Design of low-carbon and cost-efficient concrete frame buildings: a hybrid optimization approach based on harmony search

ABSTRACT

The development of sustainable building structures has been a crucial measure for carbon reduction. With consideration of both carbon emissions and costs, the sustainable design of building structures is complicated and time consuming for designers. To simplify the process of sustainable design optimization, the present study proposes a multi-objective harmony search algorithm for the design of concrete frame buildings considering low-carbon and cost-efficient requirements. This hybrid method combines structural analysis with local component optimization. Process-based life cycle assessment was used to identify carbon-intensive and high-cost structural members, and these members were optimized using discrete design variables and complicated constraints. Furthermore, a case study was conducted on a four-story frame building, in which the embodied emissions and costs were estimated as 1270.91 tCO_2e and 0.67 million USD in the initial design scheme. Beams were identified as the optimization target for this building, and a set of Pareto-optimal solutions was obtained, indicating potential emission and cost reductions of 17.9% and 12.3%, respectively, compared with the initial designs. This study provides an easy and practical approach for the sustainable design of concrete frame buildings and enables designers to better understand building structural optimization from an economic and low-carbon perspective.

Graphical abstract

KEYWORDS:

• Low-carbon building
• concrete framed structure
• carbon emission assessment
• harmony search
• multi-objective optimal design

1. Introduction

Low-carbon buildings, regarded as a crucial step to prevent serious global climate change (Häkkinen et al. 2015), are drawing attention worldwide (Wang et al. 2017). With improvements in building technologies, including efficient insulation and solar photovoltaic systems (Good et al. 2016; Moran, Goggins, and Hajdukiewicz 2017), low-carbon buildings have already been realized in the operational phase (Pan and Li 2016). Consequently, emissions from building construction are currently emphasized in the implementation of life-cycle zero-impact buildings (Dixit et al. 2010; Dutil, Rousse, and Quesada 2011).

“Cradle to site” assessment based on emission factors (namely process-based LCA) has been widely adopted to measure embodied carbon in the building pre-use phase (Hong et al. 2015; Roh and Tae 2017). Carbon emissions in this life cycle phase are primarily sourced manufacturing materials, transportation, and on-site activities. Previous studies (Zhang and Zhang 2021a) have indicated that the main structure significantly contributes to embodied carbon which can be reduced by alternative designs. Kim et al. (2015) compared the construction costs and emissions of clay brick, cement brick, and block walls. Dong et al. (2015) and Omar et al. (2014) investigated the embodied emissions of cast-in-situ and precast concrete buildings. Gustavsson and Sathre (2006) indicated that wood-framed buildings were better than concrete buildings in reducing carbon emissions. Zhang and Zheng (2020) compared the emissions of brick masonry, reinforced block masonry, and concrete structures in a mid-rise building. The aforementioned studies focused primarily on comparing and selecting structural schemes in a low-carbon context.

Furthermore, recent research has attempted to reduce building emissions by optimizing selected structural systems and members. For example, Oh, Choi, and Park (2017) proposed a CS-factor and investigated its influence on the costs and CO₂ emissions of concrete beams. Choi, Oh, and Park (2017) applied a resizing method to optimize the costs and emissions of a 37-story building based on its structural performance under a wind load. Paya-Zaforteza et al. (2009) and Camp and Huq (2013) investigated the relationship between the costs and emissions of 2D-based concrete frames, and applied simulated annealing and big bang-big crunch algorithms for structural optimization, respectively. Fraile-Garcia et al. (2015) compared the economic and environmental costs of determining the structural alternatives to concrete slabs. Yeo and Gabbai (2011) optimized the cost and embodied energy of a reinforced concrete beam based on the ACI 318–08 M Code.

As indicated above, the main objectives of previous research related to the sustainable design of building structures were to minimize emissions and costs. However, these studies had certain limitations as follows. First, although the aforementioned studies considered two objectives, they used single-objective algorithms to optimize one objective at a time. It is necessary to develop a multi-objective optimization algorithm that considers the balance between costs and emissions. Second, the optimal design at both the member and structural levels was studied, yet relatively few studies considered the combination of the two levels of research. Finally, most studies only considered the production phase of structural materials, such as steel products and concrete; however, the transportation, construction, and disposal phases were generally excluded.

To fill some the knowledge gaps, this study proposes an easy-operated approach to low-carbon sustainable design of building structures that combine the structure-level assessment with member-level optimization. Figure 1 illustrates the framework of this study, and the details are as follows:

Figure 1. Research program of the present study.

(1) Objective: reinforced concrete frame buildings are selected for investigation because it is currently one of the most popular load-bearing systems in typical buildings in China. The monetary costs and embodied carbon emissions were considered, with respect to the trade-off between economic efficiency and environmental sustainability in the optimization.

(2) Scope: material production, off-site transportation, and on-site construction phases were considered for the emission and cost assessment.

(3) Method: the optimization approach was divided into two main components and relevant method were proposed. First, embodied emissions and costs were assessed based on the initial building structure scheme to identify the key members. Second, the key members were optimized using a harmony search algorithm to reduce carbon emissions and costs.

(4) Case study: based on the proposed hybrid optimization approach, a four-story apartment building was analyzed to verify the feasibility of the approach and investigate the potential for carbon and cost reduction.

