Multi-objective sustainable design of reinforced concrete cylindrical tall structures by using metaheuristic algorithms

Abstract

While creating structural model, it is required that evaluation different and various alternative scenarios to provide sustainable conditions for the environment, and nature besides that structures have characteristics as strength and serviceability. However, this process needs extremely long times together with much effort to find out the desired properties. Concordantly, optimization technologies can be evaluated to use in overcoming the mentioned disadvantages. Regarding this, in this study, reinforced concrete cylindrical wall was dealt for generating an optimum structure by providing cost-minimization besides making possible eco-friendly design conditions. The best structural models were also evaluated according to variable concrete strengths and wall heights in separate cases as single and multi-objective ones. Meanwhile, a metaheuristic method as flower pollination algorithm was handled to detect the best values of structural parameters including total reinforcement and concrete amount, appropriate spacing between reinforcements, etc. Also, a different optimization methodology was applied for reinforced concrete structures in order to evaluate different aims, like both sustainability and economic conditions, besides independent objectives. In this respect, the minimum cost, and CO₂ can be determined together for different structural parameters like concrete compressive strength, wall height, etc. By this regard, multi-objective optimization processes can be utilized to investigate different structural models in order to focus on fundamental purposes like minimum cost, and emission values besides maximum seismic safety of structures.

Graphical abstract

Keywords

reinforced concrete / CO ₂ emission / multi-objective optimization / cost minimization / eco-friendly design

1 Introduction

The sustainability concept became a significant point in terms of different and several areas of life. The main reason for this case is based on continuing the livability of the nature and our planet, and also improving the quality of humans, animals, and plants, together with other alives’ life. In this respect, the sustainability conditions must be investigated from different perspectives, and especially, the utilized materials for any process, which spreads waste, hazardous and redundant parts, must be considered.

In this regard, nowadays, this concept takes attention widely to generate innovative and eco-friendly structural projects in the field of civil engineering, besides providing the most economic design options. However, it must be known and considered that both issues should be fulfilled by the best way to prevent the wasting of time, effort, workforce and also money, and provide efficiency.

These cases can be made realized by performing different optimization methodologies, which provide solutions fitting to the most appropriate, sustainable and cost-friendly processes. In this respect, various optimization methodologies have been handled to design of civil and structural engineering problems. For instance, Ganzerli et al. [1] conducted an analysis to find the optimum value of total cost for structures in order to reveal seismic design based on performance. Also, Aktas et al. [2] aimed to optimize both cost and safety of structural models by adjusting load factors for specification of bridge designs. Furthermore, in another research, cost optimization methodology was applied respect to precast and prestressed concrete bridge models. To realize this process, the design problem was expressed as nonlinear programming model approach [3]. Also, different approach for structural shape optimization was utilized based on isogeometric analysis of structures [4]. Besides of these researches, Zordan et al. [5] tried to generate the lightest structural model for an arch bridge within Italy. With this aim, different optimization methodology was utilized with the consideration of evolutionary optimization agorithm. On the other side, a research was realized to find the optimum value, and geometry for carbon nano tube content of polymeric nanocomposite continuum structures [6]. Also, Ghasemi et al. [7] realized a research focused on determination optimum content, and distribution of fiber content in solid fiber reinforced composites. To make possible this process, researches used adouble stage sequential optimization algorithm generated from Reliability Based Design Optimization, and Non-Uniform Rational B-Spline.

