| The available algorithms for global optimization are studied and compared. The covering method, the controlled random search, and the simulated annealing methods are implemented and evaluated. None of them was suitable for global optimization of structural systems.;Next, the study turns to the problem of finding feasible points for constrained problems. Some optimization algorithms need a feasible starting point. Also, in some instances it is important to know if the problem has a feasible domain. The penalty and the primal approaches are studied and several variations from both types are implemented and tested. The tests show that the primal approach requires less computational effort than the penalty approach. Also, a few functionals for the penalty approach can prove useful. However, none of the methods of either approach is able to determine a feasible point for all the test problems. The study reveals that the problem of finding feasible points is also a global optimization problem.;Next the study focuses on developing new algorithms for global optimization of nonlinear constrained problems that are suitable for optimization of structural systems. The Domain Elimination method is developed and the Zooming method is enhanced. They are implemented and tested on a set of standard mathematical test problems and a set of structural optimization problems. The six structures tested included a 200-member structure and a 2-bay-6-story frame. Twenty-eight test problems are devised and solved. The problems include a case with 116 design variables and 1275 constraints. Eight local minimum solutions are found for this problem.;Structural optimization problems fall into the class of nonlinear constrained problems and are well posed for most of the cases. The study shows that many test problems have multiple local minimum solutions. The solutions may have different cost values and thus it is useful to find global solutions. When many local solutions have the same cost value, they provide flexibility to the designer. The study also shows that characteristics of local solutions depend on the specific problem: element cross sectional shape, material, constraints imposed, and the way the structure is modeled (e.g., as a truss or as a rigid frame). |