The main contributions of this study are as follows:

• A multi-objective harmony search (HS) algorithm and the concept of Pareto fronts were applied for building design optimization considering conflicting low-carbon and low-cost indices.

• A hybrid approach was proposed to combine local member optimization with low-carbon building structure analysis.

• A comprehensive system boundary was defined in the case study to obtain more reliable results for emission assessment and design optimization.

The remainder of the paper is summarized as follows: first, the methods for emission assessment and design optimization are introduced; second, necessary information for the case building is presented; third, results are discussed and suggestions are proposed; finally, the study is concluded and the limitations and research extensions are discussed.

2. Methodology

2.1. Research scope

In this study, the pre-use phase (Heinonen et al. 2016) of reinforced concrete buildings, which can be divided into three main processes: material production, off-site transportation, and on-site construction, was considered. Process-based LCA was applied for the emission calculation, which was aimed at detailed carbon emission sources (Chau, Leung, and Ng 2015). Consequently, the embodied emissions E_emb are calculated as:

(1) $E_{emb}=E_{prod}+E_{tran}+E_{cons}$(1)

where E_prod,E_tran, and E_cons represent the emissions from the production, transportation, and construction processes, respectively. Furthermore, the project cost C_emb, which is the construction budget estimated in the design phase, mainly sources from labor use, material consumption, construction machinery, measure expenses, and other fees (indirect fees, profits, and taxes), and it can be evaluated as:

(2) $C_{emb}=C_{labor}+C_{mat}+C_{mac}+C_{mea}+C_{fees}$(2)

where C_labor,C_mat,C_mac,C_mea, and C_fees represent the monetary costs of labor, materials, machinery, measure expenses, and other fees, respectively. It should be noted that the estimation of project costs is indispensable and widely adopted for building projects in China, and can be accomplished according to the construction quota with the help of professional software packages. Hence, Section 2.2 focuses on the embodied emission assessment method.

As shown in Figure 1, for efficiency and practicality, an intelligent HS algorithm was adopted to implement the multi-objective optimal procedure. In recent years, various optimization algorithms, including genetic algorithms, particle swarm optimization, and simulated annealing, have been developed. As a heuristic optimization algorithm, HS was originally proposed by Geem and Kim (2001), who were inspired by musical chord creation. The HS algorithm can be widely applied to optimization problems (Cubukcuoglu et al. 2016; Mansourzadeh et al. 2019; Nazari-Heris et al. 2019) because of its simplicity, few requirements, and easy implementation. Various studies have compared the HS algorithm to other traditional and heuristic algorithms. The main advantages of the HS algorithm are as follows: (1) with respect to the applicable scope, the HS algorithm can be employed for the optimization of both continuous and discrete variables (Shabani, Mirroshandel, and Asheri 2017); (2) compared with traditional gradient algorithms, a random search method was adopted, which can reduce the probability of getting trapped in a local optimum (Lee and Geem 2005); (3) the HS algorithm is highly flexible because each desired variable can be treated independently when generating new solution vectors, and no specific initial solution is required (Fesanghary, Asadi, and Geem 2012); and (4) compared with the genetic algorithm, which generates a new solution using the information from two selected parent solutions, the HS algorithm generates a new solution from all solutions in the existing storage (Mansourzadeh et al. 2019).

2.2. Embodied emission assessment

For the pre-use phase, process-based emissions can be evaluated as the product of the quantity and relevant emission factor of the desired process (Zhang and Zhang 2020) as follows:

(3) $E_{dp}=E{F}_{dp}\cdot Q_{dp}$(3)

where E_dp,EF_dp, and Q_dp represent the embodied emissions, emission factor, and quantity of the desired process, respectively. Typically, the quantity of each process can be obtained from either building information modeling (BIM) or a bill of quantities (BOQ) (Peng 2016; Shao et al. 2014); however, emission factors are usually obtained from previous studies and field investigation (Zhang and Zhang 2020, 2021a; Zhang and Zheng 2020).

Furthermore, the present study assessed and analyzed emissions from the perspective of subprojects; which is convenient for subsequent optimization analysis. Although the main structure was regarded as the optimization target, the analysis of the entire building was considered for two reasons: first, in the context of embodied emissions, comprehensive analysis can provide insight into the influence of the main structure; second, the emissions from other components may change when resizing the structural members. Therefore, with respect to the concrete framed building, the pre-use phase was divided into five fundamental subprojects: (1) subproject of foundations, including earthwork, ground leveling, and reinforced concrete foundations; (2) subproject of a framed structure, including structural members such as columns, beams, slabs, and stairs; (3) subproject of masonry walls; (4) subproject of insulation and decoration, including interior decoration, exterior wall decoration and insulation, and roofing, and (5) temporal work, including vertical transportation, protection, lighting, and others. The first two subprojects were also referred to as load-bearing structures in the present study for convenience. For each subproject, information on material consumption, transport distance, and construction energy use was collected; subsequently, the emissions for relevant processes were calculated using Equation (3)(3) $E_{dp}=E{F}_{dp}\cdot Q_{dp}$(3) . Accordingly, the subproject-based embodied emissions can be integrated based on Equation (1)(1) $E_{emb}=E_{prod}+E_{tran}+E_{cons}$(1) .

