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This paper examines the economic optimization of reinforced concrete earth-retaining walls used in road construction. The simulated annealing algorithm is the proposed method to optimize walls. The formulation of the problem includes 20 design variables: four geometrical ones dealing with the thickness of the kerb and the footing, as well as the toe and the heel lengths; four material types; and 12 variables for the reinforcement set-up. The study estimates the relative importance of factors such as the base friction coefficient, the wall-fill friction angle and the limitation of kerb deflections. Finally, the paper presents a parametric study of commonly used walls from 4 to 10 m in height for different fills and bearing conditions. Average expressions are calculated for the total cost, the volume of concrete, the thickness of the kerb and the footing, the lengths of the footing and the heel, which may be useful for the practical design of walls. An upper bound of 50 kg/m3 of reinforcement in the kerb and 60 kg/m3 for the overall wall is reported.

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... An improvement in the design can lead to immediate improvements in the social and environmental impact associated with its construction [19]. Traditionally, the design process has been very much linked to the engineer's theoretical knowledge, technical skills and previous experience [20]. This methodology starts with the complete definition of the different structural sections, which comprehends materials selection and the establishment of passive reinforcement configurations. ...

... These techniques have been highly improved during the last decade, mainly due to the simplicity of the algorithms and their high adaptability, in addition to the ability to avoid convergence to a local optimum. Due to the importance of improving the design process and the positive characteristics of the aforementioned methodologies, several studies have applied heuristic and metaheuristic optimization to design concrete structures, such as prestressed bridges [21], retaining walls [20,22,23], bridge piers [24] and building structures [25,26]. The results establish a direct relationship between the final cost of the structure and the CO 2 emissions associated with its construction. ...

... The algorithm's evolution and exploration of the solution space are highly conditioned by the correct establishment of the complete set of parameters that define it. In the case of the initial temperature, the approach proposed in Medina [40] is considered since it has proved to function in a correct manner in previous studies of similar characteristics [20,23]. The optimization process finishes once the temperature of the problem is equivalent to a small percentage of the initial temperature or when, during a certain number of consecutive Markov chains, a new solution that improves the current one is not found. ...

Sustainable development requires improvements in the use of natural resources. The main objective of the present study was to optimize the use of materials in the construction of reinforced concrete precast hinged frames. Proprietary software was developed in the Python programming language. This allowed the structure's calculation, verification, and optimization through the application of metaheuristic techniques. The final cost is a direct representation of the use of materials. Thus, three algorithms were applied to solve the economic optimization of the frame. By applying simulated annealing, threshold accepting and old bachelor's acceptance algorithms, sustainable, non-traditional designs were achieved. These make optimal use of natural resources while maintaining a highly restricted final cost. In order to evaluate the environmental impact improvement, the carbon-dioxide-associated emissions were studied and compared with a reference cast-in-place reinforced concrete frame. The results showed designs with reduced upper slab and lateral wall depth and dense passive reinforcement. These were able to reduce up to 24% of the final cost of the structure, as well as over 30% of the associated emissions.

... However, the novel study was of Sarıbaş and Erbatur [19] which solidified the direction taken by researchers for problem formulation of RC cantilever retaining walls and is the most common reference study used by subsequent researchers. Since then multiple theses (Medhekar [20], Purohit [21], Naeem [22], Rahbari [23], and Schmied and Karlsson [24]), conference papers (Bhatti [25], Ahmadi-Nedushan and Varaee [26], Villalba et al. [27], Pei and Xia [28], Papazafeiropoulos et al. [29], Uray and Tan [30], Al Sebai et al. [31], Srivastavaa et al. [32], and Yücel et al. [33]), and journal articles (Ceranic et al. [34], Chau and Albermani [35], Babu and Basha [36], Yepes et al. [37], Khajehzadeh et al. [38], Ghazavi and Bonab [39], Kaveh and Abadi [40], Khajehzadeh et al. [41], Camp and Akin [42], Khajehzadeh and Eslami [43], Sable and Patil [44], Sable and Patil [45], Kaveh and Behnam [46], Kaveh et al. [47], Kaveh and Khayatazad [48], Khajehzadeh et al. [49], Sheikholeslami et al. [50], Talatahari and Sheikholeslami [51], Gandomi et al. [52], Kaveh and Mahdavi [53], Singla and Gupta [54], Bekdaş et al. [55], Kaveh and Farhoudi [56], Sheikholeslami et al. [57], Temür and Bekdas [58], Aydogdu [59], Kaveh and Laien [60], Gandomi et al. [61], Gandomi et al. [62], Kumar and Suribabu [63], Rahbari et al. [64], Ukritchon et al. [65], Kayhan and Demir [66], Mohammad and Ahmed [67], Kalateh-Ahani and Sarani [68], Moayyeri et al. [69],Öztürk and Türkeli [70], Uray et al. [71], Dagdeviren and Kaymak [72], Kaveh et al. [73], Kaveh et al. [74], Kayabekir et al. [75], Konstandakopoulou et al. [76], Mergos and Mantoglou [77], Kalemci et al. [78], Kayabekir et al. [79], Hoang and Cong [80], Millán-Paramo et al. [81], Kashani et al. [82], Uray et al. [83], Ravichandran et al. [84], Yücel et al. [85], Kaveh et al. [86], Sharma et al. [87], Mevada et al. [88], Uray and Çarbaş [89], Tousi et al. [90], Eroglu et al. [91], Uray et al. [92], Linh et al. [93], Dodigović et al. [94], Tutuş et al. [95], Uray et al. [96], Yücel et al. [97], Tutuş et al. [98], Temür [99], Shakeel et al. [100], Khajehzadeh et al. [101], Uray et al. [102], and Khajehzadeh et al. [103]) have been written on this topic. Despite ample work conducted that demonstrates the potential of optimization in this field, its acceptance in practical works is still little to none [100,104,105]. ...

... e cost of concrete can be expanded to include the cost of formwork, transportation, labor, vibration, Earth removal, and cost of backfill as done by Naeem [22], Villalba et al. [27], Al Sebai et al. [ [90], and Dodigović et al. [94]. e cost of varying concrete and steel strength can also be used for optimization as done by Villalba et al. [27], Yepes et al. [37], Kaveh et al. [47], Kalateh-Ahani and Sarani [68], Konstandakopoulou et al. [76], Tousi et al. [90], and Shakeel et al. [100]. e research of Mohammad and Ahmed [67] has used cost ratios to simplify the results and lessen the effect of local currency on optimal results. ...

... Deflection check is another factor taken as a part of serviceability limit state of retaining wall. Extensive work was done by Yepes et al. [37] on deflection limits and they concluded that a value of 1/150 of stem height is sufficient for practical optimized design of retaining walls. A deflection check has been included by the studies of Villalba et al. [27], Al Sebai et al. [31], Yepes et al. [37], Khajehzadeh et al. [41], Khajehzadeh and Eslam [43], Kaveh et al. [47], Khajehzadeh et al. [49], and Ravichandran et al. [84]. ...

The booming growth of computational abilities in the 21st century has led to its assimilation and benefit in all horizons of engineering. For civil engineers, these advancements have led to groundbreaking technologies such as BIM, automation, and optimization. Unfortunately, even in an era of dwindling resources and dire need for sustainability, optimization has failed to attract implementation in practice. Despite an exponential growth as an area of research interest, the optimization of engineering structures such as reinforced concrete (RC) is still a complex task that requires multidisciplinary knowledge, hindering its practicability. Although past review papers have delved into this topic, they have only been able to cover the breadth of information available by covering broader aspects of optimization of structures. This study on the other hand aims to cover this topic in depth to uncover problem specific trends and issues, by focusing only on optimization of RC cantilever retaining walls. Although there is an abundance of research studies on this topic, there is an absence of any critical review to tie them up, and concurrently with its broader scope, it suffers the same lack of applicability in the field. The in-depth review presents a summarization of all the online publications including research articles, conference papers, and theses to the best of authors’ knowledge on the topic of RC cantilever retaining wall optimization. Geographical trends, regional developments, and prominent journals have been identified. The design codes, problem formulation, objectives, constraints, variables, and their optimization techniques are tabulated for ease of understanding. Unique areas of development investigated by the different researchers have been highlighted. Lastly, comprehensive recommendations for future works have been detailed with a focus on improving its applicability and assimilation into the construction industry.

... These techniques have been used along with optimization methods for advanced analysis in a diversity of civil engineering applications, and the use of them is increasing [29][30][31]. Several studies have also been conducted on the optimum design of the retaining systems based on the various metaheuristic optimization algorithms [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. These optimization techniques are able to solve complicate problems by searching a large possible design space. ...

... The influence of the seismic load on the optimal cost of the wall was also investigated in the above-mentioned reference. Ceranic et al. [32] and Yepes et al. [33] optimized a reinforced concrete cantilever retaining structure by applying the simulated annealing optimization algorithm. The outputs of the studies are satisfying and highlight the efficiency of the applied algorithms in minimizing the retaining walls cost. ...

... The optimization of the safety factors of retaining walls conducted by Gordan et al. [31] through network and bee colony techniques under both static and dynamic conditions. Mergos et al. [32] and Koopialipoor et al. [33] applied novel optimization techniques for designing the retaining walls and compared their performance with some other algorithms. Kaveh et al. [34] used eleven metaheuristic algorithms in order to obtain the optimum design of concrete cantilever retaining walls under both static and dynamic loadings. ...

Deep large excavations in urban areas are an important engineering challenge, whereas secant piling techniques are among the best solutions to have a safe workplace environment. Optimal design of these structures will increase efficiency as well as reduce costs. In this paper, the optimum design of secant pile walls as a retaining system of a deep excavation pit is evaluated. For this purpose, an on-going Tabriz metro station project is investigated as the case study. The structural piles are made of steel material with a hollow pipe section. A layer of struts is also considered for the horizontal bracing of the excavation pit. A detailed finite element model is developed in the OpenSees platform in order to perform static analyses. The optimization of the retaining system is conducted by the mean of four different metaheuristic algorithms including genetic, particle swarm optimization, bee, and biogeography-based optimization algorithms. The total cost of retaining structures is considered as an objective function, which should be minimized in the design space of the variables. The results highlight the excellence of the bees algorithm in achieving a minimum cost, lower dispersion, and rapid convergence rate. The optimum placement of the bracing system and its effect on the soil shear stress are also investigated based on the obtained optimal results.

... Focusing on environmental, the ISO 14040 [36] defines LCA as a technique for evaluating the environmental aspect and impacts caused by a process, product, or service through a system of input flows (data) that cause output flows (impacts). The most common guide to carry out the social assessment [37] follows the same steps as this code. ISO 14040 [36] divides the LCA into four phases: ...

... In addition, the four obtained by the SOCA method that represent the social dimension are workers (W), local communities (LC), society (S), and value chain actors (VCA). Such stakeholders are in accordance with those suggested in the Guidelines [37] and are considered representative of the social context of the Spanish region where the structures under analysis are located. ...

