Environmental Impact Minimization Model for Storage Yard of In-Situ Produced PC Components: Comparison of Dung Beetle Algorithm and Improved Dung Beetle Algorithm

Abstract

If PC components are produced on site under the same conditions, the quality can be secured at least equal to that of factory production. In-situ production can reduce environmental loads by 14.58% or more than factory production, and if the number of PC components produced in-situ is increased, the cost can be reduced by up to 39.4% compared to factory production. Most of the existing studies focus on optimizing the layout of logistics centers, and relatively little attention is paid to the layout of PC parts for in-situ production. PC component yard layout planning for in-situ production can effectively reduce carbon dioxide emissions and improve construction efficiency. Therefore, the purpose of this study is to develop an environmental impact minimization model for in-situ production of PC components. As a result of applying the developed model, the optimization of the improved dung beetle optimization algorithm was verified to be efficient by improving the neighboring correlation by 22.79% and reducing carbon dioxide emissions by 18.33% compared to the dung beetle optimization algorithm. The proposed environmental impact minimization model can support the construction, reconstruction, and functional upgrade of logistics centers, contributing to low carbon dioxide in the logistics industry.

1. Introduction

The in-situ production of precast concrete (PC) components is the same process as that of a factory, in which the processed rebar is installed, concrete is poured, cured, and stacked. in-situ production can reduce environmental impact by more than 14.58% compared to factory production [1,2], and cost savings of up to 39.4% compared to factory production can be achieved by increasing the number of in-situ produced PC components [3,4,5]. Under the same conditions, in-situ production of PC components can achieve the same or better quality than factory production [6,7,8,9,10]. Therefore, studies have been conducted on the in-situ production of PC components that are competitive in terms of convenience, quality, cost, and time [11,12,13,14].

The stock yard area is more than five times larger than the production area, which is a significant proportion [15,16]. In the research on in-situ production of PC components, the main focus is on the production area [17,18,19], and there are no studies on the risk management of stock yard. In the construction storage yard studies, there is no study on the stock yard of PC component in-situ production, as it is mainly focused on the production area [20,21,22,23,24], and there is no study on storage yard management.

PC component yard layout planning for in-situ production can effectively reduce carbon dioxide emissions and improve construction efficiency. Adjusting the layout of large logistics centers to improve the logistics system and achieve ‘carbon reduction’ is important for realizing an eco-friendly logistics industry [25]. However, most existing research focuses on optimizing the layout of logistics centers, and relatively little attention has been paid to PC member yard layout for in-situ production.

Metaheuristic optimization algorithms are particularly effective for tackling complex, nonlinear, large-scale, high-dimensional problems with challenging constraints [25,26]. Their effectiveness lies in their simplicity and flexibility, which allow these algorithms to avoid becoming trapped in local optima more effectively than traditional methods [27,28]. Unlike deterministic optimization techniques, metaheuristic algorithms treat the optimization problem as a “black box,” focusing solely on input-output relationships rather than requiring derivations or analytical expressions of the objective function. This characteristic enables metaheuristic algorithms to be widely applied across diverse fields [29].

The core process of metaheuristic algorithms is an iterative “trial and error” approach. At each iteration, the algorithm updates the solution by searching for improvements, progressively moving toward an optimal or near-optimal solution. The newly generated solution is then compared against previously identified optimal solutions to determine if it offers a better outcome, refining the search in each iteration [30]. By continuously comparing new solutions with established optimal solutions, metaheuristic optimization algorithms incrementally approach the best possible solution [4]. Metaheuristic algorithms have been applied to solve various optimization problems, such as the university timetabling problems [31], network routing [32], partitional clustering [33], and solving design problems of civil engineering structures [34].

Various models have been established in the research area of distribution center layout planning. Jiang et al. [35] developed a multi-objective annealing algorithm simulating to solve the dual objectives of logistics cost and transportation facility cost and verified the proposed method through experimental cases of various sizes. Geng et al. [36] proposed a logistics complex layout optimization method integrating an extended environmental impact model, and verified it through a case study, obtained satisfactory results. Hu et al. [37] built a nonlinear model and used a genetic algorithm to minimize the total processing cost and maximize the comprehensive relationship to reduce the processing cost of enterprises.

Optimization algorithms have attracted considerable attention in the scientific community to solve data clustering problems. These methods are considered more efficient than existing techniques and provide more compelling solutions to data clustering tasks [33]. When dealing with the optimization of layout models using meta-heuristics, it has been proven that layout optimization is non-deterministic polynomial-time hard [38] and traditional optimization algorithms are insufficient to solve this problem. Therefore, recently, scholars often use intelligent optimization algorithms such as genetic algorithm (GA) [39], particle swarm optimization (PSO) [40], and hybrid algorithms [41] to solve these problems. However, as the model becomes more complex and the layout problem space expands, the algorithm converges slowly and struggles to find a solution. Xue et al. [42] proposed the DBO algorithm, which has a powerful optimization capability compared to other algorithms and is widely applicable to various domains. For example, Zhu et al. [43] developed an improved DBO algorithm to solve real-world engineering problems by integrating quantum computing and multiple models.