However, especially nowadays, the time and effort are some of the most important and valuable parameters in terms of preparation, and development of an optimal design. Hence, more advanced, speed, adaptable, and updatable methodologies can be preferred. These cases can be made realized by performing different methodologies like metaheuristic algorithms, which provide solutions fitting to optimization processes. In this respect, in the field of civil and structural engineering area, numerous researches have been performed to provide the economy efficiency priority in terms of different design models or any structural members by applying the mentioned algorithms. One of these is an optimization process realized for tubular column structure to minimize the total cost [8]. Also, Shaqfa and Orbán [9] tried to generate the best designing for reinforced concrete (RC) beam structure with the usage of harmony search (HS) algorithm from metaheuristics by adjusting the parameters for algorithm. Georgioudakis and Plevris [10] compared the performance of various versions of differential evolution algorithm with the purpose of creating the best design by determining the minimum cost level for several truss structures. On the other side, a real-size optimization problem based on the designing of RC retaining wall structures. In this problem, HS algorithm and its adaptive versions of it were utilized to size and find the best sections of wall model by minimizing the total structural cost [11]. On the other side, to control and analyze the structural responses according to dynamic forces like earthquake, wind etc., Brandão et al. [12] and Ghaderi et al. [13] carried out an optimization process by using whale optimization algorithm and special relativity search algorithm, respectively.

As to the different studies, Bekdaş et al. [14], Karimi Sharafshadeh et al. [15], and Yucel et al. [16] generated prediction models to directly determine the optimal parameter values for different structural systems by benefiting from both metaheuristics and different machine learning methodologies.

However, the evaluation of both cost-efficiency for economic structures, and the different conditions for eco-friendly design is more remarkable in terms of surviving sustainability considering as a combination. If it must be given an example to this statement, the optimal structural design for composite floor slabs tried to be generated by Lee et al. [17]. In this regard, for a 30-storey office building, multi-objective optimization for carbon dioxide (CO₂) emission, and total cost were minimized by utilizing genetic algorithm (GA). Kaveh et al. [18] also realized multi-objective optimization applications to design multi-storey RC frame structures with the aim of minimization of both factors. So, they benefited from three different metaheuristics including enhanced colliding bodies optimization, enhanced vibrating particles system and particle swarm optimization. With the consideration of the same optimization target, Yepes et al. [19] made an optimum design for earth-retaining wall structures with the help of the blackhole algorithm. Moreover, Yücel et al. [20] compared the performance of flower pollination algorithm (FPA), Jaya algorithm and HS in order to find the best one, which can provide the optimal design for RC beam structures in the direction of minimization of structural cost besides CO₂ emission level. With biogeography-based optimization, which is one of the metaheuristic methods, Negrin and Chagoyén [21] revealed a cost-effective and eco-friendly structural design for RC frame buildings. On the other hand, with the usage of HS, Tres Junior et al. [22] tried to make a multi-objective design for optimizing of cost and emission level in terms of sustainability for steel-concrete composite pedestrian bridges, besides of vertical acceleration due to human-induced vibrations. Moreover, dos Santos et al. [23] carried out a multiobjective research for RC beams to optimize both cost and amount of CO₂ emission by utilizing a different version of GA.

The main target of the present study is to make it possible to generate convenient structural designs for cylindrical wall models in terms of economy, besides sustainability for nature. To make real of this statement, both total structural cost and CO₂ emission factors were tried to be minimized with the help of a metaheuristic method known as FPA. In this respect, four different optimization cases were carried out to observe the performance of algorithm, and process about minimization of total cost together with emission factors both independently and combined way. So, the 1st and 2nd cases were assumed as single-objective; the 3rd and 4th cases were handled as multi-objective optimization processes. Also, for the mentioned processes, various combinations for design parameters of wall model were considered by selecting different ranges of parameter values (wall height and concrete compressive strength). Furthermore, the multi-objective ones were realized via two different weighted approaches where constant weight ratios were utilized for the basic factors of the objective function as CO₂ emission and total cost; and variable ratios were determined to observe the minimized values of these factors (the 4th case). By this means, to create eco-friendly, and cost-effective structures becomes possible by providing the best amount of cost, and CO₂ emissions corresponding to different wall models and utilized materials. Also, by using multiobjective optimization processes, it can be possible to generate the most sustainable, and economic structural designs in the consideration of different structural parameters like wall height, concrete compressive strength etc. On the other side, the various ratios, and effects of each objective functions can be evaluated with the usage of the current methodology. For this reason, the fundamental effects for both minimum CO₂ emission, and cost values can be determined thanks to the investigation of independent, and also multiobjective optimization processes for RC structural model.