... The conditional attribute set C = {c 1 , c 2 , c 3 , c 4 } includes annual freeze-thaw cycles, annual precipitation, the average temperature in July, and the annual acid rainfall. The decision attribute set D = {D 1 } is the durability damage level of sample components, which can be calculated according to the Standard for Durability Assessment of Existing Concrete Structures (GB/T 51355-2019) [37]. In the decision attribute set, Durability Damage Level 1 indicates that the component has no durability damage, Level 2 indicates that the component has slight mechanical damage or durability damage, Level 3 indicates that the component has more serious durability damage, and Level 4 indicates that the component has very serious durability damage. ...

Construction is one of the main sectors that generates greenhouse gases. This industry consumes large amounts of raw materials, such as stone, timber, water, etc. Additionally, infrastructure should provide service over many years without safety problems. Therefore, their correct design, construction, maintenance, and dismantling are essential to reducing economic, environmental, and societal consequences. That is why promoting sustainable construction has recently become extremely important. To help address and resolve these types of questions, this book is comprised of five chapters that explore new ways of reducing the environmental impacts caused by the construction sector, as well to promote social progress and economic growth. The chapters collect papers included in the “Sustainable Construction II” Special Issue of the Sustainability journal. We would like to thank both the MDPI publishing and editorial staff for their excellent work, as well as the 18 authors who collaborated in its preparation. The papers cover a wide spectrum of
issues related to the use of sustainable materials in construction, the optimization of designs based on sustainable indicators, the life-cycle assessment, the decision-making processes that integrate economic, social, and environmental aspects, and the promotion of durable materials that reduce future maintenance.

... The metaheuristics were calibrated in prior studies; further details are provided in Table 8. For instance, the initial temperature parameter of modified SA was adjusted to 1/20 the cost of the initial best solution in the RCC design study conducted by Yepes, V. et al. [89], which was inspired by the adjustment method devised by Medina [90]. Therefore, if the acceptance percentage of higher energy solutions is determined within 20% to 40%, the initial temperature is doubled, otherwise the initial temperature is halved. ...

... Number of new solutions = 20 (#new Neighbors), Mutation rate (m) = 0.5, Maximum number of sub-iterations = 20, Initial temperature adjustment based on Medina's method [89], [90] = 1/20 * Cost of initial best solution, Cooling coefficient (k) = 0.85 ...

In earthquake-prone zones, the seismic performance of reinforced concrete cantilever (RCC) retaining walls is significant. In this study, the seismic performance was investigated using horizontal and vertical pseudo-static coefficients. To tackle RCC weights and forces resulting from these earth pressures, 26 constraints for structural strengths and geotechnical stability along with 12 geometric variables are associated with each design. These constraints and design variables form a constraint optimization problem with a twelve-dimensional solution space. To conduct effective search and produce sustainable, economical, lightweight RCC designs robust against earthquake hazards, a novel adaptive fuzzy-based metaheuristic algorithm is applied. The proposed method divides the search space to sub-regions and establishes exploration, information sharing, and exploitation search capabilities based on its novel search components. Further, fuzzy inference systems were employed to address parameterization and computational cost evaluation issues. It was found that the proposed algorithm can achieve low-cost, low-weight, and low CO2 emission RCC designs under nine seismic conditions in comparison with several classical and best-performing design optimizers.

... Therefore, systematizing the obtaining of designs is very complicated. This complexity leads to the traditional design process depending on the responsible technician [10]. Based on existing structures, the structural engineer defines an initial design. ...

... In this context, Figure 13 shows the passive reinforcement density distribution surface as a function of the horizontal span and earth cover depth. The optimum RMHFs presented quite dense passive reinforcement designs when compared with similar structural solutions [10,11,26]. With densities ranging from 73.34 to 153.99 kg/m 3 . ...

This paper addresses a study of cost-optimal road modular hinged frames. The performance of three hybrid metaheuristics is assessed through a fractional factorial design of experiments. The results allow for selecting and calibrating the hybrid simulated annealing to solve the combinatorial optimization problem. By varying the horizontal span from 8 to 16 meters and the earth cover from 1 to 5 meters, 25 different structural configurations are studied. The calibrated methodology is applied to obtain nine different frames with optimal costs for each configuration. The study of the economic, environmental and geometrical characteristics of the 225 optimum structures allows for the development of a regression analysis. With R 2 correlation coefficients close to the unit, the expressions form a valuable tool for calculating the final cost, associated emissions, embodied energy and particular geometric characteristics. The optimum structures present slender and densely reinforced designs. In addition, some structures show considerable reductions in the shear reinforcement, something solved by localized increases in longitudinal reinforcement.

... Is the lower an object fro m a h igher energy state Is to move to the energy level. At high energy (or High temperature), the particles can move or rearrange themselves instantly, thus switching to different structures [13]. The main problem with the annealing The process is to lower the material to a lo wer energy level Ho w to reduce (or cool) to bring The Better If the solid cools very quickly, the material a W ill be arranged in the metastable or substructure. ...

... In the Parallel Simu lated Annealing Algorith m [57]. The parallel simu lated annealing algorith m consists of p components executed as processes P0, P1, ..., Pp − 1 A process divides its own annealing chain into t wo phases (lines [6][7][8][9][10][11][12][13][14][15][16][17][18]. A phase consists of several cooling stages, and the cooling stage consists of several annealing steps [58]. ...

Simulated annealing is a method of solving uncontrolled and controlled optimization problems. This method simulates the physical process of heating an object and then slowly lowering the temperature to minimize defects, thus reducing system power. Simulated Annealing is a Constant global search Is the optimization algorithm. The algorithm is attracted by annealing in metallurgy, where the metal is rapidly heated to a high temperature and then slowly cooled, which increases its strength and makes it easier to work with. Implements simulated anal search in the same way. With each repetition in the Simulated Annealing Algorithm, a new point Created approx. From the current point Distance to new point or amount of search, Probability distribution that is in proportion to the temperature. All of the algorithm Accepts intent to reduce new points, but will raise the target with a certain probability Accepts points as well. Accept the scope The algorithm that raises the scores avoids getting stuck in the local minima and Explore globally for possible solutions. Algorithm Continuing, to lower the temperature properly, annealing as the temperature drops, algorithm search size reduces and at least integrates.

... The innovative part of the algorithm was that, during the search process, it not only accepted better solutions but also introduced the possibility of accepting degraded ones. SA makes an analogy of the metallurgical process, which obtains crystals from molten masses at high temperatures (Yepes et al. 2008). In this process, if a molten metal mass is suddenly cooled, the atoms that make it up will not have enough time to create an organized pattern, leading to the appearance of internal stresses that can negatively affect the mechanical performance of the resulting material. ...

... Rights reserved. temperature, usually 1% or 2% of the initial temperature (Medina 2001;Yepes et al. 2008). This stopping criterion is known as the freezing criterion. ...

This paper studies the optimization process through the metaheuristic algorithm known as
Simulated Annealing (SA) applied to a dissipative system formed by Buckling-Restrained
Braces (BRBs) to improve the seismic behavior of existing RC framed buildings. The optimization
algorithm is aimed at finding the solution with the minimum cost of the dissipative
structure. During the process different aspects such as the distribution of the BRBs in
the frame, the use of either short or long core BRBs, and other geometrical characteristics
of the core were simultaneously considered. The seismic performance of all proposed
designs was evaluated using the Capacity Spectrum Method. The SA algorithm was implemented
in Matlab, creating a link between it and OpenSees, to allow the transfer of information
during the optimization process. The use of both platforms proved to be efficient in
the optimization of complex structures using metaheuristic algorithms. The results indicate
that the proposed procedure is capable to find solutions with a significant saving of materials,
used in the dissipative structure (up to 65%), compared to the solution obtained by a
design method specialized in this kind of systems.

... Is the lower an object fro m a h igher energy state Is to move to the energy level. At high energy (or High temperature), the particles can move or rearrange themselves instantly, thus switching to different structures [13]. The main problem with the annealing The process is to lower the material to a lo wer energy level Ho w to reduce (or cool) to bring The Better If the solid cools very quickly, the material a W ill be arranged in the metastable or substructure. ...

... In the Parallel Simu lated Annealing Algorith m [57]. The parallel simu lated annealing algorith m consists of p components executed as processes P0, P1, ..., Pp − 1 A process divides its own annealing chain into t wo phases (lines [6][7][8][9][10][11][12][13][14][15][16][17][18]. A phase consists of several cooling stages, and the cooling stage consists of several annealing steps [58]. ...

Simulated annealing is a method of solving uncontrolled and controlled optimization problems. This method simulates the physical process of heating an object and then slowly lowering the temperature to minimize defects, thus reducing system power. Simulated Annealing is a Constant global search Is the optimization algorithm. The algorithm is attracted by annealing in metallurgy, where the metal is rapidly heated to a high temperature and then slowly cooled, which increases its strength and makes it easier to work with. Implements simulated anal search in the same way. With each repetition in the Simulated Annealing Algorithm, a new point Created approx. From the current point Distance to new point or amount of search, Probability distribution that is in proportion to the temperature. All of the algorithm Accepts intent to reduce new points, but will raise the target with a certain probability Accepts points as well. Accept the scope The algorithm that raises the scores avoids getting stuck in the local minima and Explore globally for possible solutions. Algorithm Continuing, to lower the temperature properly, annealing as the temperature drops, algorithm search size reduces and at least integrates.

... La parte innovadora del algoritmo fue que, durante el proceso de búsqueda, no solo se aceptaban soluciones mejores, sino también introducía la posibilidad de aceptar algunas peores. SA hace una analogía con la formación de cristales a partir de masas fundidas a altas temperaturas [103] . Si la masa fundida es enfriada de manera súbita, los átomos que la forman no tendrán tiempo de crear un patrón organizado, dando lugar a imperfecciones en el cristal. ...

... Para controlar esto, Medina et al. [104] proponen que la temperatura inicial sea una fracción del valor de la función objetivo para la solución inicial. El algoritmo se detiene cuando la temperatura disminuye hasta un cierto porcentaje de la temperatura inicial, siendo valores usuales el 1% o 2% de ésta [103,104] , este criterio de parada es conocido como criterio de congelación. ...

Se plantea el problema de determinar el diseño óptimo de la estructura de refuerzo conformada por disipadores de energía sísmica de tipo Contraviento Restringido al Pandeo (CRP), que permita el reajuste del desempeño sísmico de marcos de hormigón armado.
Los CRP’s son elementos conformados por un núcleo metálico confinado, capaz de plastificar tanto a tracción como a compresión, característica que les permite disipar energía sísmica por medio de ciclos histeréticos. Debido a su comportamiento estable frente a acciones cíclicas, los disipadores de tipo CRP han sido utilizados tanto en el diseño como en el reajuste de estructuras ubicadas en zonas de elevado riesgo sísmico, como Japón, EU y América Latina.
Debido al comportamiento no lineal que presenta la respuesta de estructuras equipadas con disipadores de tipo CRP, los diseños candidatos a solución han sido analizados por medio de OpenSees, que es un programa de elementos finitos enfocado a la ingeniería sísmica. El desempeño sísmico de todos los diseños ha sido evaluado por medio del método del espectro de capacidad (Capacity Spectrum Method), el cual utiliza la información de análisis estáticos no lineales (Pushover) para estimar el desplazamiento máximo que presentará la estructura bajo una demanda sísmica dada.
El proceso de optimización ha sido realizo por medio del algoritmo metaheurístico conocido como Simulated Annealing (SA), teniéndose como objetivo determinar el número, disposición y características de los disipadores. Las características geométricas del núcleo de los CRP’s y su distribución en el marco fueron consideradas como variables, mientras que los elementos estructurales del marco se mantuvieron inalterados durante el proceso. El algoritmo de SA se corrió en el programa Matlab, creándose un vínculo entre este último y OpenSees para permitir la transferencia de información durante el proceso de optimización. El uso conjunto de ambos programas se mostró eficiente en la optimización de estructuras complejas por medio de algoritmos metaheurísticos.

