Öz In this study, performance of meta-heuristic methods on optimum design of reinforced concrete (RC) retaining wall has been investigated with respect to minimizing the cost and the CO2 emission. Biogeography Based Optimization (BBO) and Social Spiders optimization (SSO) methods utilized for investigation. The minimizations of the cost, the CO2 emission and multi-objective of the cost+CO2 functions are described as objective functions of the optimization problem. There are thirteen design variables are defined in the optimization problem. Eight of these variables are the cross sectional dimensions of the retaining wall. The other five design variables are the reinforcement detailing of wall members. Flexural and shear strength requirements, minimum and maximum cross section areas of the reinforcement bar, the requirement length for reinforcement details and the factor of safety for failure modes are defined as constraints functions of the optimization problem. The Flexural and shear strength requirements, minimum and maximum limitations of the reinforcement bar areas are adopted from American Concrete Institute (ACI 318-14) design code. In order to test performance of the presented optimization methods literature design examples are used. In addition, efficiency of steel and concrete classes on optimum CO2 emission and cost have been investigated by using different steel and concrete classes. Bu çalışmada, meta-sezgisel optimizasyon yöntemlerinin betonarme konsol istinat duvarlarının minimum maliyet ve CO2 salınımına göre optimum tasarımı problemindeki performansları araştırılmıştır. Araştırma için, biyo-coğrafya tabanlı ve sosyal örümcek optimizasyon algoritmaları kullanılmıştır. Minimum maliyet fonksiyonu, minimum karbondioksit salınımı fonksiyonu, minimum maliyet ve karbondioksitin salınımını içeren çok amaçlı fonksiyon optimizasyon probleminin amaç fonksiyonları olarak tanımlanmıştır. Optimizasyon probleminde on üç adet tasarım değişkeni tanımlanmıştır. Bunlardan sekiz tanesi istinat duvarının en kesitini oluşturan değişkenlerdir. Diğer beş tanesi ise duvar elemanların donatı detaylandırmasıdır. Eğilme ve kesme kapasite sınırlayıcıları, minimum ve maksimum donatı alanları, donatı detaylandırılmasında gerekli donatı uzunlukları ve göçme modların güvenlik katsayıları optimizasyon probleminin tasarım sınırlayıcıları olarak tanımlanmıştır. Eğilme ve kesme kapasitesi sınırlayıcıları ve donatı alanlarının minimum ve maksimum sınır değerleri Amerikan beton enstitüsü (ACI 318-14) tasarım şartnamesinden alınmıştır. Sunulan optimizasyon yöntemlerinin performanslarını test etmek için literatürdeki tasarım örnekleri kullanılmıştır. Buna ek olarak farklı beton ve çelik malzemeleri kullanılarak malzeme sınıflarının optimum CO2 salınımı ve maliyeti üzerindeki etkinliği araştırılmıştır.

Traditional structural optimization is mainly based on the assumption that the materials are elastic, which cannot represent real stress fields in structures. In this study, the genetic algorithm, big bang-big crunch algorithm, and hybrid big bang-big crunch algorithm were employed to optimize the design factors of ship lock heads during concrete construction. The optimization goal was to determine the minimum volume of concrete. The factors considered included the hydration heat, the early-stage creep, and the transient deformation under external loads. In the finite element analysis, three types of boundary conditions were considered. The whole construction process was simulated, and the maximum tensile and compressive stresses, the stability, and the overturning of the lock head were examined. Based on the finite element analysis, to reduce the consumption of memory, a set of implicit recursive equations were used to calculate the thermal creep stress. Thirty-four design variables were distinguished for optimization. A case study on the optimization of a ship lock head was used to demonstrate the optimization process. The optimization results showed that the hybrid big bang-big crunch algorithm was more effective, and some conclusions were derived.

This study presents a hybrid metaheuristic algorithm to obtain optimum designs for steel space buildings. The optimum design problem of three-dimensional steel frames is mathematically formulated according to provisions of LRFD-AISC (Load and Resistance factor design of American Institute of Steel Construction). Design constraints such as the strength requirements of structural members, the displacement limitations, the inter-story drift and the other structural constraints are derived from LRFD-AISC specification. In this study, a hybrid algorithm by using teachinglearning based optimization (TLBO) and harmony search (HS) algorithms is employed to solve the stated optimum design problem. These algorithms are two of the recent additions to metaheuristic techniques of numerical optimization and have been an efficient tool for solving discrete programming problems. Using these two algorithms in collaboration creates a more powerful tool and mitigates each other’s weaknesses. To demonstrate the powerful performance of presented hybrid algorithm, the optimum design of a large scale steel building is presented and the results are compared to the previously obtained results available in the literature. Keywords—Optimum structural design, hybrid techniques, teaching-learning based optimization, harmony search algorithm, minimum weight, steel space frame.