2.3. Hybrid method for the structural optimization

2.3.1. Analytical procedure

This study adopted a hybrid approach for structural optimization, from the perspectives of carbon emissions and monetary costs. Figure 2 illustrates the detailed procedure for the analysis, and the main steps are summarized as follows:

Figure 2. Analytical procedure of the hybrid approach.

Step 1: Conduct an integrated structural analysis on the initial scheme and collect relevant data for optimization.

Step 2: Assess the subproject-based emissions and costs for the desired building.

Step 3: Determine the type of members for optimization based on their contribution to the defined objectives.

Step 4: Define the key variables and constraints for optimization based on the design requirements.

Step 5, Establish objective functions and optimize them based on the HS algorithm.

Step 6: Update the design variables according to the above results; and re-analyze the structural internal forces.

Step 7: Repeat steps 4–6 until a satisfied solution is acquired.

Step 8: Analyze the optimized emissions and costs, and evaluate the reduction potentials.

In the typical concrete structure design procedure, the design variables of the key members are first evaluated, a relevant structure model is created, the internal forces are calculated by the analysis of the overall structure, and the reinforcements are designed based on the corresponding forces. Notably, when the desired members are optimized, as indicated in Figure 2, the sections and material strengths can be changed, leading to the redistribution of structural internal forces. Therefore, the forces should be re-analyzed to satisfy the updated design conditions. In this context, iterative analysis is required to reach a satisfactory solution. However, the number of iterations should be carefully determined by considering the balance between the analytical efficiency and time cost. Excessive iterative loops may also result in inappropriate or singular designs.

2.3.2. Objective functions and constraints

In this study, the optimization objectives were to minimize the embodied emissions and relevant monetary costs of concrete framed buildings. Considering that different choices of design variables can give rise to competitive results between the two objectives, a multi-objective optimization problem (Deb 2001; Fan, Li, and Gai et al. 2019) is defined to explore optimal solutions, which is formulated as:

(4) $\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s}:\text{user}\mathit{X}=\left\{x_i\right\},x_i^L\le x_i\le x_i^U,i=1,2,\cdot \cdot \cdot ,N_v$(4)

(5) $\mathrm{O}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s}:Min\hspace{0.17em}{f}_p\left(\text{user}\mathit{X}\right)\hspace{0.17em}p=1,2,\cdot \cdot \cdot ,P$(5)

(6) $\mathrm{S}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{t}\mathrm{o}:\left\{\begin{array}{c}{g}_l\left(\text{user}\mathit{X}\right)\ge 0,l=1,2,\cdot \cdot \cdot ,L\\ h_k\left(\text{user}\mathit{X}\right)=0,k=1,2,\cdot \cdot \cdot ,K\end{array}\right.$(6)

where x_i represents the ith design variable, N_v is the number of variables, X is a vector of all variables that represents an optimal solution, f_p is the pth objective function, P is the number of objectives (two in this study), g_l is the lth inequality constraint, h_k is the kth equality constraint, L and K are the relevant numbers of constraints.

For the optimization of structural members, design variables mainly include cross-sectional dimensions, strength of structural materials, and arrangement of reinforcements, which generally consist of load-bearing capacities, restriction of section dimensions and reinforcement ratio, serviceability limit states, and detailing requirements. Notably, the above variables have to be chosen from a set of discrete values during optimization, because the members are usually designed with standard sizes and materials, with respect to the manufacturing requirements and construction practices (Zhang and Zhang 2021b). The variables, objectives, and constraints are presented in Table 1. In this study, the constraints were specified by the Chinese design codes.

Table 1. Definition of the optimization problem on structural members.

Classification	Description	Expression	Note
Variable	Cross-section	bmin≤b≤ bmax hmin≤h≤ hmax	b and h are the cross-sectional width and height, respectively. The lower and upper limits of sectional dimension are constrained by the building operation requirements and construction practices
	Strength grade	gc,gs	gc and gs are the strength grades of concrete and steel, respectively. Longitudinal bars and stirrups may have different strengths
	Reinforcement	ds,ns,ls	ds,ns, and ls are the diameter, number, and length of steel bars, respectively
Objective	Carbon emission	f1 = Min(Er)	Er is the total change in emissions, of which a negative value indicates a reduction in emissions
	Monetary cost	f2 = Min(Cr)	Cr is the total change in costs, of which a negative value indicates a reduction in costs
Constraint	Load-bearing capacity	R≥ S	R and S represent member resistance and load effect, respectively; structures and components may be subjected to either separate or combined actions of axial force N, bending M, shear V, and torsion T
	Reinforcement ratio	ρmin≤ρ≤ ρmax	The reinforcement ratio ρ is limited in a certain range to avoid brittle failure of structural components
	Serviceability limit state	ω≤ ωmax	ω represents potential crack width, ωmax represents the upper limit of crack width
	Detailing requirements	fc≥fclim c≥ clim la≥lalim sv≥svlim	fclim and clim are the lower limits of concrete strength and relevant cover depth, respectively, due to durability requirements; lalim and svlim are the limits of anchorage length and spacing of stirrups, respectively

Furthermore, unlike the single-objective optimization problem, in which a unique optimum can be achieved according to the objective function, the aforementioned multi-objective problem requires optimizing two conflicting objectives simultaneously. In this context, the analysis produces a set of optimal solutions, rather than an absolute optimum, and decision-makers must evaluate the trade-off between the emissions and relevant costs. For any two solutions X₁ and X₂ within the feasible space, we consider solution X₁ to dominate solution X_2, and represent it as X₁ $\underset{\_}{\prec }$ X_2, if the solutions satisfy both of the following conditions (Marler and Arora 2004; Sivasubramani and Swarup 2011). Otherwise, neither of the solutions dominates the other.

