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UBC Theses and Dissertations

A level set global optimization method for nonlinear engineering problems Yassien, Hassen Ali


The mathematical equations used in civil engineering design procedures are predomi nantly nonlinear. Most civil engineering design optimization problems would therefore require the use of nonlinear programming (NLP) techniques for their solution. Those NLP packages with the ability to handle practical sizes of problems, and have been available on mainframe computers for many years, are only now becoming available on microcomputers. On top of this, these existing NLP techniques, which are dominated by the gradient methods, do not guarantee global solutions. As a consequence suitable optimization methods for civil engineering design are not being enjoyed by practitioners. In this thesis, the level set optimization method, whose theory was initially presented in “Integral global optimization” by [Chew & Zheng, 1988] was further developed to address, in particular, practical engineering problems. It was found that Level Set Pro gramming (LSP), offers a viable alternative to existing nonlinear optimization methods. While LSP does not radically alter the computational effort involved it has some unique characteristics which appear to be significant from the engineering users point of view. LSP which is classified as a direct search method of optimization, utilizes the set theory concept of a level set. It uses estimates of moments of the objective function values at the confirmed points within a level set to control the search advance and as a measure of convergence on the global optimum. The reliability and efficiency of LSP was verified by comparing its results with pub lished results for both mathematical and engineering test problems. In addition to the published test problems, a new parametrically adjustable mathematical test problem was designed to test global optimization methods in general and to explore the strengths and weaknesses of LSP in particular. Experience with these test problems showed that LSP gave similar results to those cited in the literature as well as improved results or more complete sets of global solution. The large number of solutions developed at each iteration of LSP permits meaningful graphical displays of the progressive reduction in the level set boundaries as the global solution is approached. Other displays were also found to provide insights into the solution process and a basis for diagnosing search difficulties.

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