Li et al. [44] improved the DBO algorithm to optimize the parameters of variational mode decomposition so that a dual-optimization wind speed forecasting model can better handle data and improve prediction accuracy. Li et al. [45] performed nonlinear optimization and proposed a multi-strategy improved dung beetle optimization algorithm. Intelligent optimization algorithms can effectively solve layout optimization problems. However, as models become increasingly complex, algorithmic improvements tailored to the specific problem at hand are essential for optimal solutions.

DBO performs novel optimizations by mimicking the behaviors of dung beetle populations, such as rolling balls, dancing, foraging, stealing, and reproducing [42,45]. However, the DBO algorithm has some disadvantages: (1) During the initialization stage, the utilization of randomly generated populations can lead to an uneven distribution within the solution space. And consequently, exploration is limited, and the algorithm can get stuck in local optima. (2) Throughout the search process, the greedy nature of the algorithm can promote premature convergence to local optima, ignoring the global optimum and leading to suboptimal results. Furthermore, as with other swarm intelligence algorithms, ignoring the evolution of specific dimensions due to interference between dimensions when solving multidimensional objective functions will result in slow convergence and poor solution quality.

Therefore, this study develops a layout optimization model for in-situ production of PC components that aims to maximize adjacent correlation and minimize carbon dioxide emissions. In other words, the purpose of this study is to develop an environmental impact minimization model for in-situ production of PC components. This paper addresses the deficiencies and limitations of the original DBO algorithm by proposing an improved dung beetle optimization algorithm (IDBO). The IDBO aims to enhance the global optimization capability of the standard DBO by introducing multiple strategies and improving the convergence accuracy and speed of the algorithm. Then, the overall performance of the IDBO algorithm is validated through experiments across various aspects.

The sequence of this study is as follows:

(1)

To review the appropriateness of the methodology of this study, the meta-heuristic algorithm is reviewed and categorized.

(2)

After analyzing the storage layout process of in-situ produced PC components, the stock yard problems are identified.

(3)

The objective function and constraints of stock yard are presented to build an optimization model.

(4)

Based on the standard DBO algorithm, a multi-objective optimization model for carbon dioxide emission minimization is built.

(5)

To improve the algorithm, it is proposed the IDBO algorithm by introducing Chebyshev chaos mapping and adaptive Gaussian Cauchy mixed mutation perturbation strategy.

(6)

The results of this study are verified by comparing the optimized layouts obtained by applying the DBO and IDBO algorithms to a real logistics center site.

2. Literature Review

2.1. Classification of Meta-Heuristic Algorithms

Metaheuristic algorithms can be categorized into four main classes: evolutionary algorithms (EA), physics-based algorithms (PhA), human-based algorithms (HBA), and swarm intelligence (SI) algorithms [46,47].

(1)

Evolutionary Algorithms (EA)

Rooted in natural evolution, evolutionary algorithms include the genetic algorithm (GA), introduced by Holland and inspired by Darwinian evolution [48]. GA primarily employs crossover and mutation operations to improve solutions by replacing less optimal ones. Other prominent EAs include differential evolution (DE) [49], evolutionary programming (EP) [50], genetic programming (GP) [51], and evolutionary strategies (ES) [52], all of which incorporate mutation, crossover, and recombination to explore the solution space. Additionally, biogeography-based optimization (BBO) emphasizes migration and information exchange [53].

(2)

Physics-Based Algorithms (PhA)

These algorithms are inspired by physical laws and processes. A classic example is simulated annealing (SA), which models the physical annealing process, where the probability of accepting suboptimal solutions diminishes as the temperature decreases, guiding the algorithm towards optimal convergence [54]. Other PhAs include atom search optimization (ASO) [55] based on molecular dynamics, charged system search (CSS) [55] inspired by Coulomb’s law and Newtonian mechanics, flow direction algorithm (FDA) [56] based on fluid dynamics, Fick’s law algorithm (FLA) [57] based on diffusion principles, gravitational search algorithm (GSA) [58], inspired by the law of the interaction of gravity and mass; Lichtenberg Algorithm (LA) [59], grounded in gravitational interactions, and others such as the light spectrum optimizer (LSO) [60], multi-verse optimizer (MVO) [61], and nuclear reaction optimization (NRO) [62], each inspired by various natural and physical phenomena. The Kepler Optimization Algorithm (KOA) [63], inspired by Kepler’s laws of planetary motion, and the Snow Ablation Optimizer (SAO) [64], inspired by the sublimation and recording of snow.