This paper presents a Cuckoo Optimization Algorithm (COA) model for the cost optimization of the one-way and two-way reinforced concrete (RC) slabs according to ACI code. The objective function is the total cost of the slabs including the cost of the concrete and that of the reinforcing steel. In this paper, One-way and two-way slabs with various end conditions are formulated as ACI code. The two-way slabs are modelled and analyzed using direct design method. The problems are formulated as mixed-discrete variables such as: thickness of slab, steel bar diameter, and bar spacing. The presented model can be applied in design offices to reduce the cost of the projects. It is also the first application of the Cuckoo Optimization Algorithm to the optimization of RC slabs. In order to demonstrate the superiority of the presented method in convergence and leading to better solutions, the results of the proposed model are compared with the other optimization algorithms.

This paper investigates discrete design optimization of reinforcement concrete frames using the recently developed meta-heuristic called Enhanced Colliding Bodies Optimization (ECBO) and the Non-dominated Sorting Enhanced Colliding Bodies Optimization (NSECBO) algorithm. The objective function of algorithms consists of construction material costs of reinforced concrete structural elements and carbon dioxide (CO2) emissions through different phases of a building life cycle that meets the standards and requirements of the American Concrete Institute’s Building Code. The proposed method uses predetermined section database (DB) for design variables that are taken as the area of steel and the geometry of cross-sections of beams and columns. A number of benchmark test problems are optimized to verify the good performance of this methodology. The use of ECBO algorithm for designing reinforced concrete frames indicates an improvement in the computational efficiency over the designs performed by Big Bang-Big Crunch (BB-BC) algorithm. The analysis also reveals that the two objective functions are quite relevant and designs focused on mitigating CO2 emissions could be achieved at an acceptable cost increment in practice. Pareto results of the NSECBO algorithm indicate that both objective yield similar solutions.

This chapter investigates discrete design optimization of reinforcement concrete frames using the recently developed metaheuristic called Enhanced Colliding Bodies Optimization (ECBO) and the Non-dominated Sorting Enhanced Colliding Bodies Optimization (NSECBO) algorithm. The objective function of algorithms consists of construction material costs of reinforced concrete structural elements and carbon dioxide (\( {\mathrm{CO}}_2 \)) emissions through different phases of a building life cycle that meets the standards and requirements of the American Concrete Institute’s Building Code. The proposed method uses predetermined section database (DB) for design variables that are taken as the area of steel and the geometry of cross sections of beams and columns. A number of benchmark test problems are optimized to verify the good performance of this methodology. The use of ECBO algorithm for designing reinforced concrete frames indicates an improvement in the computational efficiency over the designs performed by Big Bang–Big Crunch (BB–BC) algorithm. The analysis also reveals that the two objective functions are quite relevant and designs focused on mitigating \( {\mathrm{CO}}_2 \) emissions could be achieved at an acceptable cost increment in practice. Pareto results of the NSECBO algorithm indicate that both objective yield similar solutions [1].

This article presents an optimization-based computational method to assist in the design of reinforced concrete framed structures. The design of these structures is posed as a multi-objective optimization problem seeking cost minimization, strength and serviceability design objectives defined according to Eurocode 2 provisions. An entropy-based approach is used to obtain the solution of the minimax problem by minimizing a convex scalar function. Special emphasis is placed on the sensitivity analysis, which is crucial for the performance of the optimization algorithm. The discrete direct method was used to compute the sensitivities of the design objectives, the allowable values of which are dependent on the design variables. The cross-sectional dimensions of beams and columns and the longitudinal and shear reinforcement areas are the design variables. Verification examples and the optimization of a real-sized building structure are presented to illustrate the features of the developed method.

