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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%.

In this study, considering the eco-friendly design necessities of reinforced concrete structures, the acquirement of minimizing both the cost and the CO2 emission of the reinforced concrete retaining walls in conjunction with ensuring stability conditions has been investigated using harmony search algorithm. Optimization analyses were conducted with the use of two different objective functions to discover the contribution rate of variants to the cost and CO2 emission individually. Besides this, the integrated relationship of cost and CO2 emission was also identified by multi-objective analysis in order to identify an eco-friendly and cost-effective design. The height of the stem and the width of the foundation were treated as design variables. Several optimization cases were fictionalized in relation with the change of the depth of excavation, the amount of the surcharge applied at the top of the wall system at the backfill side, the unit weight of the backfill soil, the costs, and CO2 emission amounts of both the concrete and the reinforcement bars. Consequently, the results of the optimization analyses were arranged to discover the possibility of supplying an eco-friendly design of retaining walls with the minimization of both cost and gas emission depending upon the comparison of outcomes of the identified objective functions. The proposed approach is effective to find both economic and ecological results according to hand calculations and flower pollination algorithm.

This paper presents the parametric modelling process of cantilever soldier pile walls based on CO2 and cost optimization with the Harmony Search Algorithm. The study attempted to fulfil the geotechnical and structural design requirements and sustainable usage necessities simultaneously. The variants of the optimum design process are selected as the cross-sectional characteristics of cantilever soldier piles such as the length and diameter of the pile, and the other design variables are the reinforcement detailing of the pile such as the diameter and the number of reinforcement bars. Besides the volume of the concrete, the unit prices of both reinforcement and concrete are evaluated as another part of the variants. The shear and flexural strength necessities, minimum cross section of the reinforcing bars and factor of safety values are identified as the constraints of the optimization. Different objective functions are defined to provide the minimum cost, the minimum CO2 emission and the integrated multi-objective evaluation of cost and CO2. In addition, the type of steel and concrete reinforcement on the optimum CO2 emission is investigated with the use of different material emission values that are selected from current literature studies. Consequently, the results of the optimization analyses are interrogated to investigate if the attainment of both minimum CO2 and cost balance can be achieved.

In the context of this study, it is focused on the design of cantilever soldier piles under the concept of Pareto optimality with multiobjective analyses of cost and CO2 emission considering the change in the excavation depth, the shear strength parameters of the foundation soil strata, and the unit costs and unit emission amounts of structural materials. Considering this aim, the harmony search algorithm was used as a tool to achieve the integrated effects of the solution variants. The lateral response of the soil mass was determined based on the active Rankine earth pressure theory and the design process was shaped according to the beams on the elastic foundation soil assumption. Moreover, the specification envisaged by the American Concrete Institute (ACI 318-11) was used to control the structural requirements of the design. Pareto front graphs and also design charts were created to achieve the eco- and cost optimization, simultaneously, for the design with arbitrarily selected cases to compare the results of the multiobjective analysis to minimize both the cost and the CO2 emission.

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.

Control of high-rise structures under seismic excitations was investigated using a passive hybrid control system consisting of a base-isolation (BI) subsystem and a passive tuned liquid column damper (TLCD) system. Both of the systems were optimized considering using the other system in the same structure. An optimization method was developed, and a computer code was written based on dynamic analysis of the structure and metaheuristic optimization methods. Within the scope of the study, a general solution was found by using many earthquake records during the optimization process. Moreover, one of the most suitable and successful metaheuristic algorithms was used in this study. In addition, numerical simulations were performed on a benchmark high-rise building structure to investigate the effectiveness of the optimized hybrid control system in controlling the seismic response of the building. The performance of the base-isolated TLCD-controlled structure was examined when the TLCD was placed on the base floor by using a set of 44 recorded ground motions as base excitations. Based on the results obtained from this study, the use of a base-isolation subsystem decoupling the superstructure from the ground motions by lowering the structure’s fundamental natural frequency reduces the structural responses of the building in most cases. The responses of the base-isolation subsystem were not too large since the parameters of the BI subsystem were optimized specifically for the investigated structure. Nevertheless, displacements of BI might exceed the maximum limit to undesirable values in some cases. The TLCD system appears to be quite effective in protecting the base-isolation subsystem by reducing its displacements to the maximum allowable limit or below when attached to it. Moreover, the proposed passive hybrid control system can effectively reduce the structural responses under seismic excitations.

