dc.contributor.author Qiao, Tian dc.date.accessioned 2015-12-10 19:38:13 (GMT) dc.date.available 2015-12-10 19:38:13 (GMT) dc.date.issued 2015-12-10 dc.date.submitted 2015-12-08 dc.identifier.uri http://hdl.handle.net/10012/10043 dc.description.abstract In this thesis, we describe the design of tubular network systems that must occupy, as best as possible, regions that demonstrate some kind of longitudinal symmetry. In order to simplify the problem, the region of the container is discretized into a sequence of prism blocks . The problem is decomposed into two parts: 1. Pack tubes in these blocks, 2. Connect these packed tubes at the ends of each block. en In the first part, since each block is prismatic, the problem of packing tubes is equivalent to the packing of circles in the cross-sectional area of each block. In this case, we assume that the cross-sectional area of each block is a polygon. We investigate a series of algorithms to pack circles, including a rather naive approach as well as the GGL [2] circle packing algorithm. Then we modify the GGL algorithm to pack circles in regions that are more complicated. Based on the GGL, we will also invent new algorithm that provides more satisfactory packing results. In the second part, we connect the packed tubes from Part one to form a complete network system. First we consider the simplest case -- constructing a tubular system in a container with no variations, i.e., a single block. We solve this problem in terms of the travelling salesman problem (TSP) which is a classical problem in discrete optimization. For containers with varying cross-sections, we connect tubes at end of each block independently instead of constructing a complete system. This problem can be reduced to a perfect matching (PM) problem at each end. We apply similar integer programming algorithms to both perfect matching problem and TSP. However, the design of complete tubular network system in a container exhibiting longitudinal symmetry remains an open problem for future work. dc.language.iso en en dc.publisher University of Waterloo en dc.subject tubular network en dc.subject Circle packing en dc.subject Computational geometry en dc.subject Combinatorial optimization en dc.subject TSP en dc.subject Matching en dc.subject Integer Programming en dc.title Design of Tubular Network Systems Using Circle Packing and Discrete Optimization en dc.type Master Thesis en dc.pending false uws-etd.degree.department Applied Mathematics en uws-etd.degree.discipline Applied Mathematics en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Vrscay, Edward uws.contributor.advisor Mendivil, Franklin uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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