The proposed contribution describes the formulation of the optimization design of a utility tunnel lining. The objective function is defined as a multicriterial problem and includes economic and environmental aspects associated not only with concrete member production but also with maintenance during utilization (life cycle assessment). The constraining conditions expressed by relations derived from equations of equilibrium (the solution of optimization calculations for a structure with a Winkler foundation using the Finite Element Method), the reliability conditions of a reinforced concrete structure and the continuity of deformations define the range of allowable solutions from the mathematical viewpoint. The thickness of the tunnel lining and areas of the top and bottom reinforcement in cross-sections are optimized. A method (algorithm) for obtaining a serviceable reinforcement design (via the implementation of reinforcement types) from an optimal solution is described. The obtained results are compared and analysed.

The music-inspired metaheuristic method, called harmony search (HS), is an effective tool in optimization of engineering design problems. HS has been applied for the optimum design of reinforced concrete (RC) members so as to find the best solution, balancing the usability of the design and economy. In this chapter, the optimum design of RC members is presented after optimization of RC members. Then, HS-based optimization applications, such as RC slender columns, RC shear walls, and post-tensioned RC axially symmetric cylindrical walls, are also discussed. The HS-based methods are feasible in finding the optimum design in such problems.

The increasing numbers of design variables and constraints have made many civil engineering problems significantly more complex and difficult for engineers to resolve in a timely manner. Various optimization models have been developed to address this problem. The present paper introduces Symbiotic Organisms Search (SOS), a new nature-inspired algorithm for solving civil engineering problems. SOS simulates mutualism, commensalism, and parasitism, which are the symbiotic interaction mechanisms that organisms often adopt for survival in the ecosystem. The proposed algorithm is compared with other algorithms recently developed with regard to their respective effectiveness in solving benchmark problems and three civil engineering problems. Simulation results demonstrate that the proposed SOS algorithm is significantly more effective and efficient than the other algorithms tested. The proposed model is a promising tool for assisting civil engineers to make decisions to minimize the expenditure of material and financial resources.

The implications of optimised structural designs in the life cycle carbon performance of buildings have been systematically overlooked in previous studies. The paper addresses this common limitation offering an integrated sustainable structural analysis at building level. To achieve this, a BIM-embedded approach was established utilising embodied carbon metrics and results from heuristic structural optimisation. A real building scenario was used to test the proposed approach in the context of multi-storey reinforced concrete (RC) buildings. Results show how the building life cycle performance is affected by the use of structurally optimised designs. The structural floors in particular, not only cover the largest proportion of the embodied carbon in the structure but they are also responsible for a large proportion of the carbon emissions of the tested building elements. The results obtained in this paper justified the need for more comprehensive efforts in the design optimisation of RC floors. Overall, it is suggested that the unclear interpretation of the optimisation outputs would result in the selection of structural designs that could compromise the buildings carbon performance.

The embodied CO2 emissions of reinforced concrete (RC) structures can be significantly reduced by structural optimization that maximizes structural efficiency. Previous studies dealing with design of RC structures for minimum CO2 emissions do not address seismic design provisions. This is the case despite the fact that in many countries around the world, including most of the top-10 countries in CO2 emissions from cement production, RC structures have to be designed against earthquake hazard. To fill a part of this gap, this study, using exhaustive search, examines optimum designs of RC beam and column members for minimum embodied CO2 emissions according to Eurocode-8 for all ductility classes and compares them with optimum designs based on material cost. It is shown that seismic designs for minimum CO2 footprint lead to less CO2 emissions but are more expensive than minimum cost designs. Their differences strongly depend on the assumed values of the environmental impact of reinforcing steel and concrete materials. Furthermore, it is concluded that seismic design for high ductility classes can drive to significant reductions in embodied CO2 emissions.

The distance from extreme compression fiber to neutral axis (c) is depended to combinations of axial load and flexural moment capacities of reinforced concrete (RC) columns. Since c is depended to different internal forces, the value of c cannot be found without assuming the final design. Thus, it can be iteratively searched in order to find the flexural moment capacity of columns under an axial loading. By using the presented method, the solution with the minimum cost ensuring maximum flexural moment and axial load is found. A random search technique is explained in this chapter for optimum design of uniaxial RC columns with minimum cost. In optimization, design of RC columns is done by considering the design rules described in ACI 318- Building Code Requirements for Structural Concrete. The random search technique (RST) for optimization of RC uniaxial columns is effective on finding optimum cross-sections and reinforcement design with minimum cost.