... The main function of these structures is to support deep excavation in basement construction, road construction, bridge abutment construction, etc. Therefore, design an optimal cantilever retaining wall is an important task in civil engineering [2][3][4][5][6][7][8]. It is desired to obtain an optimal shape of cantilever 4(47) (2021) [1][2][3][4][5][6][7][8] retaining walls, which results in a low material cost and satisfaction of all safety requirements including safety against overturning/sliding and safety of bearing capacity [9]. ...

... Therefore, design an optimal cantilever retaining wall is an important task in civil engineering [2][3][4][5][6][7][8]. It is desired to obtain an optimal shape of cantilever 4(47) (2021) [1][2][3][4][5][6][7][8] retaining walls, which results in a low material cost and satisfaction of all safety requirements including safety against overturning/sliding and safety of bearing capacity [9]. ...

Design of cantilever retaining walls is an important task in various construction projects. This study aims at constructing an evolutionary algorithm based cantilever retaining wall design approach. Differential Evolution (DE) and the feasibility rule based constraint-handling (FRBCH) method is integrated achieve the research objective. A DE based software program incorporating FRBCH has been developed with Visual C# .NET to facilitate its implementation. A case study of cantilever retaining wall design has been used to validate the capability of the FRBCH-DE integration.

... The optimization of this type of structures allows them to be carried out in a more economical or environmentally friendly way depending on the objective of the optimization. Therefore, different works have been carried out related to the optimization of this type of structures either in terms of cost [9], [10], CO2 emissions [11] or comparing the differences between the optimization of both optimization objectives [12]. In some research works, the typology of retaining walls has been analyzed evaluating their life cycle [13], [14] comparing the different types of wall according to their impact. ...

... Once this experiment is carried out, it is decided to perform the response surface method with the two variables that have the greatest influence on the objective function, being the wall thickness (e) and the heel length (t). The rest of the variables are blocked with the dimensions obtained from the study conducted by Yepes et al. [9]. The value of the blocked variables is 0.20 m for the length of the toe (p), 0.47 m for the edge of the shoe (h) and 0 m for the value of the thickness of land in the intrados (et). ...

This paper describes the introduction of response surface methodology in a postgraduate course. This case study is carried out in the subject of the predictive models of optimization of concrete structures subject. This subject is inside the curricula of concrete engineering master. In this course students learn concepts such as structures’ optimization using algorithms, multi-criteria decision making, techniques do design of experiments, and metamodels such as the response surface in order to obtain optimum results. In this case study, the objective is to obtain a design solution of a reinforced concrete wall, using the CO2 emissions as an objective function to reduce its impact. In order to apply this methodology, the students need to use specific software. On the one hand, to carry out the statistical analysis that allow obtaining the response surface Minitab software has been used by students. On the other hand, students need to check the strength of the structure using Cype structural calculation software. As a result of applying this methodology to obtain an optimum reinforced concrete wall allow students to reach a better level in transversal competencies, such as design and project, critical thinking, analysis and problem solving or the use of specific software. This paper will introduce future research studies related to the use of structures optimization techniques by students applying other different optimization
techniques.

... Los métodos jerárquicos tienen como objetivo formar agrupaciones de forma sucesiva con el objetivo de minimizar alguna distancia o maximizar alguna medida de similitud. Dichos métodos pueden ser aglomerativos, cuando todos los casos se agrupen en un mismo conglomerado o disociativos cuando, se empieza a través de un conglomerado y con sucesivas divisiones se forman grupos más pequeños hasta llegar a tantas agrupaciones como casos se tenga (Yepes, Alcala, Perea, & Gonzáles-Vidosa, 2008). ...

En el presente documento se desarrolla un análisis de los mercados financieros internacionales en respuesta a diferentes eventos de crisis. El objetivo del trabajo fue evaluar el impacto de estos eventos ocurridos a partir del año 2007 hasta el año 2022. Mediante la exploración de diferentes índices bursátiles representativos de los mercados de capitales internacionales se pudo observar la dinámica en la valoración de las acciones, asimismo la aplicación de modelos de aprendizaje automático y técnicas de agrupación como clustering jerárquico permitió comprobar que los mercados tuvieron respuestas diferenciadas a estos eventos las cuales se encuentran asociadas a la ubicación geográfica de cada mercado. Abstract In this paper, an analysis of the international financial markets was developed in response to different crisis events. The aim of this work is to evaluate the impact of these events that occurred from the year 2007 to 2022. Through the exploration of different representative stock indices of the international capital markets, it was possible to observe the dynamics in the valuation of the shares, as well as the application of machine learning models and grouping techniques such as hierarchical clustering made it possible to verify that the markets had differentiated responses to these events, which are associated with the geographical location of each market. JEL Classification: C53, C63, G14, G15

... La optimización de estructuras de hormigón armado tales como tableros pretensados (Jaouadi et al., 2020¸ Martí et al., 2013Pons et al., 2018) y las pilas (Kripka et al., 2013;Martínez-Martín et al., 2012) de diferentes tipologías de puentes, así como muros contrafuerte (Yepes et al., 2008;Temur, 2021), ha demostrado obtener resultados especialmente interesantes. Mediante la aplicación de algoritmos que basan su funcionamiento en la búsqueda por descenso se consiguen reducciones considerables en los costes finales de la estructura, algo que conlleva un mejor uso de los materiales. ...

Los marcos articulados prefabricados de hormigón armado son una estructura de uso común en las redes de carreteras. Los avances en las técnicas de optimización permiten mejorar el proceso de diseño tradicional, consiguiendo minimizar factores como el coste final de la estructura. El estudio llevó a cabo la optimización económica de un marco articulado prefabricado de hormigón armado mediante la técnica metaheurística híbrida de recocido simulado con operador de mutación. Los parámetros del algoritmo fueron calibrados mediante un diseño de experimentos factorial, consiguiendo que el algoritmo tuviera un muy buen rendimiento. Tras su calibración, la metaheurística híbrida fue aplicada, consiguiendo diseños con costes finales reducidos. Finalmente, se mencionan una serie de características principales de los marcos óptimos, pudiendo destacar diseños esbeltos con densidades de armado elevadas. Los resultados sitúan la tipología estructural considerada como una alternativa especialmente interesante frente a las estructuras ejecutadas in situ.

... Traditionally, structural design processes depend on methods based on common practice. Once the analysis of this first design is done, the geometry of the sections and the grade of the materials are modified based on the experience of the technician (Yepes et al. 2008). Researchers have implemented optimization methods to obtain structural designs through automated processes to reduce this need for expertise. ...

Bridge optimization can be complex because of the large number of variables involved in the problem. In this paper, two box-girder steel–concrete composite bridge single objective optimizations have been carried out considering cost and CO2 emissions as objective functions. Taking CO2 emissions as an objective function allows to add sustainable criteria to compare the results with cost. SAMO2, SCA, and Jaya metaheuristics have been applied to reach this goal. Transfer functions have been implemented to fit SCA and Jaya to the discontinuous nature of the bridge optimization problem. Furthermore, a Design of Experiments has been carried out to tune the algorithm to set its parameters. Consequently, it has been observed that SCA shows similar values for objective cost function as SAMO2 but improves computational time by 18% while also getting lower values for the objective function result deviation. From a cost and CO2 optimization analysis, it has been observed that a reduction of 2.51 kg CO2 is obtained by each euro reduced using metaheuristic techniques. Moreover, for both optimization objectives, it is observed that adding cells to bridge cross-sections improves not only the section behavior but also the optimization results. Finally, it is observed that the proposed design of double composite action in the supports allows to remove continuous longitudinal stiffeners in the bottom flange in this study.

... The concluding remark which was drawn that the use of these optimum cross-sections will reduce the costs substantially. Victor Yepes, Julian Alcala, Cristian Perea, and Fernando Gonz´alez-Vidosa [11] examined reinforced concrete earth-retaining walls in connection with road construction for economic optimization. The optimization of walls was proposed by using a simulated annealing algorithm method. ...

The design of the Gravity retaining wall (GRW) is a trial and error process. Prevailing conditions of backfill are used to determine the profile of GRW, which proceeds with the selection of provisional dimensions. The optimum section is having factors of safety of stability higher than the allowable values and stresses in the cross-section smaller than permissible. The cross-section is designed to fulfill conditions of stability, subjected to very low stresses. The strength of the material, which is provided in the cross-section remains unutilized. A computer program is developed to find stresses at various locations on the cross-section of GRW using the Finite Element Method (FEM). A discontinuity in the form of a rectangular cavity is introduced in the cross-section of GRW to optimize it. The rectangular cavity is introduced in the cross-section of GRW at different locations. An attempt is made in this paper to find the stress distribution in the gravity retaining wall cross-section and to study the effect of the rectangular cavity on the stress distribution. Two cases representing different locations are considered to study the effect of the cavity. The location of the cavity is distinguished by the parameter w, the effects of cases with varied was 0.2305 (Case-I) and 0.1385 (Case-II) are observed. The cavity, which is provided not only makes the wall structurally efficient but also economically feasible.

... In order to select the final design out of the set of acceptable designs, optimisation tools can be employed for the desired performance criterion. In recent years, numerous design optimisation approaches have been developed and performed on various earth structures in which the design objectives were constrained to the construction cost and the system uncertainties that are handled implicitly by the factor of safety concept (Saribas and Erbatur 1996;Ceranic, Fryer, and Baines 2001;Yepes et al. 2008;Khajehzadeh et al. 2010;Camp and Akin 2012). Out of the available design optimisation approaches, the genetic algorithm has been found significantly effective in managing design optimisation of embedded footing, which incorporates numerous input variables, design objectives, and complex constraints (Pei and Xia 2012; Juang, Liu, and Atamturktur 2013). ...