(7) $\mathrm{\forall }p\in \left\{1,2,\cdot \cdot \cdot ,P\right\}:\hspace{0.17em}{f}_p\left({\mathit{X}}_1\right)\le f_p\left({\mathit{X}}_2\right)$(7)

(8) $\mathrm{\exists }q\in \left\{1,2,\cdot \cdot \cdot ,P\right\}:\hspace{0.17em}{f}_q\left({\mathit{X}}_1\right)<f_q\left({\mathit{X}}_2\right)$(8)

The above concept can be applied to compare the optimal solutions for multi-objective problems. Generally, X₁ is defined as a non-dominated (Pareto-optimal) solution, if no alternative solution dominates X₁ within the entire feasible set, and the set of all non-dominated solutions is called the Pareto front (Wang, Olsson, and Liu 2018).

2.3.3. Optimization based on the HS algorithm

The multi-objective HS algorithm was adopted to account for discrete design variables in structural optimization. With a comprehensive consideration of the problem definition and the concept of Pareto optimality, the analytical procedure of this algorithm is divided into the following steps as shown in Figure 3.

Figure 3. Main processes of the harmony search algorithm.

Step 1: Initialize the problem, establish input variables, objective functions, and constraints, as indicated in Table 1, and determine the decision space considering the defined domains of each variable.

Step 2: Determine the specialized parameters of the HS algorithm (Zhang and Geem 2019). The harmony memory size (HMS) represents the number of solution vectors in the harmony memory, which remains unchanged during the optimization. The harmony memory considering rate (HMCR) and pitch adjustment rate (PAR) are controlled parameters within the range of [0, 1], which determine the path to generate and adjust a new solution vector in harmony. The maximum number of improvisations (NI) determines the HS termination criterion.

Step 3: Initialize the harmony memory (HM) within the decision space as:

(8) $\mathbf{H}{\mathbf{M}}_0=\left\{\text{user}{\mathbf{X}}_j\right\}\hspace{0.17em}j=1,2,L,\mathrm{H}\mathrm{M}\mathrm{S}$(8)

where HM₀ is the initial harmony memory matrix that stores the solution vectors X_j. The solutions in HM should be generated independently, and the value of each discrete variable should be randomly selected within the decision space.

Step 4: Improvise a new harmony HM_new subject to the rules of memory consideration, pitch adjustment, and random generation (Wang, Gao, and Zenger 2015). For the improvisation of a solution X_j = {x_ij} in HM_new, first, the design variable x_ij is chosen either from the historical values stored in HM with the probability represented by HMCR, or randomly from the entire decision space with the probability of (1-HMCR). Second, in cases where x_ij is selected from the historical HM, x_ij is examined to determine whether pitch adjustment is performed. A discrete variable will be pitch-adjusted with the probability of PAR, indicating that the value of x_ij is replaced by a neighboring value in its definition domain. Notably, the parameters HMCR and PAR can be changed dynamically during optimization (Hasancebi, Erdal, and Saka 2010; Kumar et al. 2014; Peraza et al. 2016;), to improve algorithm performance.

Step 5: Update HM by comparing the performance of historical and newly generated harmonies, by exploiting the fast non-dominated sorting (NSGA-II) method proposed by Deb et al. (2002).

(1) Establish a combined harmony HM_sum of historical and newly generated harmonies.

(2) For each solution vector in HM_sum, examine whether the constraints are satisfied, and calculate the relevant constraint violation (VI). For example, with respect to the optimization of bending beams, VI can be calculated as indicated in Table 2.

Table 2. Assessment of the constraint violation (VI) for the optimization of bending beams.

Constraint violation	Expression	Note
VI of the bending resistance	$V{I}_M=max\left(0,\frac{A_{s,min}-A_s}{A_{s,min}},\frac{A_s-A_{s,max}}{A_{s,max}}\right)$	As is the amount of longitudinal reinforcement based on the values of variables in a solution vector, As,min and As,max are the lower and upper limits of reinforcement depending on the bending capacity and limits of reinforcement ratios
VI of the shear resistance	$V{I}_V=max\left(0,\frac{s_{v,lim}-s_v}{s_{v,lim}},\frac{V-V_{lim}}{V}\right)$	sv is calculated spacing of stirrups based on the values of variables in a solution vector; svlim is the minimum spacing of stirrups; Vlim is the maximum shear force according to the limit conditions of oblique compression failure
VI of the crack width	$V{I}_{\omega }=max\left(0,\frac{\omega -{\omega }_{max}}{{\omega }_{max}}\right)$	ω is the crack width estimated based on the values of variables in a solution vector, ωmax is the maximum crack width limited by the design code
Total VI	$VI=V{I}_M+V{I}_V+V{I}_{\omega }$	The total VI is taken as the linear combination of the above three components.