2 Flower pollination algorithm

FPA is one of the metaheuristic methods, which provide reaching the optimum points for desired parameters, and was first proposed by Yang [24]. The main metaphor of this algorithm is based on the natural behavior and ability possessed to flowery plants. The mentioned ability realizes with the help of different pollinator agents like flies, bees, bats, wind, water, etc., and is called as pollination occurred between different flower members, or in itself of any flower. In this direction, the first expression for this ability is known as global pollination; the other one is also named as self-pollination (Eq. (1)):

(1)

where X_{i,\mathrm{n}\mathrm{e}\mathrm{w}} and X_{i,j} express the new and old namely initial value of jth candidate solution corresponding ith design parameter, respectively. X_{i,{\mathrm{g}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}} also defines the best candidate solution in terms of the amount for the objective function. Besides that both X_{i,\mathrm{a}} and X_{i,\mathrm{b}} are random solutions that are chosen among all solution members for ith design parameter. L\text{é}vy expression means a flight function distributed randomly between 0 and 1 (Eq. (2)), too.

(2)L\text{é}vy=\left(\frac{1}{\sqrt{2\text{π}}}\right){\left(\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}\left(0,1\right)\right)}^{-1.5}{\mathrm{e}}^{\left(-\frac{1}{2\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}\left(0,1\right)}\right)}.

On the other side, there is a special parameter for FPA utilized during optimization processes. This parameter is known as switch possibility (sp), which provides to select and improve the optimization phases (namely search type). The illustration of all stages within optimization process carried out via FPA is reflected via Fig.1.

3 Optimization process for cylindrical wall model

In the current study, a RC cylindrical wall model was handled to create both eco-friendly namely sustainable, and economic structural design by minimizing CO₂ emission and total cost amount. In this process, while realizing the mentioned designing targets, a metaheuristic methodology called FPA was evaluated by considering the previous research outcomes where this algorithm has the best performance in terms of ensuring the minimized emission, and total cost for a similar model to the current structure. Furthermore, some structural properties including the utilized total concrete volume, steel weight, reinforcement number, etc., are also optimized. To realize the structural designing process, wall designs were handled according to the conditions and rules within the document of TS500-Turkish Standard Requirements for Design and Construction of Reinforced Concrete Structures [25], too.

3.1 The structural model of wall

The investigated structure is a RC axially symmetric cylindrical wall, which is full of water as liquid, and has simple with pinned support on the low end, illustrated in Fig.2 and Fig.3, besides that top end of it can also move freely. Here, design properties like wall thickness, height of wall etc. can be seen in detail.

Where H defines the wall height, which has handled within different ranges to evaluate the efficiency of optimization process. r and t_w are the radius and thickness of wall structure, respectively. In Tab.1, all of the design details about parameters and design rules can be seen clearly.

Here, some corrections should be fulfilled to provide the strength requirements by staying on safe side. For this reason, the below calculations as Eqs. (3) and (4) are conducted for various properties including the compressive strength of concrete (f_{\mathrm{c}}) and yield strength of steel (f_{\mathrm{y}}) respectively, by considering the design information ensured by TS-500 Structural Regulation. Where f_{\mathrm{c}\mathrm{d}} and f_{\mathrm{y}\mathrm{d}} express the design values of concrete compressive, and steel yield strengths, respectively.

(3)f_{\mathrm{c}\mathrm{d}}=\frac{f_{\mathrm{c}}}{1.5},

(4)f_{\mathrm{y}\mathrm{d}}=\frac{f_{\mathrm{y}}}{1.15}.

Also in Tab.2, unit amounts of carbon emission for concrete and steel materials as {\mathrm{C}\mathrm{O}}_2^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}} and {\mathrm{C}\mathrm{O}}_2^{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}} are reflected [26-27]. Besides, unit cost values, which can be seen for various compressive strengths of concrete (C_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}}) and constant steel tensile strength (C_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}), are provided via a document published by Republic of Turkey Ministry of Environment and Urbanization [28] where different types of unit costs are reflected in terms of materials and workforce for the construction sector. If it must be expressed, all of the unit costs are also converted to US dollars ($) according to the changing rate determined on 27.07.2022. An additional application to these, at the same time, various heights of wall structure are also handled as variables between 1 and 15 with the increase of 1 m to evaluate the multi-objective optimization cases from different perspectives.