This paper presents a quantitative framework to optimise embedded footing performance subjected to extreme historical climate events with respect to the uncertainties associated with site-specific soil and climatic parameters. The proposed framework is developed based on partially saturated soil mechanics principles in conjunction with a multi-objective optimisation algorithm called Non-dominated Sorting Genetic Algorithm (NSGA-II) to develop a robust optimised design procedure. The proposed method was applied to two semi-arid climate sites, Riverside and Victorville, both situated in California, United States. The results show that the proposed method generally improves the embedded footing design compared to conventional methods in terms of cost and performance. Based on the findings, under the extreme climate conditions, the proposed method estimates the average soil degree of saturation within the footing influence zone between 52% and 95%, with a mean value of 63.1% for the Victorville site, and 57% and 90% with a mean value of 81.6% for the site in Riverside. It is also found that the optimal design from the proposed method shows a lower total construction cost, 44% and 19%, for the Victorville and Riverside sites, respectively, compared to the ones designed by the conventional methods.

... Broad use of genetic algorithms [28,15,58,45,49,40,44,13,27,50,46,16,17,3,18,9,19,38], particle swarm optimization [61,41,62,2,60,21,63,22], simulated annealing method [56], or neural network [43] can be found in the literature. Even though these methods are well suited for a poorly defined problem with insufficient data, they come with a higher computational cost. ...

This paper introduces an automated deterministic method for the calibration of the Modified Cam-Clay and hypoplastic clay model. The calibration is structured in a hierarchical order established based on the apriori sensitivity study performed. The proposed method favours the clear physical meaning of the model parameters to a complete optimization of the objective error function. The method requires only basic laboratory experiments and it is currently implemented in the free-to-use online application called ExCalibre.

... A variety of stochastic methods have been employed to determine constitutive model parameters. These include the genetic algorithm-based calibration method [3, 9, 15, 17-20, 28, 29, 36, 38, 44-46, 49, 50, 60], the differential evolution method [52,64], and other stochastic methods such as the particle swarm optimization [2,22,23,40,62,63,65,66], the simulated annealing method [57] or neural network [43]. The stochastic methods are capable of determining stationary points over the defined domain and thus can provide a good picture of the objective function properties. ...

This paper discusses an automated deterministic approach to parameters calibration of the hypoplastic model for sand. The calibration is performed on results from basic laboratory experiments such as the oedometric test, isotropic compression test, and the drained and undrained triaxial shear tests. The calibration method is structured in a hierarchical order and implemented into a free-to-use online application called ExCalibre. The method is based on the sensitivity study performed prior to the development of the calibration method. The calibration procedure respects the physical meaning of the calibrated parameters and their influence on the stiffness and asymptotic states, rather than performing a blind optimization of an objective function.

... One of them is the field of structural engineering, which is one of the sub-branches of civil engineering, where studies are carried out within the scope of structural design. Examples of optimization problems in which metaheuristic algorithms are used in structural engineering are beams (Coello et al., 1997;Rafiq and Southcombe, 1998;Govindaraj and Ramasamy, 2005;Akın and Saka, 2010;Fedghouche and Tiliouine, 2012;Bekdaş and Nigdeli, 2013;Kayabekir et al., 2019;Zhao et al., 2021), columns (Bekdaş and Nigdeli, 2014;2016a;2016b;de Medeiros and Kripta, 2014;Nigdeli et al., 2015;Cakiroglu et al., 2021), frames Nigdeli and Bekdaş, 2016;Ghatte, 2021), foundations Kashani et al., 2021), retaining walls (Ceranic et al., 2001;Yepes et al., 2008;Camp and Akin, 2011;Kayabekir et al., 2020;Yücel et al., 2021;Martínez-Muñoz et al., 2021;Shalchi Tousi et al., 2021), Carbon Fiber Reinforced Polymer retrofit (Kayabekir et al., 2017;2018) and cylindrical walls (Bekdaş, 2014;2015;2018;2019;Kayabekir, 2021). ...

Optimization is a widely used phenomenon in various problems and fields. Because time and resources are very limited in today's world, it can be said that the usage area of the optimization process will be expanded and spread in all areas of life. Although different methods are used in the realization of the optimization process, the performance of metaheuristic algorithms in solving problems has led to an increase in research on these methods. As in other fields, the application examples of these algorithms are diversifying and increasing in the field of structural engineering. In this study, the performance comparison of five different algorithms for the optimum design of an axisymmetric cylindrical wall with a dome is investigated. These algorithms are Jaya (JA), Flower pollination (FPA), teaching-learning-based optimization (TLBO) algorithms and two hybrid versions of these algorithms. ACI 318 regulation was used in reinforced concrete design with a flexibility method-based approach in the analyses. In the analyzes with five different situations of the wall height, some statistical values , and data of analysis numbers were obtained by running the algorithms a large number of times. According to the analysis results, Jaya algorithm is slightly better in terms of the speed of reaching the optimum result, but also all algorithms are quite effective and reliable in solving the problem.

... Ceranic et al. (2001) presented a method employing the simulated annealing (SA) algorithm to find the optimum dimensions that provide minimum cost. Similarly, Yepes et al. (2008) also performed an optimization process with SA for minimum cost design of earth-retaining walls. The study researched several design variables, including reinforcement detail and material types, as well as geometrical properties. ...

In this study, a hybrid method was developed to predict optimum dimensions of reinforced concrete (RC) cantilever-type retaining walls. The metaheuristic-based optimization process of RC retaining walls needs iterative analysis, including the consideration of two different design limit states. These limit states defined as design constraints are geotechnical and structural limit states. Since the optimization process is long, it is aimed to generate a prediction model for optimum dimensions of RC cantilever retaining walls. For this purpose, artificial intelligence and machine-learning methods can be combined with metaheuristic algorithms used in the optimization of the problem. The method uses artificial neural networks (ANNs) for prediction results without iterative process and flower pollination algorithm (FPA) to obtain training data for machine learning. The proposed hybrid model is called flower pollination algorithm-based artificial neural network (FPA-ANN). To verify the prediction model, mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) values are calculated for the optimum data set. Because this is the first proposed prediction model for a real structural engineering application related to RC cantilever-type retaining walls, the model was tested on different input values that are not included in the machine-learning process. Also, the relations between height, unit soil weight, internal friction angle, and surcharge load are investigated via the prediction model.

... The formulation of the SA should guarantee the algorithm's convergence, which implies a slow reduction of parameter T. Establishing its reduction ratio can be a problem if the computation time is too high. Although there are studies in the literature that propose a fairly high reduction ratio (66%), such as the paper by Abuajwa et al. [40], we chose a ratio that is more frequently used (10%) to ensure this convergence [52], with a low computing time of 60 s for the five optimisations. ...

Recent increases in incidents make it unlikely for emergency systems to be able to meet incident requirements. In this paper, we formulate a new territorial measurement approach for the reliability of fire departments, the collapse index, to help decision makers determine their response capability. This new index expresses the maximum simultaneous workload in a pixel over one year, measured over time. Based on this index, we propose a new fire station (FS) optimum location model by applying the simulated annealing method in conjunction with a geographic information system. The formulation of the cost function as the minimum standard deviation of the FS workload, combined with the constraint that the maximum collapse index in any pixel must be less than a certain threshold, are two contributions of this work. Five optimisation processes are developed to locate between up to five FS and create collapse index maps in the Madrid Region. The maximum collapse index in a pixel with a new FS decreases from its initial value of 10,485 min to 2500 min when five new FS are built. The conclusion is that the proposed optimisation model meets the need for reliability in the emergency services and that the collapse index is a good measure to prevent overlapping in the system.

... The optimum design of RC retaining walls is one of the areas that have been researched extensively. Various metaheuristic methods such as Simulated Annealing (SA) [10,11], PSO [12], Harmony search (HS) [13] Big Bang Big Crunch (BB-BC) [14], Firefly Algorithm (FA) [15], FPA [16] have been used in the design of RC retaining walls. In addition to these studies, there are also studies where performance evaluation of algorithms [17] is performed and modified or hybrid algorithms [18] are used. ...

In the optimum design of structural systems, the robustness and the performance are related to the best tuning of the parameters of the method. For metaheuristic algorithms inspired by phenomena in life, algorithm-specific parameters exist in addition to general parameters that are the population of the generated candidate solution and the number of iterations that are needed to find the final optimum solution. In the optimum design of reinforced concrete (RC) structures, the dimensions are optimized by considering the minimization of the total cost. These problems are highly constrained by the design requirements presented in design codes. Especially, RC retaining walls involve the check of stability conditions as geotechnical state limits in addition to structural state limits. This situation makes the optimization problem challenging. A better and robust algorithm is always in search. In the present study, two specific parameter-free metaheuristic algorithms are employed. These algorithms are teaching-learning-based optimization (TLBO) and Jaya algorithm (JA). Since JA is a single-phase algorithm and both phases of TLBO defined as teacher and learner phases are consequently applied, a switch probability is not needed. Also, the existing factor is defined randomly. These two algorithms were tested on three cases and the results were compared with three classical algorithms such as Genetic Algorithm (GA), Differential Evaluation (DE), and Particle Swarm Optimization (PSO). In this verification, JA needs less function evaluation to reach the optimum results. As conclusions, both TLBO and JA are robust methods for the optimization problem.

... Researchers have studied the emissions produced by concrete projects [8][9][10] or construction procedures [11][12][13]. Other studies have focused on the optimization of concrete structures such as prestressed bridges [14,15] and earth-retaining walls [16][17][18][19]. Other researchers have studied CO 2 fixation by carbonation processes and their influence on the emissions [20,21] and the concrete recycling ratio [22][23][24]. ...

Achieving sustainability is currently one of the main objectives, so a consensus between different environmental, social, and economic aspects is necessary. The construction sector is one of the main sectors responsible for environmental impacts worldwide. This paper proposes the life cycle assessment (LCA) and comparison of four bridge deck alternatives for different span lengths to determine which ones are the most sustainable solutions. The ReCiPe method is used to conduct the life cycle analysis, by means of which the impact value is obtained for every alternative and span length. The Ecoinvent 3.3 database has been used. The life cycle has been divided into four phases: manufacturing, construction, use and maintenance, and end of life. The associated uncertainties are considered, and the results are shown in both midpoint and endpoint approaches. The results of our research show that for span lengths less than 17 m, the best alternative is the prestressed concrete solid slab. For span lengths between 17 and 25 m, since the box-girder solution is not used, then the prestressed concrete lightened slab is the best alternative. For span lengths between 25 and 40 m, the best solution depends on the percentage of recycled structural steel. If this percentage is greater than 90%, then the best alternative is the composite box-girder bridge deck. However, if the percentage is lower, the cleanest alternative is the prestressed concrete box-girder deck. Therefore, the results show the importance of recycling and reusing structural steel in bridge deck designs.

... Furthermore, the design of retaining wall structures depends on several parameters such as elevation difference between soil levels, soil properties, groundwater, construction area, intended use, and cost. The effect of parameters on the optimal design of a retaining wall was investigated in a parametric study, and the results have been presented here [15,16]. Although there are many studies on optimal retaining wall design [17][18][19], there has been no detailed study presenting a pre-design guide for different soil types to the best of our knowledge. ...

A pre-design guide for cantilever retaining walls and a detail parametric study of such walls
is presented here. Mathematical models based on statistical methods were improved for
calculating safety factors of sliding, overturning, and slope stability of those walls. The
harmony search algorithm (HSA)-a metaheuristic optimization method-was employed to
realize reasonable results of the pre-design guide from all distinct cases. Through the design
algorithm, the optimal design was determined for varied soil types differently from
suggestions of design codes. Thus, an optimal pre-design guide for safe and economic wall
design was realized in a shorter time compared to the conventional method.