(3) For solutions whose VI equals zero (i.e. feasible solutions), estimate the objective function values (namely, f₁ and f₂ in Table 1), the non-domination ranks of Pareto front (RPs) (Mishra et al. 2018), and the crowding distances (CDs) that represents the density of solutions (Lei et al. 2018).

(4) Perform non-dominated sorting and update HM accordingly. The priority of sorting is as follows: first, select feasible solutions with small RPs; second, select feasible solutions with small CDs if the RPs are the same, and finally, select the solutions with smaller VI among the infeasible solutions.

Step 6: Repeat Steps 4 and 5 until the numbers of improvisation reach NI.

Step 7: Evaluate the Pareto-optimal set in the final HM.

3. Case study

A case study was conducted in a four-story apartment located in China. The gross floor area and total height of the assessed building were 2693.9 m² and 13.65 m, respectively. The building was initially designed and analyzed with a reinforced concrete framed structure, according to general experiences and practices. To conform to the requirements of the Chinese design codes, the strength grades of concrete and steel for the main structural members were 30 MPa and 400 MPa, respectively. The case building structure was subjected to the combined actions of (1) vertical loads including structural self-weight (both load-bearing members and non-load-bearing masonry walls), decoration loads, and floor and roof live loads (2.0 kN/m²); (2) horizontal loads including wind load (0.65 kN/m²) and earthquake action (the seismic intensity is designed to seven-degree).

For the integrated structural analysis, the internal forces of both the initial and optimized schemes were determined using the PKPM software package, a popular and powerful structural design tool in China. For local member optimization, MATLAB was applied to the programming based on the previously-described HS algorithm and the building case characteristics. The program comprised the following main modules: (1) the main module, which defines the input parameters, main loop, and output solution vectors; (2) the improvisation module, which initializes the harmony memory and generates new harmonies; (3) the violation module, which calculates the value of VI for each harmony according to design constraints; (4) the sorting module, which applies the NSGA-II method to sort harmonies and generate new harmony memory; (5) other modules that output mechanical indices, emission factors, and material prices according to the parameters in improvised harmonies.

To assess the building embodied emissions and costs, the present study analyzed the BOQ based on the construction budget and relevant quota. The material consumption and machinery energy use for each subproject were assessed accordingly, and the transportation distances of the materials were estimated based on the location of the construction site and suppliers. Table 3 summarizes the subproject-based engineering quantities for the initial scheme.

Table 3. Engineering quantities based on subprojects for the initial building scheme.

Subproject	Content	Engineering quantity
Foundation	Ground leveling	929.9 m^2
	Mechanical excavation	1054.2 m^2
	Manual excavation	105.4 m^2
	Backfilling	624.1 m^3
	Manufacturing, casting, and curing concrete cushion	64.7 m^3
	Manufacturing, casting, and curing concrete foundation	196.9 m^3
	Manufacturing and processing foundation reinforcement	15.3 t
	Formwork for concrete cushion	41.9 m^2
	Formwork for concrete foundation	486.5 m^2
Framed structure	Manufacturing, casting, and curing concrete column	100.8 m^3
	Manufacturing and processing column reinforcement	19.1 t
	Formwork for concrete column	862.1 m^2
	Manufacturing, casting, and curing concrete beam	151.0 m^3
	Manufacturing and processing beam reinforcement	48.2 t
	Formwork for concrete beam	1487.4 m^2
	Manufacturing, casting, and curing concrete slab	254.7 m^3
	Manufacturing and processing slab reinforcement	22.2 t
	Formwork for concrete slab	2192.2 m^2
	Manufacturing, casting, and curing concrete stair	62.0 m^3
	Manufacturing and processing stair reinforcement	3.9 t
	Formwork for concrete stair (projected area)	473.6 m^2
	Manufacturing, casting, and curing concrete for other components	41.5 m^3
	Manufacturing and processing reinforcement for other components	3.0 t
	Formwork for other concrete components	465.7 m^2
Masonry wall	Concrete block masonry wall (thickness 200 mm)	444.1 m^3
	Concrete block masonry wall (thickness 100 mm)	59.0 m^3
	Manufacturing, casting, and curing concrete structural column	25.2 m^3
	Manufacturing and processing wall reinforcement	6.4 t
	Formwork for concrete structural column	313.1 m^2
Insulation and decoration	Leveling and plastering of concrete floor	2693.9 m^2
	Floor insulation (Polystyrene foam)	188.6 m^3
	Plastering, whitening, and painting of concrete column	862.1 m^2
	Plastering, whitening, and painting of masonry wall	5486.1 m^2
	Plastering, whitening, and painting of concrete beam and wall	1004.1 m^2
	Plastering, whitening, and painting of ceiling	3664.24 m^2
	Leveling, plastering, and painting of exterior wall surface	1170.0 m^2
	Insulation of exterior wall (Polystyrene foam)	1170.0 m^2
	Manufacturing and installation of plastic-steel window	354.2 m^2
	Manufacturing and installation of fireproof door	160.7 m^2
	Manufacturing and installation of wood door	86.4 m^2
	Roofing leveling (two layers with thickness of 20 mm)	673.5 m^2
	Roofing insulation by polystyrene foam board	94.3 m^3
	Roofing insulation by expanded perlite	70.7 m^3
	SBS-modified asphalt waterproofing (three layers)	673.5 m^2
	Manufacturing and casting, and curing of fine aggregate concrete	27.2 m^3
	Isolation and protection layers	673.5 m^2
Temporal work	Transportation and installation of tower crane	once
	Manufacturing, casting, and curing concrete foundation for tower crane	36.0 m^3
	Vertical transportation estimated by building area	2693.9 m^2
	Scaffolding estimated by building area	2693.9 m^2
	Building closure and safety net	1640.7 m^2
	Temporal electricity for lighting and others	5.0 MWh

