than a comparable LBP-based profitmaking approach. • An LBP-based framework which allows the algorithm to be used to solve supply chain formation problems in which goods are exchanged in multiple units, a first for a fully decentralised technique. As well as multiple-unit exchanges, we also model in this scenario realistic constraints such as factory capacities and input-to-output ratios. LBP continues to be able to match or outperform an extended version of the existing state-of-the-art approach in this scenario. • Introduction of a dynamic supply chain formation scenario in which participants are able to alter their properties or to enter or leave the process at any time. Our results suggest that LBP is able to deal easily with individual occurences of these alterations and that performance degrades gracefully when they occur in larger numbers.

Decentralized supply chain formation using max-sum loopy belief propagation

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.

Geometric spectral accuracy of airborne remote sensing

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Using the max-sum algorithm for supply chain emergence in dynamic multiunit environments

Supply chain formation (SCF) is the process of determining the set of participants and exchange relationships within a network with the goal of setting up a supply chain that meets some predefined social objective. Many proposed solutions for the SCF problem rely on centralized computation, which presents a single point of failure and can also lead to problems with scalability. Decentralized techniques that aid supply chain emergence offer a more robust and scalable approach by allowing participants to deliberate between themselves about the structure of the optimal supply chain. Current decentralized supply chain emergence mechanisms are only able to deal with simplistic scenarios in which goods are produced and traded in single units only and without taking into account production capacities or input-output ratios other than 1:1. In this paper, we demonstrate the performance of a graphical inference technique, max-sum loopy belief propagation (LBP), in a complex multiunit unit supply chain emergence scenario which models additional constraints such as production capacities and input-to-output ratios. We also provide results demonstrating the performance of LBP in dynamic environments, where the properties and composition of participants are altered as the algorithm is running. Our results suggest that max-sum LBP produces consistently strong solutions on a variety of network structures in a multiunit problem scenario, and that performance tends not to be affected by on-the-fly changes to the properties or composition of participants.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

Triples of Positive Integers with the same Sum and the same Product

It is proved that for every k there exist k triples of positive integers with the same sum and the same product.

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.