In this study, the music-inspired Harmony Search (HS) algorithm is modified for the optimization of active tuned mass dampers (ATMDs). The modification of HS includes the consideration of the best solution with a defined probability and updating of algorithm parameters such as harmony memory, considering rate and pitch adjusting rate. The design variables include all the mechanical properties of ATMD, such as the mass, stiffness and damping coefficient, and the active controller parameters of the proposed proportional–integral–derivative (PID) type controllers. In the optimization process, the analysis of an ATMD implemented structure is done using the generated Matlab Simulink block diagram. The PID controllers were optimized for velocity feedback control, and the objective of the optimization is the minimization of the top story displacement by using the limitation of the stroke capacity of ATMD. The optimum results are presented for different cases of the stroke capacity limit of ATMD. According to the results, the method is effective in reducing the maximum displacement of the structure by 53.71%, while a passive TMD can only reduce it by 31.22%.

By finding the minimum total potential energy of a structural system with a defined degree of freedoms assigned as design variables, it is possible to find the equilibrium condition of the deformed system. This method, called total potential optimization using metaheuristic algorithms (TPO/MA), has been verified on truss and truss-like structures, such as cable systems and tensegric structures. Harmony Search (HS) algorithm methods perfectly found the analysis results of the previous structure types. In this study, TPO/MA is presented for analysis of plates for plane stress members to solve general types of problems. Due to the complex nature of the system, a novel hybrid Harmony Search (HHS) approach was proposed. HHS is the hybridization of local search phases of HS and the global search phase of the Flower Pollination Algorithm (FPA). The results found via HHS were verified with the finite element method (FEM). When compared with classical HS, HHS provides smaller total potential energy values, and needs less iterations than other new generation metaheuristic algorithms.

In this paper, the design of cantilever soldier pile retaining walls embedded in frictional soils is investigated within the insight of an optimization algorithm to acquire cost and dimension equilibrium by ensuring both geotechnical and structural requirements simultaneously. Multivariate parametric analyses with different fictionalized cases are performed to evaluate the effects of design variants and to compare the effectiveness of the preference of optimization solutions rather than detailed advanced modeling software. The harmony search algorithm is used to conduct parametrical analyses to take into consideration the effects of the change of excavation depth, shear strength angle, and unit weight of soil, external loading condition, and coefficient of soil reaction. The embedment depth and diameter of the soldier pile are searched as design dimensions, and the total cost of a cantilever soldier pile wall is calculated as an objective function. The design dimension results of the parametric optimization analysis are used to perform finite element analysis with a well-known commercial geotechnical analysis software. The results of optimization and finite element solutions are compared with the use of maximum bending moment, factor of safety, and pivot point location values. As the consequence of the study, the influence rates of design variants are procured, and the effectiveness of the usage of optimization algorithms for both cost and dimensional equilibrium is presented.

The locations of structural members can be provided according to architectural projects in the design of reinforced concrete (RC) structures. The design of dimensions is the subject of civil engineering, and these designs are done according to the experience of the designer by considering the regulation suggestions, but these dimensions and the required reinforcement plan may not be optimum. For that reason, the dimensions and detailed reinforcement design of RC structures can be found by using optimization methods. To reach optimum results, metaheuristic algorithms can be used. In this study, several metaheuristic algorithms such as harmony search, bat algorithm and teaching learning-based optimization are used in the design of several RC beams for cost minimization. The optimum results are presented for different strength of concrete. The results show that using high strength material for high flexural moment capacity has lower cost than low stretch concrete since doubly reinforced design is not an optimum choice. The results prove that a definite metaheuristic algorithm cannot be proposed for the best optimum design of an engineering problem. According to the investigation of compressive strength of concrete, it can be said that a low strength material are optimum for low flexural moment, while a high strength material may be the optimum one by the increase of the flexural moment as expected.

Design engineers may find various options of metaheuristic method in optimization of their problems. Because of the randomization nature of metaheuristic methods, solutions may trap to non-optimum solutions which are just optimums in a limited part of the selected range of the design variables. Generally, metaheuristics use several options to prevent this situation, but the same optimization process may solve different performances in every run of the process. Due to that, a comparative study by using ten different algorithms was done in this study. The optimization problem is the cost minimization of an L-shaped reinforced concrete (RC) retaining wall. The evaluation is done by conducting 30 multiple cycles of optimization, and comparing minimum cost, average cost and standard deviation values.