4. Results and discussion

4.1. Embodied emissions and costs of the initial scheme

The embodied emissions and relevant project costs of the initial building scheme were assessed and are summarized in Table 4. The total emissions in the pre-use phase were estimated to be 1270.91 tCO_2e, which is 0.47 tCO_2e per floor area in square meters. The production of materials was identified as the major contributor (88.4%), whereas transportation and construction accounted for only 4% and 7.6%, respectively. With respect to the subprojects, the results demonstrated that the loading-bearing system incorporating the foundation and framed structure contributed 45.7% to the embodied emissions, followed by insulation and decoration (35.3%).

Table 4. Building embodied emissions and costs of the initial scheme.

Objective	Process	Subproject
		Foundation	Framed structure	Masonry wall	Insulation & decoration	Temporal work	The entire building
Emission (tCO2e)	Production	110.16	426.99	120.94	433.56	32.14	1123.80
	Transportation	5.72	14.78	14.85	14.42	0.92	50.69
	Construction	8.80	14.38	0.74	1.14	71.36	96.42
	Total	124.68	456.16	136.53	449.12	104.42	1270.91
Cost (10^3 USD)	Labor	7.52	25.29	11.34	79.77	2.82	126.74
	Material	26.14	99.48	41.48	143.42	0.06	310.57
	Machinery	4.15	2.58	0.15	0.38	4.57	11.85
	Measure cost	3.95	44.23	3.98	5.92	44.09	102.18
	Other fees	6.38	30.55	9.06	71.22	3.15	120.37
	Total	48.15	202.14	66.02	300.71	54.69	671.71

Furthermore, Table 4 indicates that the total monetary costs were estimated at 0.67 million USD, of which material consumption and labor input contributed 46.2% and 18.9%, respectively. In addition, the loading-bearing system accounted for 37.3% of the total budget, yet insulation and decoration were the largest contributor (44.8%) from the perspectives of subprojects, owing to the higher costs of labor input and relevant fees which were not considered in the assessment of emissions.

Based on the above analysis, it can be concluded that the load-bearing structure and insulation and decoration subprojects were the main sources of both embodied emissions and relevant costs in the pre-use phase. Although building insulation and decoration are dominated by regional climate conditions and aesthetic requirements, the load-bearing structure can be optimized by improving the design schemes which are emphasized in the following sections. Furthermore, to determine the key structural members for optimization, this study conducted a detailed analysis of the contribution of these components to pre-use emissions and costs. As shown in Figure 4, comparison of the results was made among important structural members such as concrete foundations, columns, beams, slabs, and stairs. The beams appeared to be significant in terms of both emissions and costs, of which the production process dominated; therefore, beams were selected as the optimization target. Figure 4 also indicates that the slabs contributed considerably to the emissions and costs. However, the dimensions and reinforcements of the slabs were mainly determined by conceptual design requirements (such as the minimum thickness of slabs and the minimum diameter and maximum space of steel bars) rather than the load-bearing capacities. Consequently, limited benefits can be obtained by optimizing slabs.

Figure 4. Comparison of the embodied emissions and relevant costs for structural components of the assessed building. “E” and “C” represent emissions and costs respectively.

4.2. Multi-objective structural optimization

Based on the method proposed in Section 2.3, a structural analysis of the entire building was performed to compute the internal forces (such as bending moments and shear forces) of concrete beams, which are the fundamental conditions for design optimization. The main design variables were determined by considering the design experiences and engineering practices as follows: (1) sectional dimensions including width (the same as the thickness of walls) and height of the cross-section (400–700 mm); (2) strength grades of concrete (C30–C50), longitudinal reinforcement (335–500 MPa), and stirrup (300–500 MPa); (3) diameters (16–22 mm) and numbers (2–10) of longitudinal reinforcements at the top and bottom of the section, respectively; (4) diameter (8–12 mm) and spacing (100–200 mm) of stirrups. The beams were classified into five groups based on their ease of design and construction.

Furthermore, if the beams are optimized by resizing the cross-sections or changing the concrete strength, the quantities of other building components and subproject activities might be affected. For example, the height of beams can affect the height of masonry walls and the area of the framework, the reinforcement of slabs is related to the concrete strength of beams because the strengths of these two types of members are generally the same for cast-in-situ structures considering construction convenience. In this context, the optimization objectives were determined as the reduction of total embodied emissions and costs, combining the changes in beams and relevant components, as discussed above.