... Using such slabs decreases material consumption and improve the insulation properties which enhances the sustainability of the structures (Alfeehan et al., 2017). Lastly, a parametric study has been done for the optimum solution of cantilever retaining walls such as slab (Uray, 2019), earth-retaining walls (Yepes et al., 2008), and reinforced concrete columns (Bektaş and Nigdeli, 2016). ...

In this study, the effect of different types of slabs on dynamic characteristics of structures under the lateral loading was investigated. For this purpose, four different types of slabs namely, beamed slab, flat slab, one way ribbed (hollow core) slab and waffle slab have been modeled in buildings having 3, 4 and 5 storeys with the same geometric dimensions, in accordance to design and construction requirements (TS 500) and Turkish building seismic codes (TBDY, 2018). Seismic analysis calculations of the modeled buildings were done using the equivalent seismic load method. The assumed local soil class was taken from the geotechnical report as ZD. As a result of the analysis, natural periods, base shear forces, maximum horizontal displacements and relative storey drifts of the buildings were compared. Seismic analysis and calculations of the buildings were completed using SAP2000 finite element software.

... Optimum design studies of reinforced concrete cantilever retaining walls started in the 1980s, and after the 2000s, the focus was on the applicability of metaheuristic algorithms in optimization. The optimum design of the reinforced concrete retaining wall under static loads, using Simulated Annealing (SA) algorithm inspired by the annealing of metals, has been studied on the parameters that affect the minimum cost (Yepes et al., 2008) and economic design (Ceranic et al., 2001). The optimum design of the reinforced concrete retaining wall under static and dynamic loads was made by the methods of Collision Bodies Optimization (CBO) and Democratic Particle Swarm Optimization (DPSO) (Kaveh and Soleimani, 2015). ...

In this study, the optimum dimensioning of a reinforced concrete retaining wall that meets the safety conditions under static and dynamic loads in terms of cost has been performed using Jaya algorithm, which is one of the metaheuristic algorithms. In the optimization process, reinforced concrete design rules and ground stress, sliding and overturn tests have been determined as design constraints for the safe design of the retaining wall. While 5 cross-section dimensions of the retaining wall are defined as the design variable, the objective function is targeted as the total cost per unit length of the retaining wall. In the study, optimum results are also presented by examining the changes of the toe projection length of the retaining wall, which is one of the design variables, narrowing between 0.2-10 m. The design variables minimizing the objective function were found via Jaya algorithm that have single-phase. In addition to achieving optimum dimensioning results in terms of safety and cost with the optimization method used as a result of the reinforced concrete design made by applying the rules of the regulation on buildings to be constructed in earthquake zones, the change in cost in seismic and static conditions was examined.

... Another widely used metaheuristic method is Simulated Annealing (SA). Proposed in 1983 by Kirkpatrick et al. [37], the SA has quickly gained widespread acceptance and has been applied to various optimization problems in many disciplines, including structural optimization [38][39][40]. One attractive property of SA is that its convergence to the global optimum is guaranteed provided that the iterations are performed sufficiently slowly (i.e. by selecting a low cooling rate) and a sufficient number of random initializations have been used. ...

Process optimization using metaheuristic algorithms is rapidly gaining interest from engineering practitioners and researchers. This study uses the cuckoo search algorithm (CSA) to find the optimum parameters of a novel smart damper under seismic excitations. For this purpose, seismic responses of four-story and nine-story building configurations under seven pairs of ground motions have been considered. The smart damper is a shear polyurethane friction (SPF) passive control device, made up of shape memory alloy (SMA) plates, friction devices, and polyurethane springs. The damper was installed using braced frame shear links of Y-shaped inverted type, in the form of a vertical link beam placed in the eccentrically braced frames. Because the shear mode of failure is common in such a configuration, the SPF damper is expected to reduce the residual inter-story drifts of the building subjected to strong earthquake loading. Numerical optimization and time-domain simulations were carried out using the MATLAB and OpenSees software programs, respectively. The targeted optimization criteria include the peak values of inter-story drift, residual drift, and floor acceleration; and the design parameters consist of SMA cross-sectional area, friction force, and the polyurethane stiffness of the SPF-SMA system. The results of this study demonstrate the suitability of CSA for the determination of optimum parameters of the SPF-SMA system for the buildings and ground motions considered. Future studies will investigate the generalizability of the proposed method to other building configurations and ground motions.

... The reason is that design optimization of RC corresponds to pre-processing research of rebars optimization, while CWM of rebars covered in this study corresponds to post-processing research. As a result of reviewing some of the literature related to design optimizations of rebars, it was confirmed that they are related to design optimization of RC components such as slab [50][51][52][53][54][55][56][57], beam [58][59][60][61], column [62][63][64][65], foundation [64], and wall [66][67][68], and design optimization of RC frames such as bridges [69][70][71] and building [72]. In addition, many studies related to design optimization have been well-organized in the review article [37]. ...

Rebar, the core resource of reinforced concrete structures, generates more carbon dioxide per unit weight than any other construction resource. Therefore, reducing rebar cutting wastes greatly contributes to the reduction of greenhouse gas (GHG). Over the past decades, many studies have been conducted to minimize cutting wastes, and various optimization algorithms have been proposed. However, the reality is that about 3 to 5% of cutting wastes are still generated. In this paper, the trends in the research on cutting waste minimization (CWM) of rebar for sustainable work are reviewed in a systematic method with meta-analysis. So far, the literature related to cutting waste minimization or optimization of rebar published has been identified, screened, and selected for eligibility by Preferred Reporting Items for Systematic Reviews and Meta-Analyses, and the final 52 records have been included in quantitative and qualitative syntheses. Review by meta-analysis was conducted on selected literatures, and the results were discussed. The findings identified after reviewing the literature are: (1) many studies have performed optimization for the market length, making it difficult to realize near-zero cutting wastes; (2) to achieve near-zero cutting wastes, rebars must be matched to a specific length by partially adjusting the lap splice position (LSP); (3) CWM is not a one-dimensional problem but an n-dimensional cutting stock problem when considering several rebar combination conditions; and (4) CWM should be dealt with in terms of sustainable value chain management in terms of GHG contributions.

... For several RC structural participants, there have been several optimization strategies proposed. In the optimization of RC retaining walls, multiple methods using metaheuristic algorithms, such as simulated annealing [7,8], harmony search [9], large bang-big crunch [10] and charged device search [11], were used. Several RC participants in the optimization, the music-inspired metaheuristic algorithm called harmony search was used, such as continuous beams [12], T-shaped RC beams [13], columns [14] and frames [15]. ...

Designing a reinforced concrete column to resist an axial load and bending moment is an iterative procedure which involves tedious calculations. The design is influenced by many variables, such as load eccentricity, column cross-section size, steel percentage, neutral axis location, steel grade, and concrete grade, requiring the use of interaction diagrams. In the present research, an attempt was made to determine the optimum design under direct load, uniaxial and biaxial moments of reinforced concrete columns that meets all ACI-318 code specifications and therefore results in minimum cost. The purpose of the paper is to achieve the optimum design of the columns of reinforced concrete. Column optimisation results in cost savings. The objective function is to minimize the total cost of the column. It is consists of the cost of concrete, reinforcement, formwork and links per unit length of column. Concrete and steel strength, cross-sectional dimensions, and steel bar diameters used as longitudinal reinforcement and tie were treated as design variables in the formulation of the optimal design problem. The optimal design was performed using the program MATLAB (The Mathworks, Inc.). The problem of optimization was conceived as a problem of nonlinear, restricted minimization. Many problems have been formulated and the best solutions have been obtained. It was noticed that the most economical design is provided by the solutions. The use of optimal quantities of reinforcement advances the goal of enhancing the sustainability of the construction of reinforced concrete.

... Several studies introduce retaining wall design optimization by metaheuristics. For instance, Ceranic et al. [18] and Yepes et al. [19] suggested optimum solutions by SA; Kaveh and Abadi [20] examined the same problem by HS; Khajehzadeh et al. [21] and Ahmadi and Varaee [22] covered the design process by PSO; Ghazavi and Bonab [23,24] decreased the construction cost by ACO. Different PSO and evolutionary algorithms have been used to find the optimum design solution by Kashani et al. [25], Gandomi and Kashani [26], and Gandomi et al. [27] Moreover, a computerized approach for designing mechanically stabilized earth walls has been suggested by Yalcin et al. [28]. ...

Retaining walls need to be designed optimally since huge cost savings are probable considering their dimensions and materials used in the design and construction. Even better savings are possible when they are constructed in earthquake-prone regions. In this study, an improved flower pollination algorithm (IFPA) is used to optimize the design of the reinforced concrete cantilever retaining wall subjected to dynamic loadings. The mathematical model contains three constraints including geotechnical, structural, and geometrical considerations. As the previous FPA applications revealed the efficiency of this method for retaining wall problems, some modifications have been made on the existing method when dynamic loadings are included. To reveal the performance of IFPA, sensitivity analyses are carried out using a variety of soil parameters. Also, tuning of IFPA parameters is illustrated with two different retaining wall case studies reported in the literature. The results indicate that IFPA is a viable alternative to the well-known metaheuristics. This study also reveals that there is space for further improvements to cover wider range of geotechnical engineering-related optimization problems.

... The optimization algorithm applied in this work was a hybrid simulated annealing (SA) algorithm. The algorithm was selected from the study by Yepes et al. [49] and modified using a mutation operator (SAMO2). This algorithm allows a combination of the advantages of the diversity of genetic algorithms with the good convergence of SA. ...

The importance of construction in the consumption of natural resources is leading structural design professionals to create more efficient structure designs that reduce emissions as well as the energy consumed. This paper presents an automated process to obtain low embodied energy buttressed earth-retaining wall optimum designs. Two objective functions were considered to compare the difference between a cost optimization and an embodied energy optimization. To reach the best design for every optimization criterion, a tuning of the algorithm parameters was carried out. This study used a hybrid simulated optimization algorithm to obtain the values of the geometry, the concrete resistances, and the amounts of concrete and materials to obtain an optimum buttressed earth-retaining wall low embodied energy design. The relation between all the geometric variables and the wall height was obtained by adjusting the linear and parabolic functions. A relationship was found between the two optimization criteria, and it can be concluded that cost and energy optimization are linked. This allows us to state that a cost reduction of €1 has an associated energy consumption reduction of 4.54 kWh. To achieve a low embodied energy design, it is recommended to reduce the distance between buttresses with respect to economic optimization. This decrease allows a reduction in the reinforcing steel needed to resist stem bending. The difference between the results of the geometric variables of the foundation for the two-optimization objectives reveals hardly any variation between them. This work gives technicians some rules to get optimum cost and embodied energy design. Furthermore, it compares designs obtained through these two optimization objectives with traditional design recommendations.