The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a small variation of these initial uncertain parameters can have a big influence on the structural behavior. The objective of robust design optimization is to obtain an optimum design with the lowest possible variation of the objective functions. For this purpose, a probabilistic optimization is necessary to obtain the statistical parameters that represent the mean value and variation of the objective function considered. However, one of the disadvantages of the optimal robust design is its high computational cost. In this paper, robust design optimization is applied to design a continuous prestressed concrete box-girder pedestrian bridge that is optimum in terms of its cost and robust in terms of structural stability. Furthermore, Latin hypercube sampling and the kriging metamodel are used to deal with the high computational cost. Results show that the main variables that control the structural behavior are the depth of the cross-section and compressive strength of the concrete and that a compromise solution between the optimal cost and the robustness of the design can be reached.

The cost and carbon efficiency of building structures could be enhanced by the current developments in design automation and optimisation techniques. New ways to systematically assess design alternatives based on cost and carbon parameters are necessary. The study proposes a multilevel optimisation approach that combines Building Information Modelling (BIM) data and Finite Element Modelling (FEM) with a constrained genetic algorithm. The optimisation methodology is tested in a prototypical building floor system. Structural grid configurations, floor thicknesses and columns sizes and reinforcement details are identified. The results showed that the cost optimum design is 3% cheaper than the carbon optimum design but it has 7% more carbon. In addition, the concrete in the floor is the biggest contributor in both total cost and carbon. Relationships between costand carbonoptimum designs for the tested structural configuration are also discussed.

The construction economy is one of the major goals of engineers and only an experienced engineer can make an economical design after several trial efforts. Whereas, the optimum design of structures can be found by using metaheuristic methods. Especially, the optimum design of reinforced concrete (RC) structures is challenging since two materials with different price and behavior are used. In that case, the optimization problem is highly non-linear and the developed methods employing harmony search (HS) algorithm is effective to solve the problem in several random stages. As the numerical example, the method was tested for two-story two-span RC frames. The results show that the metaheuristic based methodology is feasible.

The combined economic and emission dispatch (CEED) problem where objective function is highly non linear, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper proposes a Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm technique for solving the CEED. Six generator test and IEEE 30 standard bus system was used for testing and validation purposes. The preference of the HBB–BC is compared with other heuristic methods. The results show, clearly, that the proposed method gives better optimal solution as compared to the other methods.

The buffer allocation problem (BAP) aims to determine the optimal buffer configuration for a production line under the predefined constraints. The BAP is an NP-hard combinatorial optimization problem and the solution space exponentially grows as the problem size increases. Therefore, problem specific heuristic or meta-heuristic search algorithms are widely used to solve the BAP. In this study two population-based search algorithms; i.e. Combat Genetic Algorithm (CGA) and Big Bang-Big Crunch (BB-BC) algorithm, are proposed in solving the BAP to maximize the throughput of the line under the total buffer size constraint for unreliable production lines. Performances of the proposed algorithms are tested on existing benchmark problems taken from the literature. The experimental results showed that the proposed BB–BC algorithm yielded better results than the proposed CGA as well as other algorithms reported in the literature.

The big bang-big crunch (BB-BC) algorithm is a popular metaheuristic optimization technique proposed based on one of the theories for the evolution of the universe. The algorithm utilizes a two-phase search mechanism: big-bang phase and big-crunch phase. In the big-bang phase the concept of energy dissipation is considered to produce disorder and randomness in the candidate population while in the big-crunch phase the randomly created solutions are shrunk into a single point in the design space. In recent years, numerous studies have been conducted on application of the BB-BC algorithm in solving structural design optimization instances. The objective of this review study is to identify and summarize the latest promising applications of the BB-BC algorithm in optimal structural design. Different variants of the algorithm as well as attempts to reduce the total computational effort of the technique in structural optimization problems are covered and discussed. Furthermore, an empirical comparison is performed between the runtimes of three different variants of the algorithm. It is worth mentioning that the scope of this review is limited to the main applications of the BB-BC algorithm and does not cover the entire literature.

The aim of this state-of-the-art review is to present the recent progress about the design optimization and applications of metaheuristic algorithms in civil engineering. In this chapter, the importance of optimization in civil engineering and differences with other engineering disciplines are emphasized in the first section. The best suitable techniques concerning metaheuristic methods and several approaches have been summarized and reviewed. These algorithms are effective in dealing with nonlinear design optimization with complex constraints, practical discrete design variables, and user-defined special conditions. The modifications of these algorithms have been carried out and then applied to civil engineering applications. Finally, results are presented with discussion about further potential improvements.