With respect to the numbers and discrete ranges of dimension and strength variables, at least 2.69 × 10²⁸ types of different schemes were estimated to be randomly generated for this multi-objective optimization, making it difficult and expensive to solve the problem using exhaustive or classical methods. Hence, a heuristic harmony search algorithm was adopted and the maximum number of improvisations – NI – was tested considering both the efficiency of the optimization and the performance of the results. Moreover, to accelerate the convergence speed, the initial structural design was considered as one of the solutions for HM₀. As illustrated in Figure 5, the results become stable towards 10,000 times of improvisations for the studied case, and NI was therefore decided as 10,000.

Figure 5. Trend of the maximum emission and cost reduction of the optimization results when the number of improvisations increases.

To avoid potential local optimum in a single optimization, the HS algorithm was applied to the defined problem and repeated for ten independent trials, in order. Table 5 compares the results of the above trials from the perspectives of time cost, number of feasible solutions, maximum cost, and carbon reduction. The time cost was approximately 250 s for every 1000 improvisations in the test, which was actually associated with the computer configurations. The maximum cost reduction ranged from 7.9 to 8.1 thousand USD, and simultaneously, the maximum emission reduction ranged from 29.3 to 29.5 tCO_2e, which were nearly 11.6% and 17.3% of the pre-use cost and emissions by beams in the initial scheme. In addition, the results indicated that the optimized values of the two objectives were similar for the different trials; thus, they verified the feasibility of the defined algorithm and the relevant parameters.

Table 5. Comparison of the optimization results for ten independent trials.

Trial	Time cost per thousand improvisations (s)	Performance of result
		Maximum efficient improvisations^a	Number of feasible solutions	Maximum cost reduction (10^3 USD)	Maximum emission reduction (tCO2e)
01	2578.0	7231	83,347	8.075	29.446
02	2536.3	7616	83,487	8.071	29.446
03	2570.5	6160	84,643	8.075	29.446
04	2517.9	4215	84,356	8.068	29.446
05	2419.8	7938	78,687	7.962	29.376
06	2454.7	1984	82,650	8.074	29.446
07	2499.5	1611	84,928	8.066	29.446
08	2453.1	6519	80,388	7.978	29.376
09	2468.8	3935	80,582	7.952	29.376
10	2506.0	6183	85,381	8.075	29.446

^aThe number of improvisations after which both the maximum cost and emission reduction remained unchanged till the end of the HS simulation.

Furthermore, a Pareto front comprising 20 solutions was obtained by comprehensively considering the above optimization trials. The heights of the beams were found to be the same for 11 of the Pareto-optimal solutions, whereas the heights of the beams in the other solutions were changed, which can lead to the redistribution of structural internal forces. Therefore, another round of optimization was conducted based on the reanalysis of the updated structural model, and the results were combined with the above 11 solutions in the first stage to identify the corresponding Pareto-optimal solutions.

Figure 6 shows the optimized emissions and cost reductions based on the HS algorithm. The feasible set consists of dominated solutions collected throughout the optimization process, and Pareto fronts I1 and I2 include the Pareto-optimal solutions of the first and second optimization iterations, respectively. As indicated in Figure 6, the highest emission reduction in solution C is 30.4 tCO_2e, which is 5.4% more than that in solution A. Meanwhile, the highest cost reduction in solution A is 8.55 thousand USD, which is 14.5% more than that in solution C. Therefore, solution A has a better potential to reduce carbon emissions than solution C, even though the relevant cost will be slightly increased. In this context, an intermediate optimal solution such as solution B can be an alternative for balancing costs and emissions. Moreover, average carbon emission and cost reduction of 29.63 tCO_2e and 7.92 thousand USD were obtained for solutions in the final Pareto front.

Figure 6. Optimization results of emission and cost reduction based on the harmony search algorithm. Figure 6b demonstrates a partial view of Figure 6a to make the Pareto fronts clear. I1 and I2 represent the first and the second stages of optimization; A, A1, B, C, and C1 are five representative Pareto-optimal solutions.

Table 6 compares the main design variables and relevant optimization results with the initial scheme. As shown in Table 6, the sectional dimensions and concrete strength of the beams for optimal solutions remain the same after the second stage of optimization. Therefore, the internal forces of the beams remained unchanged, and a third round of iterations was not required. Overall, the final Pareto-optimal solutions can provide a maximum emission reduction of 17.9% and 6.7% compared to the initial pre-use emissions of beams and the entire framed structure, respectively, and simultaneously, decrease the monetary cost by up to 12.3% and 4.2%, respectively.

Table 6. Main design variables and results of representative solutions for beams optimization.

Variable and result		Initial scheme	Solution A1	Solution C1	Solution A	Solution C
Sectional dimension of beams (h, b)	L1 and L2	(600, 200)	(600, 200)	(600, 200)	(550, 200)	(550, 200)
	L3 and L4	(600, 200)	(600, 200)	(600, 200)	(600, 200)	(600, 200)
	L5	(500, 200)	(500, 200)	(500, 200)	(500, 200)	(500, 200)
Strength grade (MPa)	Concrete	30	30	30	30	30
	longitudinal bars	400	500	500	500	500
	stirrups	400	300	400	300	400
Quantity of longitudinal bar (t)		41.65	29.95	29.90	30.07	29.99
Quantity of stirrups (t)		6.56	6.06	5.42	5.95	5.32
Concrete consumption (m^3)		150.97	150.97	150.97	146.71	146.71
Emission reduction (tCO2e)		0	27.95	29.45	28.84	30.41
Cost reduction (10^3 USD)		0	0.81	0.70	0.86	0.75