... Gravitational search algorithm (GSA) was opted for finding the best cost design of 3 m and 5.5 m high retaining wall by Khajehzadeh and Eslami [9]. Yepes et al. [10] used simulated annealing (SA) for analyzing parameters of 4 m to 10 m retaining walls by considering soil properties variation. Ant colony optimization (ACO) was used by Bonab [11] for designing 3 m, 4 m, and 5 m-high retaining walls. ...

A retaining wall is a structure used to resist the lateral pressure of soil or any backfill material. Cantilever retaining walls provide resistance to overturning and sliding by using backfill weight. In this paper, the weight and cost of the cantilever retaining wall have been minimized using a hybrid metaheuristic optimization technique, namely, h-BOASOS. The algorithm has been developed by the ensemble of two popular metaheuristics, butterfly optimization algorithm (BOA) and symbiosis organism search (SOS) algorithm. BOA’s exploratory intensity is coupled with SOS’s greater exploitative capacity to find the superior algorithm h-BOASOS. The newly developed algorithm has been tested with a suite of 35 classical benchmark functions, and the results are compared with several state-of-the-art metaheuristic algorithms. The results are evaluated statistically by the Friedman rank test, and convergence curves measure the convergence speed of the algorithm. It is observed in both cases that h-BOASOS is superior to other algorithms. The suggested approach is then used to solve four real-world engineering design problems to examine the problem-solving capacity of the proposed algorithm, and the results are contrasted with a wide range of algorithms. The proposed h-BOASOS is considered to be the winner on each occasion. Finally, the newly suggested algorithm is applied to find the cost and weight of the cantilever retaining wall problems of two different heights, 3.2 m and 6.3 m. The obtained results are compared with the component algorithms and found that the new algorithm works better than the compared algorithms.

... Ceranic et al. [12] developed an SA-based method for cost optimization. Then, also by using SA, a parametric study was conducted by Yepes et al. [13]. PSO was employed by for the design of optimum variables of RC retaining walls. ...

In the optimum design of reinforced concrete (RC) structural members, the robustness of the employed method is important as well as solving the optimization problem. In some cases where the algorithm parameters are defined as non-effective values, local-optimum solutions may prevail over the existing global optimum results. Any metaheuristic algorithm can be effective to solve the optimization problem but must give the same results for several runs. Due to the randomization nature of these algorithms, the performance may vary with respect to time. The essential and novel work done in this study is the comparative investigation of 10 different metaheuristic algorithms and two modifications of harmony search (HS) algorithm on the optimum cost design of RC retaining walls constrained with geotechnical and structural state limits. The employed algorithms include classical ones (genetic algorithm (GA), differential evaluation (DE), and particle swarm optimization (PSO)), proved ones on structural engineering applications (harmony search, artificial bee colony, firefly algorithm), and recent algorithms (teaching–learning-based optimization (TLBO), flower pollination algorithm (FPA), grey wolf optimization, Jaya algorithm (JA)). The modifications of HS include adaptive HS (AHS) concerning the automatic change of algorithm parameters and hybridization of AHS with JA that is developed for the investigated problem. According to the numerical investigations, recent algorithms such as TLBO, FPA, and JA are generally the best at finding the optimum values with less deviation than the others. The adaptive-hybrid HS proposed in this study is also competitive with these algorithms, while it can reach the best solution by using a lower population number which can lead to timesaving in the optimization process. By the minimization of material used in construction via best optimization, sustainable structures that support multiple types of constraints are provided.

... Methods for obtaining cost and sizing equilibrium of reinforced concrete retaining walls have been the main objective of many studies over the years and continue to be relevant due to the developments in information and computer technologies. Metaheuristic algorithms such as the genetic algorithm (GA) [12,[26][27][28], big bang big crunch (BBBC) [29,30], particle swarm optimization (PSO) [31,32], firefly algorithm (FA) [33,34], harmony search (HS) algorithm [35,36], ant colony optimization (ACO), bat algorithm (BA) [37], charged system search (CSS) [38], simulated annealing (SA) [39][40][41], biogeography-based optimization algorithm (BBO) [42], teaching learning-based optimization (TLBO) [43], jaya algorithm (JA) [44], and flower pollination algorithm (FPA) [45] can be counted as the applied mew methods for the optimization process of retaining wall systems. ...

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.

... The polygon that defines the position of the structure corresponds to the upper vertex in contact with the ground surface ( Figure 2). The distance between the polygon which defines the direction of the wall and the axis of the road is determined by various factors: structural conditions which allow the geometric fit of the structure with respect to the platform [15], aspects related to visibility which will determine the minimum distance [16], geotechnical aspects [17,18], etc. ...

Sustainability and interoperability are two closely related concepts. By analyzing the three fundamental facets of sustainability—economic, ecological and ethical/social—it is easier to address their connection with the concept of interoperability. This paper focuses on the economic aspect, in the field of civil engineering. In this area, due to the local nature of many of the software tools used, interoperability problems are frequent, with few studies addressing the economic impact of this, especially in small engineering firms. The main contribution of this paper is a design methodology for linear works based on the federation of building information modelling (BIM) models created with different software tools, conceived to break the interoperability issues between these applications. As an example, this methodology is applied to a mountain road widening project. A detailed economic analysis of the application of this methodology by an engineering Spanish firm reveals the important cost reductions that the integration of the software tools provides versus the prior practices.

... More recently, it is important to note the studies that optimize structural concrete frames by genetic algorithms [11], [12]. In the last decade, our research group has applied the heuristic methods to the optimum design of cantilever walls, road frames, building frames, bridge piers and precast beam bridge decks [13]- [17]. The method followed in this study has developed firstly a structural evaluation module of slab-deck bridges, where cross-section dimensions, materials and passive and active reinforcement have been taken as design variables. ...

Purpose
The purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.
Design/methodology/approach
Two-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.
Findings
This paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.
Originality/value
Optimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

The paper presents the formulation and implementation of the problem of finding a rational external geometry of a retaining wall. The purpose of the research is to formulate and test the mathematical model of the specified problem. In this connection, the working hypothesis is the assumption of accepting the criteria for rationalizing the system in the form of requirements for minimizing the potential strain energy of system (PSE) on the set of allowable values of variable parameters and equalizing the potential strain energy density (PSED) within the designated model. These criteria are an integral structural part of the bioenergetic optimization method, however, this paper considers the problem of improving external (geometric) parameters based on the exploitation of only the 1st criterion. In the framework of the exploitation of the Coulomb theory, the procedure of formation of the geometry of the structure is defined when the pressure of the ground on it is applied. The simplest example is the algorithm for solving the problem of finding rational geometry of the rear face of a subsurface wall with its given horizontal projection. The essence of the proposed approach is the approximation of the curvilinear forming the rear face of the subsurface wall by a broken line. For each section of the divided structure key dependencies are built for the components of the stress-deformed state of the structure. It is shown that for given soil characteristics, the value of the potential energy of deformation of the system can be described through a combination of the slope angles of each of the sections. The problem is reduced to finding a combination of these angles in which the entered criterion takes the minimum (exact lower bound) value. The conclusion about the representativeness of the obtained solution is made on the basis of the compiled alternative information model. The implementation of the approach is illustrated by a numerical example. The results obtained can be applied in the search for a rational geometry of a retaining wall in the process of building design.

Transportation of bulk cargo occupies one of the leading positions in the market of transport services. According to analysts’ forecasts, in the future, the volume of transportation of such bulk cargoes as grain, cement, mineral fertilizers, etc. will only increase. The creation of vehicles designed for the transportation of bulk cargo with improved technical and economic indicators is an important and urgent task that cannot be effectively solved without a study of the loading of the vehicle with bulk cargo. The analysis of the applied methods for calculating the active and passive pressure of bulk cargo, including taking into account the vertical and horizontal accelerations acting on the vehicle, is carried out. Nowadays, equations used to determine bulk cargo pressure acting on vehicle body walls are applicable only for nearly vertical walls. Their use in calculating pressure for sloping walls for which angle of inclination to horizon is less than 80º leads to incorrect results. Paper is devoted to determination of compact analytical equations that can be applied to calculate pressure of bulk cargo acting on vehicle body walls in range of wall inclination angle to horizon equal to from 0 to 90º.

As all engineering disciplines, structural engineering problems are needed to be optimized and due to the nonlinear behavior of these problems, it is not possible to solve them mathematically, but metaheuristic methods are very successful in iterative optimization by assuming values for the design variables within a desired range of the user. In structural engineering problems, metaheuristic methods including swarm-intelligence-based algorithms are used in two groups of problems. Design optimization is the first group and the design like dimension, amount of material and orientations are optimally found for minimizing objectives related to cost, weight, CO2 emission and others. In these problems, constraints are found via design codes like steel and reinforced concrete structure design regulations. This group belongs to a design of a structure. The second group includes optimum tuning and it generally covers structural control applications. This group involves the optimum tuning of the additional control system of the structure that can be added to the newly constructed structure for better performance or existing ones to correct the failure or increase the existing performance. The role of engineers is to make the best possible structural design and optimization is important. More especially, tuning optimization is a must to provide acceptable performance. In this chapter, a review of existing studies about the design optimization of structural systems is presented for swarm intelligence-based algorithms. Then, optimum tuning applications are mentioned including the most important studies about tuned mass dampers. Finally, optimization problems are presented for design and tuning optimization. The RC retaining wall optimization was presented for two cases with and without toe projection and the optimization of a toe is 5% effective on reduction of cost. In span length optimization of frame structures, frame models with different stories have similar optimum span lengths. Active tuned mass dampers are up to 22.08% more effective than passive tuned mass dampers.KeywordsStructural engineeringOptimum designOptimizationMetaheuristicSwarm intelligence

For the optimum design of RC frame structures, a simplified but effective discrete optimization algorithm is introduced in this paper. To determine the member force to be based on the design procedure, a plastic analysis considering the sequential development of plastic hinges in beams and columns up to the point of collapse is conducted, with the subsequent optimum design then devised via a direct search method. The construction of a database for predetermined discrete RC sections and interconnections of all design variables in an RC section with a single design variable associated with the section identification number makes it possible to adopt the direct search method instead of a sophisticated mathematical approach that includes many complicated descriptive functions pertaining to RC beams and columns. The use of the plastic analysis also reduces the maximum member force through moment redistribution, and the direct search method makes it possible to find a true optimum section regardless of the assumed initial section. The efficiency and applicability of the introduced algorithm are verified through correlation studies for typical frame structures. In particular, given that all design criteria in design codes and practical limitations required when undertaking the actual design are already considered while determining RC sections in the section database, the obtained results can be directly applied to the creation of designs. In advance, the use of the obtained optimum design results as initial sections in the preliminary design stage will greatly reduce the number of design steps for the determination of RC sections.

