Design optimization of structures has become an important method to study and develop these days. Due to the fact that the world's population is increasing, and the worlds' resources are decreasing. An optimum design algorithm is a useful tool that can help to minimize the weight of a structure. Over the last four decades, several number of algorithms have been developed to solve engineering optimization problems, for example, metaheuristic algorithms. An example of metaheuristic algorithms is the Harmony Search algorithm (HS). HS algorithms make use of the analogy between the performance process of natural music and searching for solutions to optimization problems. In this research, the HS was applied on the College of Engineering Building at Temple University Main Campus in Philadelphia, PA. The HS algorithm searches for minimum cross-sectional areas that leads to find optimal steel sizes considering design constrains such as: stress, deflection, and lateral displacement limitations. The HS algorithm obtained lighter weight of steel frames by selecting a suitable steel section from the American Institute of Steel Construction (AISC) and by following the specification of Allowable Stress Design method (ASD). The results show that HS yielded lighter steel moment frames with approximately 20% weight reduction. Keywords: Harmony Search Algorithm, Steel Moment Frame, Optimization. / Civil Engineering

Harmony search method based optimum design algorithm is presented for the grillage systems. This numerical optimization technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. For instance, jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design algorithm considers the displacement and strength constraints which are implemented from LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction). It selects the appropriate W (Wide Flange)-sections for the transverse and longitudinal beams of the grillage system among 272 discrete W-section designations given in LRFD-AISC so that the design limitations described in LRFD are satisfied and the weight of the system is confined to be minimal. Number of design examples is considered to demonstrate the efficiency of the algorithm presented.

Harmony search method based optimum topology design algorithm is presented for single layer lamella domes. The harmony search method is a numerical optimization technique developed recently that imitates the musical performance process which takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The optimum design algorithm developed imposes the behavioral and performance constraints in accordance with LRFD-AISC. The optimum number of rings, the height of the crown and the tubular cross-sectional designations for dome members are treated as design variables. The member grouping is allowed so that the same section can be adopted for each group. The design algorithm developed has a routine that build the data for the geometry of the dome automatically that covers the numbering of joints, and member incidences, and the computation of the coordinates of joints. Due to the slenderness and the presence of imperfections in dome structures it is necessary to consider the geometric nonlinearity in the prediction of their response under the external loading. Design examples are considered to demonstrate the efficiency of the algorithm presented.

In this thesis, the optimum design algorithm is presented for reinforced concrete special moment frames. The objective function is considered as the total cost of reinforced concrete frame which includes the cost of concrete, formwork and reinforcing steel bars. The cost of any component is inclusive of material, fabrication and labor. The design variables in beams are selected as the width and the depth of beams in each span, the diameter and the number of longitudinal reinforcement bars along the span and supports. In columns the width and the depth of the column section, the number and the diameter of bars in x and y directions are selected as design variables. The column section database is prepared which includes the width and height of column section, the diameter and the number of reinforcing bars in the column section is constructed. This database is used by the design algorithm to select appropriate sections for the columns of the frame under consideration. The design constraints are implemented from ACI 318-05 which covers the flexural and shear strength, serviceability, the minimum and maximum steel percentage for flexural and shear reinforcement, the spacing requirements for the reinforcing bars and the upper and lower bound requirements for the concrete sections. The optimum design problem formulated according to ACI 318-05 provisions with the design variables mentioned above turns out to be a combinatorial optimization problem. The solution of the design problem is obtained by using the harmony search algorithm (HS) which is one of the recent additions to meta-heuristic optimization techniques which are widely used in obtaining the solution of combinatorial optimization problems. The HS algorithm is quite simple and has few parameters to initialize and consists of simple steps which make it easy to implement. Number of design examples is presented to demonstrate the efficiency and robustness of the optimum design algorithm developed.

Cellular beams became increasingly popular as an efficient structural form in steel construction since their introduction. Their sophisticated design and profiling process provides greater flexibility in beam proportioning for strength, depth, size and location of circular holes. The purpose of manufacturing these beams is to increase overall beam depth, the moment of inertia and section modulus, which results in greater strength and rigidity. Cellular beams are used as primary or secondary floor beams in order to achieve long spans and service integration. They are also used as roof beams beyond the range of portal-frame construction, and are the perfect solution for curved roof applications, combining weight savings with a low-cost manufacturing process. The purpose of the current research is to study optimum design, ultimate load capacity under applied load and finite element analysis of non-composite cellular beams. The first part of the research program focuses on the optimum design of steel cellular beams using one of the stochastic search methods called &ldquo / harmony search algorithm&rdquo / . The minimum weight is taken as the design objective while the design constraints are implemented from the Steel Construction Institute. Design constraints include the displacement limitations, overall beam flexural capacity, beam shear capacity, overall beam buckling strength, web post flexure and buckling, vierendeel bending of upper and lower tees and local buckling of compression flange. The design methods adopted in this publication are consistent with BS5950. In the second part of the research, which is the experimental work, twelve non-composite cellular beams are tested to determine the ultimate load carrying capacities of these beams under using a hydraulic plug to apply point load. The tested cellular beam specimens have been designed by using harmony search algorithm. Finally, finite element analysis program is used to perform elastic buckling analysis and predict critical loads of all steel cellular beams. Finite element analysis results are then compared with experimental test results for each tested cellular beam.