In this paper, the Harmony Search (HS) algorithm is utilized to perform single and multivariate parametric studies to acquire the optimization of both size and cost of reinforced concrete (RC) retaining walls embedded in pure frictional soils. The geotechnical properties of the backfill and foundation soil such as shear strength angle, unit weight, and the ultimate bearing pressure of the soil have been used to create different cases for evaluating the effects of site properties on the size and cost of the wall. The change of depth of excavation and surcharge loading condition is fictionalized for generating different environmental conditions for all envisaged soil profiles to predict possible rates of influences. The unit cost of the concrete has also been evaluated as a variant to show the economic constraints on the selection of structural materials. The results of the analyses represent the integrated influences of different significant parameters on the achievement of minimum cost-dimension optimization. Besides, a well-known commercial geotechnical engineering software is used to compare the appropriateness of the suggested designs in terms of both the attainment of geotechnical stability and the structural requirements. Consequently, this study can guide both researchers and designers to select the proper and optimal sections of RC-retaining wall systems with simultaneous analyses of parameters that are influenced by the design process. Furthermore, the optimization results indicate that a significant cost reduction may be achieved when compared with the traditional pre-design method.

Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is an alternative tool for the analysis of structures. It is shown that this emerging method is advantageous in solving nonlinear problems like trusses, tensegrity structures, cable networks, and plane stress systems. In the present study, TPO/MA, which does not need any specific implementation for nonlinearity, is demonstrated to be successfully applied to the analysis of plane strain structures. A numerical investigation is performed using nine different metaheuristic algorithms and an adaptive harmony search in linear analysis of a structural mechanics problem having 8 free nodes defined as design variables in the minimization problem of total potential energy. For nonlinear stress-strain relation cases, two structural mechanics problems, one being a thick-walled pipe and the other being a cantilever retaining wall, are analyzed by employing adaptive harmony search, which was found to be the best one in linear analyses. The nonlinear stress-strain relations considered in these analyses are hypothetical ones due to the lack of any such relationship in the literature. The results have shown that TPO/MA can solve nonlinear plane strain problems that can be encountered as engineering problems in structural mechanics.

This study presents a hybrid approach integrating metaheuristic optimization and machine learning methods to quickly and reliably estimate the optimum design parameters of dome-shaped axially symmetric cylindrical reinforced concrete (RC) walls. A comprehensive dataset was created using the Jaya algorithm to minimize total material cost for hinged and fixed support conditions. For each optimized design case, total wall height (H), dome height (Hd), dome thickness (hd), and fluid unit weight (γ) were considered as input parameters; optimum wall thickness (hw) and total cost were determined as output parameters. Using the obtained dataset, a total of thirteen different regression-based machine learning algorithms, including linear regression-based models, tree-based ensemble methods, and neural network models, were trained and tested. Hyperparameter adjustments for all models were performed using the Optuna framework, and model performances were evaluated using a ten-fold cross-validation method and holdout dataset results. The results showed that machine learning models can learn the optimum design space obtained from metaheuristic optimization outputs with high accuracy. In optimum wall thickness estimation, Gradient Boosting-based models provided the highest accuracy under both hinged and fixed support conditions. In total cost estimation, the Gradient Boosting model stood out under hinged support conditions, while the XGBoost model yielded the most successful results for fixed support conditions. The findings clearly show that no single machine learning model exhibits the best performance for all output parameters and support conditions. The proposed approach offers significantly higher computational efficiency compared to traditional iterative optimization processes and allows for rapid estimation of optimum design parameters without the need for any iterations. In this respect, this study provides an effective decision support tool that can be used especially in the preliminary design phases and contributes to sustainable, cost-effective reinforced concrete structure design.