The main purpose of this study is to investigate the performance of the proposed hybrid teaching-learning based optimization algorithm on the optimum design of reinforced concrete (RC) cantilever retaining walls. For this purpose, three different design examples are optimized with 100 independent runs considering continuous and discrete variables. In order to determine the algorithm performance, the optimization results were compared with the outcomes of the nine powerful meta-heuristic algorithms applied to this problem, previously: the big bang-big crunch (BB-BC), the biogeography based optimization (BBO), the flower pollination (FPA), the grey wolf optimization (GWO), the harmony search (HS), the particle swarm optimization (PSO), the teaching-learning based optimization (TLBO), the jaya (JA), and Rao-3 algorithms. Moreover, Rao-1 and Rao-2 algorithms are applied to this design problem for the first time. The objective function is defined as minimizing the total material and labor costs including concrete, steel, and formwork per unit length of the cantilever retaining walls subjected to the requirements of the American Concrete Institute (ACI 318-05). Furthermore, the effects of peak ground acceleration value on minimum total cost is investigated using various stem height, surcharge loads, and backfill slope angle. Finally, the most robust results were obtained by HTLBO with 50 populations. Consequently the optimization results show that, depending on the increase in PGA value, the optimum cost of RC cantilever retaining walls increases smoothly with the stem height but increases rapidly with the surcharge loads and backfill slope angle.

Optimal design of cantilever retaining wall structures is among the most commonly geotechnical structures supporting vertical or near-vertical slopes of soil. These structures are used in many locations such as highways, bridges, and railway infrastructures. This study aims to employ the recently developed population-based metaheuristic algorithm which is called Plasma Generation Optimization (PGO) for the optimal design of reinforced concrete cantilever retaining wall structures. The design is based on the ACI 318–19 requirements, and optimizing construction cost is considered as the goal of the optimization problem. Two well-known theories including the Rankin and Coulomb theories are used in order to estimate the lateral earth pressure for the static loading condition. However, Mononobe–Okabe theory is utilized to determine this pressure for seismic loading condition. To investigate the efficiency of the PGO, two practical examples consisting of the cantilever retaining wall with shear key and cantilever retaining wall with sloped base are optimally designed based on the above-mentioned theories. Comparing the results acquired by the PGO with those of two well-known metaheuristics, namely Cuckoo Search and teaching–learning-based optimization, indicates the efficiency of PGO for the reinforced concrete cantilever retaining wall structures.

This paper presents an approach to design reinforced concrete retaining walls based on the attainment of both sustainable geotechnical design and structural optimization simultaneously with the use of a special algorithm Harmony Search to utilize the influence of both the structural material and the surrounding soil properties. Harmony Search algorithm is applied to design problem with the use of two different objective functions. The first function aims to minimize the total material cost and the second function aims to minimize the CO2 emission value associated with the supplement of geotechnical safety and structural necessities. The envisaged optimization problem considers several different variants such as the geometric variables (top and bottom thickness of the stem, length of the toe and the heel encasements and the height of the stem), the soil variables (unit weight of soil and shear strength angle), the cost of materials (the unit cost of concrete and steel), the amounts of the CO2 emission (the unit amount of emission for concrete and steel). The outcomes of the analysis show that Harmony Search algorithm is a convenient meta-heuristic optimization method to achieve optimum design for RC retaining walls considering both geotechnical and structural multi-variants. Besides, the significant effects of the geotechnical and structural parameters are emphasized and demonstrated in detail because of their early position through the construction process.

The purpose of this state-of-the-art review is to present the latest advances in design optimization and applications of metaheuristic algorithms in structural engineering. In the first part of this chapter, the importance of optimization in structural engineering and its differences with engineering problems are emphasized. Metaheuristic methods and the most appropriate techniques for various approaches are 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. Modifications of these algorithms have been made and applied to structural engineering applications. Finally, the results are presented with discussion about further potential improvements.

In this study; a reinforced concrete retaining wall was dimensioned under static and dynamic loads at optimum cost using the Jaya algorithm, which is one of the metaheuristic algorithms. As an objective function, the total cost for the unit length of the retaining wall and the cross-sectional dimensions are defined as design variables. Thanks to the single phase of the Jaya algorithm, the solution was reached quickly, and the best design variables were obtained with the minimal solution in the objective function compared to regular calculations. In addition to achieving optimum dimensioning results in terms of safety and cost, the relationship between earthquake and cost has been examined with the optimization method used as a result of the reinforced concrete design made by applying the regulations on the Buildings to be built in Earthquake Zones (DBYBHY 2007).

A systematic robust design optimization methodology is presented in this study for cantilever retaining wall backfilled with shredded tire in the face of earthquake hazards. Regarding the merits of application of shredded tire backfill in seismically active areas, the uncertainties in properties of this material (e.g., friction angle and cohesion) as well as uncertainties in earthquake load (e.g., peak ground acceleration) necessitate examining the robustness of design along cost efficiency in geotechnical design procedures. The wall tip deflection was treated as the response of concern for which a response surface was developed based on the design and random (uncertain) variables. Coupling with Monte Carlo simulations, the optimization in terms of cost and standard deviation of response as a measure of robustness yielded a set of preferred designs, or Pareto front, and the final optimal design was determined via selection procedures based on knee point concept.

This paper deals with the economic optimization of reinforced concrete framed structures typically used in road construction. It shows the efficiency of heuristic optimization by the simulated annealing algorithm (SA), the threshold acceptance method (TA) and the tabu search method (TS). The evaluation of solutions follows the Spanish Code for structural concrete. Stress resultants and envelopes of framed structures are computed by an internal matrix method program. Design loads are in accordance to the national codes for road bridges. The algorithm is applied to a 13 m horizontal span RC box road frame. This example has 50 discrete variables, 3 geometrical, 3 types of concrete and 44 reinforcement bars and bar lengths. The evaluation module includes the ULS of fatigue plus other commonly checked limit states of service and ultimate flexure, shear and deflections. The comparison of the three heuristic methods shows lower deviation from the best solution for the threshold accepting algorithm when compared with SA-TS methods. Structural results are reasonably slender, i.e. top slab of 0.95 m depth (1/14 slab/span ratio) and walls of 0.40 m thickness (1/15 wall/height ratio); and they indicate the importance of the inclusion of the fatigue limit state, since its ignorance leads to more economic but unsafe designs.

This paper examines the application of three methods of heuristic optimization for the design of reinforced concrete road vaults used in artificial tunnels. The structure is defined by 49 discrete design variables. Penalty functions are used for unfeasible solutions. The three heuristic methods used are the global best descent local search (GB), the simulated annealing (SA) and the threshold acceptance (TA). All methods are applied to a vault of 12.40 m of diameter. The paper presents two original moves of neighbourhood search and an algorithm for the calibration of SA-TA algorithms. The TA algorithm appears to be more efficient that the GB and the SA algorithms. The optimization method indicates savings of about 10% with respect to a traditional design.

This paper describes a methodology to design reinforced concrete (RC) cantilever earth-retaining walls typically used in road construction based on minimum embedded CO 2 emissions. The traditional approach to design does not fully optimize the use of materials. However, structural optimization methods are a clear alternative to designs based only on experience. Here, the design involves optimization by a simulated annealing (SA) algorithm applied to two objective functions, namely the embedded CO 2 emissions and the economic cost of reinforced concrete walls. The formulation of the problem includes 20 design variables: four geometrical ones dealing with the thickness of the kerb and the footing, as well as the toe and the heel lengths; four material types; and 12 variables for the reinforcement set-up. All the structural constraints have been imposed using Spanish codes, as well as habitual recommendations in this type of projects. Results from the SA algorithm application indicate that embedded emissions and cost are closely related and that more environmentally-friendly solutions than the lowest cost solution are available at a cost increment which is less than 1.4%. In addition, it is verified that a reduction of 1 euro in cost causes a reduction of 2.20 kg of emissions of CO 2 . Further, the economic walls use in average 4.9% more concrete than the best environmental solutions, though the latter solutions need 1.8% more steel. Finally, the methodology described will enable structural engineers to mitigate CO 2 emissions in their RC structural designs.

A design procedure implementing a genetic algorithm is developed for discrete optimization of reinforced concrete frames RC-GA. The design procedure conforms to the American Concrete Institute ACI Building Code and Commentary. The objective of the RC-GA procedure is to minimize the material and construction costs of reinforced concrete structural elements subjected to serviceability and strength requirements described by the ACI Code. Examples are presented demonstrating the efficiency of the RC-GA procedure for the flexural design of simply-supported beams, uniaxial columns, and multi-story frames.

Tabu search, also called adaptive memory programming, is a method for solving challenging problems in the field of optimization. The goal is to identify the best decisions or actions in order to maximize some measure of merit (such as maximizing profit, effectiveness, quality, and social or scientific benefit) or to minimize some measure of demerit (cost, inefficiency, waste, and social or scientific loss).
Practical applications in optimization addressed by tabu search are exceedingly challenging and pervade the fields of business, engineering, economics, and science. Everyday examples include problems in resource management, financial and investment planning, healthcare systems, energy and environmental policy, pattern classification, biotechnology, and a host of other areas. The complexity and importance of such problems has motivated a wealth of academic and practical research throughout the past several decades, in an effort to discover methods that are able to find solutions of higher quality than many found in the past and capable of producing such solutions within feasible time limits or at reduced computational cost.
Tabu search has emerged as one of the leading technologies for handling optimization problems that have proved difficult or impossible to solve with classical procedures that dominated the attention of textbooks and were considered the mainstays of available alternatives until recent times. A key feature of tabu search, underscored by its adaptive memory programming alias, is the use of special strategies designed to exploit adaptive memory. The idea is that an effective search for optimal solutions should involve a process of flexibly responding to the solution landscape in a manner that permits it to learn appropriate directions to take along with appropriate departures to explore new terrain. The adaptive memory feature of tabu search allows the implementation of procedures that are capable of searching this terrain economically and effectively.

This paper reports on the application of a simulated annealing (SA) algorithm to the minimum cost design of reinforced concrete retaining structures. Cantilever retaining walls are investigated, being representative of reinforced concrete retaining structures that are required to resist a combination of earth and hydrostatic loading. To solve such a constrained optimisation problem, a modified SA algorithm is proposed that avoids the simple rejection of infeasible solutions and improves convergence to a minimum cost. The algorithm was implemented using an object-orientated visual programming language, offering facilities for continual monitoring, assessing and changing of the SA control parameters. Results show that the SA algorithm can be successfully applied to the minimum cost design of reinforced concrete retaining walls, overcoming the difficulties associated with the practical and realistic assessment of the structural costs and their complex inter-relationship with the imposed constraints on the solution space.

As regards the SA procedure, it has proved an efficient search algorithm for the 4 case studies of walls, portal and box frames used in road construction and building frames. The study of earth retaining walls optimization shows that the inclusion of a limit of 1/150 on the deflection of the top of the walls is needed. Otherwise, results of the SA optimization are excessively deformable. Results of the optimization of portal road frames indicated the need of including the rarely checked ULS of fatigue in the list of structural restrictions for the optimization of road structures. The study of road box frames shows the importance of the inclusion of the SLS of deflections and the ULS of fatigue. The SA optimization of the 13 m free horizontal span box frame results in a slender and highly reinforced top slab. Results of the optimization of the building frame indicate that instability in columns and flexure, shear and deflections in beams are the main restrictions that condition its design.