Also in Tab.3, design constraints provided via TS-500 Regulation rules can be detailly seen. These constraints are beneficial to limit the undesired conditions like failure, over stress, displacement etc. and provide the most convenient namely optimum, and safe, besides cost-effective with sustainable structural designs.

In Tab.3, M_y and V_y are values of the ultimate flexural moment and shear forces detected by realizing the structural analysis processes, respectively. The mentioned forces are occurred from the support points along wall surfaces of structures due to the arisen effects and forces by liquid inside of the wall, and cannot exceed the design capacities for wall sections (M_d and V_d). Additionally, ρ and ρ_min are design values, and the minimum amount for reinforcement ratios corresponds to longitudinal bars. Besides that s, s_max, and s_min express the spacings among longitudinal bars in terms of design value, the biggest and smallest ratios, respectively. \beta is also a coefficient calculated according to the properties of wall.

3.2 Optimization process for minimization of CO₂ emission and total cost

For the optimization processes, four different cases are applied to minimize the desired factors namely CO₂ emission and total structural cost. These cases include the detection of minimized values of the mentioned factors independently (the 1st and 2nd cases), and also multi-objective process for these factors by using constant-weights (the 3rd case) and variable-weights (the 4th case) in terms of basic objective function. In this way, for the 1st and the 2nd cases, optimum properties of wall structures were tried to find for generating sustainable besides economic conditions with the consideration of Eqs. (5) and (6), respectively.

(5)\begin{array}{rl}{\mathrm{O}\mathrm{b}\mathrm{j}.\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_1:\mathrm{M}\mathrm{i}\mathrm{n}{(\mathrm{C}\mathrm{O}}_2)=& V_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}}{\mathrm{C}\mathrm{O}}_2^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}}\\ & +{W_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}\mathrm{C}\mathrm{O}}_2^{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}},\end{array}

(6)\begin{array}{rl}{\mathrm{O}\mathrm{b}\mathrm{j}.\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_2:\mathrm{M}\mathrm{i}\mathrm{n}\left(\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}\right)=& V_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}}{C}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}}\\ & +W_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}}{C}_{\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{e}\mathrm{l}},\end{array}

where V_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{e}} is the total volume of concrete, and W_{\mathrm{s}} also means the total amount of steel weight ensured for the wall structure.

As to the multi-objective optimization applications for 3rd and 4th cases, the below formula in Eq. (7) should be considered for determining of the best combination for amounts of the used materials as concrete and reinforcement, and the contribution rate of both objective functions. Also, w_1 and w_2 are the objective function weights namely contribution ratios of minimum CO₂ emission and total cost, respectively. In this process, these ratios are selected as constant for 3rd case at 0.5, and variable for the 4th case between 0.1 and 0.9 by increasing 0.2 (the summation of these ratios must be 1.0).

(7)\begin{array}{rl}& {\mathrm{O}\mathrm{b}\mathrm{j}.\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_3:\mathrm{M}\mathrm{i}\mathrm{n}({\mathrm{C}\mathrm{O}}_2+\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t})\\ =& w_1{\mathrm{O}\mathrm{b}\mathrm{j}.\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_1+w_2{\mathrm{O}\mathrm{b}\mathrm{j}.\mathrm{F}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}_2.\end{array}

4 Numerical applications

In this section, different numerical investigations are made to observe the performance of optimization processes. For this reason, various design parameters are selected within variable ranges to compare the optimization success from several directions. In this regard, wall heights and concrete compressive strengths are determined as variable values. So, for the 1st and 2nd cases, the parameter values are selected as in Tab.1; for the 3rd, and 4th cases, concrete compressive strengths, and wall heights are determined as different amounts between 25 and 45 MPa by increasing 5 MPa together with 10–20 m with 1 m increment, respectively. With this aim, all of the optimization processes and outcomes are represented in the below sections.

