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Rapid Mathematical Programming

Please always quote using this URN: urn:nbn:de:0297-zib-8346
  • The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances.

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Author:Thorsten KochORCiD
Document Type:Doctoral Thesis
Tag:Location Planning in Telecommunications; Mixed Integer Programming; Modelling Languages; Steiner Tree Packing in Graphs; UMTS
MSC-Classification:68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Nxx Software / 68N19 Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B18 Communication networks [See also 68M10, 94A05]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C27 Combinatorial optimization
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C90 Applications of mathematical programming
Granting Institution:Technische Universität Berlin
Date of first Publication:2005/02/16
Series (Serial Number):ZIB-Report (04-58)
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