There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom
in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given
function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization
of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and
provides an unfamiliar perspective on traditional optimization problems and methods.

Metaheuristics for Hard Optimization comprises of three parts. The first part is devoted to the detailed presentation of the four most widely known metaheuristics: - the simulated annealing method; - the tabu search; - the genetic and evolutionary algorithms; - the ant colony algorithms. Each one of these metaheuristics is actually a family of methods, of which we try to discuss the essential elements. Some common features clearly appear in most metaheuristics, such as the use of diversification, to force the exploration of regions of the search space, rarely visited until now, and the use of intensification, to go thoroughly into some promising regions. Another common feature is the use of memory to archive the best encountered solutions. One common drawback for most metaheuristics still is the delicate tuning of numerous parameters; theoretical results available by now are not sufficient to really help in practice the user facing a new hard optimization problem. In the second part, we present some other metaheuristics, less widespread or emergent: some variants of simulated annealing; noising method; distributed search; Alienor method; particle swarm optimization; estimation of distribution methods; GRASP method; cross-entropy method; artificial immune systems; differential evolution. Then we describe some extensions of metaheuristics for continuous optimization, multimodal optimization, multiobjective optimization and contrained evolutionary optimization. We present some of the existing techniques and some ways of research. The last chapter is devoted to the problem of the choice of a metaheuristic; we describe an unifying method called "Adaptive Memory Programming", which tends to attenuate the difficulty of this choice. The delicate subject of a rigorous statistical comparison between stochastic iterative methods is also discussed. The last part of the book concentrates on three case studies: - the optimization of the 3G mobile networks (UMTS) using the genetic algorithms. After a brief presentation of the operation of UMTS networks and of the quantities involved in the analysis of their performances, the chapter discusses the optimization problem for planning the UMTS network; an efficient method using a genetic algorithm is presented and illustrated through one example of a realistic network; - the application of genetic algorithms to the problems of management of the air traffic. One details two problems of air traffic management for which a genetic algorithm based solution has been proposed: the first application deals with the en route conflict resolution problem; the second one discusses the traffic management in an airport platform; - constrained programming and ant colony algorithms applied to vehicle routing problems. It is shown that constraint programming provides a modelling procedure, making it possible to represent the problems in an expressive and concise way; the use of ant colony algorithms allows to obtain heuristics which can be simultaneously robust and generic in nature. One appendix of the book is devoted to the modeling of simulated annealing through the Markov chain formalism. Another appendix gives a complete implementation in C++ language for robust tabu search method

This paper deals with the multiobjective optimization of reinforced concrete framed structures typically used in building construction. It shows the efficiency of a multiobjective simulated annealing (MOSA) algorithm applied to two objective functions dealing with the economic cost
of the frames and with the number of bars of the reinforcement setup. The latter objective being considered important as regards the constructability of the framed structure, since lower number of bars structures are easier to construct. The evaluation of solutions follows the Spanish Code
for structural concrete. Stress resultants and envelopes of framed structures are computed by an internal matrix method program. Design loads are in accordance to the national codes for building structures. The example studied is a symmetrical building frame of 2 bays and 4 floors. This example
has 81 design variables including 8 material types of concrete, the type of steel, 24 cross-section dimensions and 48 passive reinforcement bars following a standard setup in columns and beams. Pareto results of the MOSA algorithm indicate that more practical solutions that the lower cost
solution are available at a cost increment acceptable in practice. It is concluded that MOSA optimization algorithms are a forthcoming option for improving the design of real RC building framed structures.

A genetic algorithm is used-to perform the discrete optimization of reinforced concrete plane frames subject to combinations of gravity loads and lateral loads. Difficulties in finding optimum sections from a semi-infinite set of member sizes and reinforcement arrangements are alleviated by constructing data sets, which contain a finite number of sectional properties of beams and columns in a practical range. Construction practice is also implemented by linking columns and beams by group and by considering "connectivity" between columns located in the same column line. It is shown that the developed genetic algorithm obtained an optimal design for reinforced concrete plane frames.

: This article aims to describe a methodology to design RC building frames based on a multiobjective simulated annealing (MOSA) algorithm applied to four objective functions, namely, the economic cost, the constructability, the environmental impact, and the overall safety of RC framed structures. The evaluation of solutions follows the Spanish Code for structural concrete. The methodology was applied to a symmetrical building frame with two bays and four floors. This example has 77 design variables. Pareto results of the MOSA algorithm indicate that more practical, more constructable, more sustainable, and safer solutions than the lowest cost solution are available at a cost increment acceptable in practice. Results Ns-SMOSA1 and Ns-SMOSA2 of the cost versus constructability Pareto front are finally recommended because they are especially good in terms of cost, constructability, and environmental impact. Further, the methodology proposed will help structural engineers to enhance their designs of building frames.

The present paper outlines an application of genetic algorithm based strategies to a class of optimization tasks associated with the design of steel reinforced concrete structures. In this particular case, the principal design objective is to minimize the total cost of a structure. The resulting structure, however, should not only be marked with a low price but also comply with all strength and serviceability requirements for a given level of the applied load. To solve such a complex optimization problem with a number constraints calls for an efficient and yet reliable optimization technique. Here, the problem is addressed with the help of the augmented simulated annealing method. As an example, a simple continuous steel reinforced beam is analyzed to assess applicability of the proposed approach.

This paper is concerned with optimum design and sensitivity of retaining structures. The optimum design formulation in terms of a constrained nonlinear programming problem, is given for reinforced concrete-cantilever retaining walls. The objective function may be chosen as the cost or weight of the wall. The solution is carried out by a specially prepared computer program (RETOPT). Illustrative problems are solved, and their results are presented and discussed. The formulation allows for a detailed sensitivity analysis to be made for selected design parameters, also depicted with numerical examples.

A three-step local search algorithm based on a probabilistic variable neighborhood search is presented for the vehicle routing problem with a heterogeneous fleet of vehicles and soft time windows (VRPHESTW). A generation mechanism based on a greedy randomized adaptive search procedure, a diversification procedure using an extinctive selection evolution strategy, and a postoptimization method based on a threshold algorithm with restarts are considered to solve the problem. The results show the convenience of using an economic objective function to analyze the influence of the changes in the economic environment on the transportation average profit of vehicle routing problems. Near real-world vehicle routing problems need (1) an economic objective function to measure the quality of the solutions as well as (2) an appropriate guide function, which may be different from the economic objective function, for each heuristic method and for each economic scenario.

Optimizing most structural systems used in practice requires considering design variables as discrete quantities. The paper presents a simple genetic algorithm for optimizing structural systems with discrete design variables. As genetic algorithms (GAs) are best suited for unconstrained optimization problems, it is necessary to transform the constrained problem into an unconstrained one. A penalty-based transformation method is used in the present work. The penalty parameter depends on the degree of constraint violation, which is found to be well-suited for a parallel search using genetic algorithms. The concept of optimization using the genetic algorithm is presented in detail using a three-bar truss problem. All the computations for three successive generations are presented in the form of tables for easy understanding of the algorithm. Two standard problems from literature are solved and results compared. The application of the genetic algorithm to design optimization of a larger problem is illustrated using a 160-bar transmission tower.

A computational environment suitable for optimum design of structures in the general class of plane frames is described. Design optimization is based on the use of a genetic algorithm in which a population of individual designs is changed generation by generation applying principles of natural selection and survival of the fittest. The fitness of a design is assessed using an objective function in which violations of design constraints are penalized. Facilities are provided for automatic data editing and reanalysis of the structure. The environment is particularly useful when parametric studies are required. The use of the environment is illustrated in a study of a cable-stayed bridge structure.

A new time-domain method for separating incident and reflected waves in wave flumes using any number of wave gauges is presented. The method (named LASA) is based on a local approximation model considering linear and Stokes II nonlinear components, and a simulated annealing algorithm to calculate the parameters of the local approximation model. The LASA method is directly applicable to experiments in wave flumes with an arbitrary number of wave gauges, but the LASA concept may be extended to laboratory and field three-dimensional experiments by selecting the appropriate local approximation model. The LASA method has been compared to the two-point and Kimara's method and has proved to be very robust. The application of the LASA method to physical experiments using nonstationary regular and random waves generated estimations of incident and reflected waves with relative mean squared errors lower than 3% for regular waves and ranging from 4 to 16% depending on the spectral shape.

We present an optimization model for the design of rectangular reinforced concrete beams subject to a specified set of constraints. Our model is more realistic than previously published models because it minimizes the cost of the beam on strength design procedures, while also considering the costs of concrete, steel and shuttering. Thus our method leads to very practical designs. As there is an infinite number of possible beam dimensions and reinforcement ratios that yield the same moment of resistance, an efficient search technique is preferred over the more traditional iterative methods. We employ a simple genetic algorithm as the search engine, and we compare our results with those obtained via geometric programming. Since the adjustment of parameters in a genetic algorithm (e.g., population size, crossover and mutation rates, and maximum number of generations) is a significant problem for any application, we present our own methodology to deal with this problem. A prototype of this system is currently being tested in Mxico, in order to evaluate its potential as a reliable design tool for real world applications.

FEA (finite element analysis) has been widely used to simulate
package behaviour in the recent years and proved to be a powerful tool
to obtain a better understanding of package performance. However, as FEA
becomes increasingly popular, new requirements are raised. Among them
are the feasibility of using FEA to do DOE and design optimizations. In
these applications, the packages have similar geometry but the component
parameters (dimensions and material properties) are changeable. APDL
(Ansys Parametric Design Language) was used to write FEA programs which
can automatically build the required model, solve it, retrieve the
results and do other complicated operations and calculations. By using
this kind of programs, FEA becomes a powerful tool for DOE (design of
experiments) and design optimizations

Collection of earth retaining structures for roads. Madrid: M. Fomento

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Heuristic optimization of reinforced concrete road bridge frames. Doctoral thesis. Dep. Construction Eng., Valencia; Tech. Un. Valencia

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Perea C. Heuristic optimization of reinforced concrete road bridge frames.
Doctoral thesis. Dep. Construction Eng., Valencia; Tech. Un. Valencia;
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A simulated annealing approach to the economic optimization of reinforced concrete cantilever retaining walls

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Alcala J, Carrera M, Gonzalez F, Yepes V. A simulated annealing
approach to the economic optimization of reinforced concrete cantilever
retaining walls. Hormigon y Acero 2005;236:97-108 [in Spanish].

Code of structural concrete. Madrid: M. Fomento

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Fomento M. EHE: Code of structural concrete. Madrid: M. Fomento;
1998 [in Spanish].

Heuristic optimization applied to the economic design of reinforced concrete earth retaining walls

- V Yepes

Yepes V. Heuristic optimization applied to the economic design of
reinforced concrete earth retaining walls. Research report CST/GPRC-06.
Valencia: Department of Construction Engineering, Technical University
of Valencia; 2006 [in Spanish].

Muros de contención y muros de sótano. Madrid: Intemac

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Calavera J. Muros de contención y muros de sótano. Madrid: Intemac.
2001.