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Ph.D. – Ant Colony Optimization Based Simulation of 3D Automatic Hose/Pipe Routing, Department of Electronic and Computer Engineering, College of Engineering, Design and Physical Sciences, Brunel University, UK (2009)
Abstract: This thesis focuses on applying one of the rapidly growing non-deterministic optimization algorithms, the ant colony algorithm, for simulating automatic hose/pipe routing with several conflicting objectives. Within the thesis, methods have been developed and applied to single objective hose routing, multi-objective hose routing and multi-hose routing. The use of simulation and optimization in engineering design has been widely applied in all fields of engineering as the computational capabilities of computers has increased and improved. As a result of this, the application of non-deterministic optimization techniques such as genetic algorithms, simulated annealing algorithms, ant colony algorithms, etc. has increased dramatically resulting in vast improvements in the design process. Initially, two versions of ant colony algorithms have been developed based on, respectively, a random network and a grid network for a single objective (minimizing the length of the hoses) and avoiding obstacles in the CAD model. While applying ant colony algorithms for the simulation of hose routing, two modifications have been proposed for reducing the size of the search space and avoiding the stagnation problem. Hose routing problems often consist of several conflicting or trade-off objectives. In classical approaches, in many cases, multiple objectives are aggregated into one single objective function and optimization is then treated as a single-objective optimization problem. In this thesis two versions of ant colony algorithms are presented for multi-hose routing with two conflicting objectives: minimizing the total length of the hoses and maximizing the total shared length (bundle length). In this case the two objectives are aggregated into a single objective. The current state-of-the-art approach for handling multi-objective design problems is to employ the concept of Pareto optimality. Within this thesis a new Pareto-based general purpose ant colony algorithm (PSACO) is proposed and applied to a multi-objective hose routing problem that consists of the following objectives: total length of the hoses between the start and the end locations, number of bends, and angles of bends. The proposed method is capable of handling any number of objectives and uses a single pheromone matrix for all the objectives. The domination concept is used for updating the pheromone matrix. Among the currently available multi-objective ant colony optimization (MOACO) algorithms, P-ACO generates very good solutions in the central part of the Pareto front and hence the proposed algorithm is compared with P-ACO. A new term is added to the random proportional rule of both of the algorithms (PSACO and P-ACO) to attract ants towards edges that make angles close to the prespecified angles of bends. A refinement algorithm is also suggested for searching an acceptable solution after the completion of searching the entire search space. For all of the simulations, the STL format (tessellated format) for the obstacles is used in the algorithm instead of the original shapes of the obstacles. This STL format is passed to the C++ library RAPID for collision detection. As a result of using this format, the algorithms can handle free-form obstacles and the algorithms are not restricted to a particular software package.
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M.Sc. (Computer Science) – Designing Sinhala Characters using Bézier Curves and B-Spline Curves, Department of Computer Science & Information Management, Asian Institute of Technology (AIT), Bangkok, Thailand (2002)
Abstract: In character design in the computer industry, the mathematical models like Bézier curves and B-Spline curves play a very important role. Earlier characters were stored in the bitmaps, and the designer had to keep a separate file for each size of each font. But after Adobe introduced the PostScript fonts into the market, the fonts were represented by Bézier curves and those fonts can be scalable to any size. Further, this needs only one or two files for storing the entire font type. Existing methods of representing characters and theoretical background about Bézier curves and B-Spline curves are reviewed in this study. Further, we have developed a Visual Basic program called “Fontica” for designing characters by using Bézier and B-Spline curves. With the help of this new program, we could design 10 Sinhala (my mother language) characters. In addition, we have proposed a new technique for approximating the degree reduction of Bézier curves. This approximation appears to perform satisfactorily.
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M.Sc. (Industrial Mathematics) – Improved Newton’s Method for Solving Nonlinear Equations, Department of Mathematics, University of Sri Jayewardenepura, Sri Lanka (1998)
Abstract: An iterative scheme is introduced improving Newton’s method which is widely used for solving nonlinear equations. The method is developed for both functions of one variable and two variables. The proposed scheme replaces the rectangular approximation of the indefinite integral involved in Newton’s Method by a trapezium. It is shown that the order of convergence of the new method is at least three for functions of one variable. Computational results overwhelmingly support this theory and the computational order of convergence is even more than three for certain functions. Algorithms constructed were implemented by using the high-level computer language Turbo Pascal (Ver. 7)
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