5. Conclusions and perspectives

In this study, a hybrid approach to investigate the optimal designs for reinforced concrete framed buildings that minimize embodied emissions and relevant monetary costs was developed. Based on the combination of integrated structural analysis and local member optimization, a process-based LCA was adopted for the emission and cost assessment based on structural analysis to determine carbon- and cost-intensive members, and a multi-objective harmony search algorithm was proposed for the design optimization of key structural components, considering the specific variables, objectives, and constraints in designs. The proposed method was applied to a four-story apartment building in China, and the main findings are as follows:

• Considering foundation, framed structure, masonry, insulation, decoration, and other temporal work, the total embodied emissions and costs of the case building were estimated as 1270.91 tCO_2e and 0.67 million USD, respectively.

• Based on the contribution of all structural components to the emissions and costs, beams were identified as the optimization target for this concrete frame building.

• With respect to the beams, a series of Pareto-optimal solutions was obtained based on two stages of optimization iterations, for which the maximum emission and cost reduction of 30.4 tCO_2e (17.9%) and 8.55 thousand USD (12.3%), respectively, was attained.

The above results indicated that the combination of integrated structural analysis with optimization of key members can be a feasible approach for decreasing building embodied emissions. Overall, the present study helps understand the importance of structural embodied emissions and costs, and can provide a possible approach for the design optimization of low-carbon and cost-efficient concrete frame buildings, thereby contributing to the green construction industry. The limitations and prospects of this study are noticed as follows. First, the proposed method was examined based on a concrete frame building. In future, it will be interesting to study the variables, constraints, and procedures for optimizing other commonly used building structures and members. Second, the investigation on the potential improvement of the proposed approach remains to be performed, by discussing the algorithm parameters and modeling of the problem.

Nomenclature

Table

Abbreviations
BIM	building information modeling
BOQ	bill of quantities
HM	harmony memory
HMCR	Harmony memory considering rate
HMS	Harmony memory size
HS	harmony search
LCA	life cycle assessment
NI	maximum number of improvisations
PAR	pitch adjustment rate
USD	U.S. dollar
VI	constraint violation
Notations
Cemb	project cost
Cfees	other fees
Clabor	monetary costs from labor quantities
Cmac	monetary costs from machinery
Cmat	monetary costs from material
Cmea	measure expenses
Cr	total change in costs
Econs	emissions from the construction process Edpembodied emissions of a desired process
Eemb	embodied emissions
Eprod	emissions from the production process
Er	total change in emissions
Etran	emissions from the transportation process
EFdp	emission factor of a desired process
Qdp	quantity of the desired process
Parameters
As	amount of longitudinal reinforcement
As,max	upper limit amount of reinforcement
As,min	lower limit amount of reinforcement
CD	crowding distance
c	concrete cover depth
clim	lower limit of concrete cover depth
fc	concrete strength
fclim	lower limit of concrete strength
K	numbers of equality constraints
L	numbers of inequality constraints
la	anchorage length
lalim	limit of anchorage length
M	bending
N	axial force
Nv	number of variables
P	number of objectives
R	member resistance
RP	non-domination rank of Pareto front
S	load effect
sv	stirrup spacing
svlim	limit of stirrup spacing
T	torsion
V	shear
ρ	reinforcement ratio
ω	calculated crack width
ωmax	maximum crack width limited by the design code
Variables, vectors, and matrices
b	cross-sectional width
ds	diameter of steel bars
h	cross-sectional height
gc	strength grade of concrete
gs	strength grade of steel
ns	number of steel bars
ls	length of steel bars
xi	ith design variable
xij	ith design variable in jth solution vector
HM0	matrix of initial harmony memory
HMnew	new harmony memory
HMsum	combined harmony memory
X	solution vector containing all variables
X	jjth solution vector
Functions
fp(X)	pth objective function
gl(X)	lth inequality constraint
hk(X)	kth equality constraint

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Essential research data have been included in the published article. Further information is also available from the corresponding author on reasonable request.

Additional information

Funding

This work was sponsored by the National Natural Science Foundation of China (52108152) and the Natural Science Foundation of Zhejiang Province (LQ22E080001).

Notes on contributors

Xiaocun Zhang

Xiaocun Zhang is an associate professor at School of Civil and Environmental Engineering, Ningbo University, China. He received his Ph.D. from Harbin Institute of Technology, China. His research interest includes low-carbon design of building structures, carbon emission assessment, and sustainable buildings. Xueqi Zhang is a Ph.D. candidate at School of Architecture, Xi’an University of Architecture and Technology, China. She currently conducts research on building energy conservation and low carbon design.

Xueqi Zhang

Xiaocun Zhang is an associate professor at School of Civil and Environmental Engineering, Ningbo University, China. He received his Ph.D. from Harbin Institute of Technology, China. His research interest includes low-carbon design of building structures, carbon emission assessment, and sustainable buildings. Xueqi Zhang is a Ph.D. candidate at School of Architecture, Xi’an University of Architecture and Technology, China. She currently conducts research on building energy conservation and low carbon design.