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In this thesis, the classical methods of structural optimization were studied and compared. After a comprehensive study on different methods of structural optimization, a reduced number of methods were selected in order to be used in this research. Exterior penalty function method, linear and quadratic extended penalty function methods were the selected constrained optimization methods. For unconstrained optimization, univariate method, Powell method, steepest descent method, Fletcher-Reeves method, and quasi-Newton methods of DFP and BFGS were used. And from different one-dimensional search methods studied, we used the golden section method. The structures which were optimally designed by... 

In minimum cut problem we aim at finding a set of edges with minimum overall cost possible, such that removing them would separate two specific vertices, source and sink. This problem has been studied thoroughly, however the available algorithms were not proven to be time-wise optimal. Nowadays, planar graphs have attracted more attention because of their applications in cities and countries map. Moreover,their characteristics and properties, make some problems easier to solve in planar case. In this thesis, we will have a survey on algorithms for minimum cut on planar graphs. Our motivation to choose these algorithms is the balance between how easily they could be implemented and how fast...