4.1 Independent optimization of the minimum CO₂ emission and total cost

In these cases, minimum CO₂ emission and total cost values are found separately in two different cases. For this reason, these both applications are performed by using 25 multiple optimization cycles with the evaluation of 10 population vectors, besides 1000 iteration stages for cost and CO₂ minimization, respectively. In the final step, all of the outcomes of cycles are evaluated according to different statistical measurements and represented in Tab.4 and Tab.5 for the 1st and 2nd cases as minimization of emission and total cost, respectively.

4.2 Multi-objective optimization for cost and CO₂ emission with constant weight ratios

For the first multi-objective optimization as the 3rd case, weight ratios of CO₂ emission, and total cost are considered as 0.5 rate with the assumption that the contributions of both factors are equal. Also, in this process, the optimization applications are continued with the same values for algorithm properties as iteration and population numbers. The provided optimum design parameters, and objective outputs for different combinations generated with respect to RC wall structure can be seen in Appendix A in Supplementary materials, and Fig.4(a)–Fig.4(e) in terms of each wall height, and concrete compressive strength, respectively.

4.3 Multi-objective optimization for cost and CO₂ emission with variable weight ratios

For the second multi-objective optimization as 4th case, minimum CO₂ emission, and total cost values are tried to find by considering via variable weight ratios. In the same way, this case is conducted with the usage of equal values for algorithm parameters, too. The achieved results for optimization processes, which are determined as best levels in terms of multi-objective function values among the used whole weight ratios, are represented via Fig.5(a)–Fig.5(e) in the way of the consideration of heights for wall structure besides concrete compressive strengths (here, the best amounts of the combined objective functions can be ensured via 0.9 and 0.1 weights for total cost and CO₂ emission, respectively). Also, all of the results for each combination of parameters were shown in Appendix B in Supplementary materials in terms of wall structures.

5 Results

5.1 Independent optimization of minimum CO₂ emission and total cost

According to Tab.4 and Tab.5, it can be seen that the minimum CO₂ emission and total cost can be provided by deviating with pretty low error rates respect to the usage of multiple optimization cycles in terms of all wall heights as 10, 12.5, and 12 m. It shows that the optimization process is extremely reliable due to that the best namely minimized level of objective functions determined stable in terms of all of the cycles. Furthermore, both the optimum design properties as diameter and number of bars together with a spacing value between bars show a change along the increasing of wall height. Here, for the 1st case as minimization of CO₂ emission, volume of the used concrete reduces due to the thickness value of wall that decreases toward H = 15 m. However, the best levels/optimum values for cost, and the minimum emission values increase due to that a bigger increment was seen for the used steel weight. For the 2nd case as minimization of cost, along with increasing the thickness of wall toward H = 15 m, all of the properties (V_c and W_s) together with optimized emission and minimum cost values show an increment. As a summarization, when all of the provided results with respect to the optimization process are investigated, the used metaheuristic algorithm as FPA can be accepted as extremely effective and reliable cause of that the minimization of both CO₂ emission and cost can be realized with really small deviations namely error rates in terms of changing of wall heights and multiple analysis processes, too.

5.2 Multi-objective optimization both cost and CO₂ emission via constant weights

In this application, the multi-objective optimization process was applied respect to wall model in the way of minimizing of the emission and total cost values by considering the constant weight ratios for them. In this regard, constant weights are determined as 0.5 for both objective functions. With this respect, with the help of Fig.4, the changing of minimum level of objective functions (emission and total cost) together with a combined value of them, number and diameter of bars etc. can be seen along with increasing the values of H, and changing of concrete compressive strength. It can be recognized that both minimum CO₂ emission, with total cost and so the combined multi-objective function value shows an increment along the increasing of wall height and compressive strengths. But, on the determination of the minimum combined multi-objective function values, the effect of minimum CO₂ emission levels is bigger than the cost values.

Furthermore, for minimum CO₂ level, the changing of values shows a similar behavior except for C45 MPa compressive strength. Here, it can be seen that the biggest value of emission is calculated as almost 1.31E+08 kg in terms of 20 m wall. Additionally, for minimum cost, the best levels are also provided with the usage of C45 MPa (almost 2.4E+07 $ for 20 m wall structure). In a summary, the most minimized level for both objectives and combined value can be provided with the usage of C45 MPa concrete.

5.3 Multi-objective optimization of cost and CO₂ emission via variable weights

In the 2nd multi-objective optimization process, the weight factors for CO₂ emission and total cost are determined as variables between 0.1 and 0.9 by increasing 0.2. In this meaning, with Fig.5, it can be recognized that the minimized CO₂ emission levels are ensured in the way of decreasing along with increasing concrete compressive strength values. However, the best levels for total cost values can be decreased with less ratio in terms of the mentioned compressive strengths. Additionally, these behaviors were realized similarly for C30, C35, and C40 MPa. According to the combined multi-objective function levels, it can be seen that these values increase along rising of wall height and compressive strengths. Nevertheless, the maximum levels for the multi-objective function values arise with the usage of C25 MPa concrete strength on 20 m wall (almost 4.2E+07). Besides these outputs, this is extremely clear that the major effect proceeds from the level of the minimized CO₂ emission for the multi-objective function values. Furthermore, when the total number and diameter value of the utilized reinforcement bars are investigated, the basic behavior occurred almost similarly for C35, C40, C45 MPa by fluctuating. When the biggest value of numbers of the utilized reinforcement bars are recognized that it realizes on C25 and C30 MPa with 17 bars.

Moreover, the difference between minimum emission and total cost increase largely along changing of wall height as increasing. However, while the concrete compressive strengths are changing from 25 to 45 MPa, these differences between both objectives show a decrease.

To add more, the best levels namely minimized values for emission and total costs can be provided with the weight ratios of 0.9 and 0.1 for cost and emission in terms of all wall heights and concrete compressive strengths, respectively.

6 Conclusions

According to the all results for each optimization case realized for different combinations of wall structures, it is clear that the single objective function applications for the optimization process are extremely successful to determine the desired levels for emission and total cost in terms of variable wall structures. The reason for this is related to the detection of the best levels for objective functions with extremely small error rates. For this reason, both metaheuristic algorithms and optimization processes can be accepted as effective, reliable and sensitive tools for determining of optimum parameters of structural design.

Furthermore, it can be seen that the minimum levels of total cost and CO₂ emission can be decreased with the usage of variable concrete compressive strengths from 25 to 45 MPa. However, it can be understood that the minimum CO₂ emission values show an increment in terms of 10 m wall structure with the usage of C35 concrete in the way of the evaluation of multi-objective optimization applications. The main reason for this is based on the changing of CO₂ emission value from 5.09E+06 to 2.81E+07 kg along with passing from the single objective optimization (the 1st case) to multi-objective ones (the 3rd and the 4th cases).

Also, the most sustainable design in terms of the minimization of CO₂ emission can be created with the usage of C35 MPa (with single objective optimization application). Here, the best level of minimum emission is ensured as 5.09E+06 kg. On the other side, the most economic design is provided via both single and multi-objective optimization applications at the rate of 6.78E+06 $ in terms of 10 m wall. As the numbers and diameters of reinforcement bars are investigated for these applications, it can be understood that there is little change in the amounts.

As a summary, for the cylindrical tall structure, the best solutions can be provided via C45 MPa in terms of multi-objective functions according to the whole values of wall heights. Although the best solutions for minimum emission is ensured via C35 MPa in the single-objective application, C45 MPa concrete strength can be accepted as effective and successful to decrease all objectives as total cost, emission and also the combined value for them due to the major aim is assumed the minimization of both total cost and emission. For this reason, these two single and multi-objective application alternatives can be thought and evaluated for structural designs independently.

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