(3)

Human-Based Algorithms (HBA)

These algorithms draw from human behaviors, such as Teaching-Learning-Based Optimization (TLBO), which emulates the process of learning in teacher and learner phases [65,66,67]. Other examples include collision body optimization (CBO) [68], based on physical body collisions; chef-based optimization algorithm (CBOA) [69], inspired by culinary learning; collective decision optimization (CSO) [70], based on human decision making; and several others, including equilibrium optimizer (EO) [71], Knowledge Sharing Gain (GSK)-based algorithms [72], league championship algorithm (LCA) [73], and mountain climbing team-based optimization (MTBO) [74], Poor and Rich Optimization (PRO) [75], based on the efforts of poor and rich people to achieve a better life; inspired by what successful people learn to improve their lives. The collective intelligence of humans is used to obtain the appropriateness of hyper-parameterization [76].

(4)

Swarm Intelligence (SI) Algorithms

These algorithms are inspired by the collective behaviors of animal groups. Examples include the aquila optimizer (AO), which mimics the hunting behavior of the aquila bird through four distinct methods [77], and artificial rabbit optimization (ARO) [78], based on rabbits’ survival tactics. The nutcracker optimization algorithm (NOA) [79], the shrimp and goby association (SGA) algorithm [80], inspired by cooperative behaviors in nature, and the snake optimizer (SO) [81], which emulates snake mating behaviors, are additional SI algorithms illustrating nature-inspired approaches to complex optimization problems.

Each of these classes leverages a unique source of inspiration—whether natural, physical, or human behavioral—to solve challenging optimization tasks by employing distinct strategies that adapt to the complexity and constraints of high-dimensional problems. Meta-heuristic optimization algorithms are effectively applied to complex layout optimization problems. Due to their simple principles and great flexibility, these algorithms are suitable for solving a variety of high-dimensional and nonlinear optimization problems. In particular, the DBO, one of the SI algorithms, is a meta-heuristic algorithm with powerful optimization capabilities and has been used effectively in various domains. While the DBO performs well in terms of exploration and convergence speed, it can fall into local optima in problems with complex constraints. To solve this, the IDBO is designed to enhance the global exploration capability by introducing chaos mapping and adaptive mutation strategies and to derive more stable optimal solutions. In addition, in the research on simulation and optimization for in-situ production, Lim et al. [19] analyzed the factors affecting the PC quantity estimation for in-situ production. And the simulation model developed in this paper was applied to six scenarios to derive the appropriate quantity. Lim and Kim [1] defined the influencing factors of in-situ production, derived the objective function, and developed a minimization model for environmental load optimization. In other words, there is no research on the optimization of the environmental impacts of the space arrangement for the in-situ production of PC components using metaheuristic algorithms including DBO and IDBO. Therefore, in this study, the DBO and IDBO are applied to develop a yard layout environmental impact minimization model for in-situ production of PC components.

2.2. Analyzing the Process of Stock Yard Layout PC Components Produced on Site

When PC components are actually constructed in the field, they are produced in the order of in-situ production, stock yard, and erection, and the process is as shown in Figure 1 [23,24]. The in-situ production of PC components is carried out in the order of installing processed rebar, pouring concrete, and curing as shown in Figure 1a. As the production, stock yard, and erection quantities are the same, it is necessary to check PC components to be erected. As shown in Figure 1b, the number of stock yard components and stock yard area based on one storage yard are calculated for yard layout, and the required yard area is calculated as the product of the number of yard components. For yard simulation, the crane movement is analyzed and the possibility of utilizing the yard space is reviewed. The stock yard space is determined by dividing it into before and during PC member erection. It is important to determine the order of utilization of the stock yard and arrange the storage yard by reviewing the possibility of utilizing the yard space according to the in-situ production schedule. As shown in Figure 1c, PC components are erected. For this, the number of cranes is determined according to the in-situ production time for the erection of PC components, and the crane specifications are determined by considering the crane working radius and working capacity [82].

The storage yard layout for in-situ produced PC components is a hybrid layout problem that requires consideration of both the layout of the stock yard and the routing of transportation lines, which is the same as the layout of a general logistics facility. The layout of a logistics center is important in terms of how to arrange the location relationship between each area to ensure in-situ efficiency. Based on the assumptions in

Table 1. Assumptions for Layout Optimization Modeling.

No.	Assumptions
1	The sum of the areas of all stock yards must be less than the total site area.
2	A safe distance must be maintained between stock yards and PC components.
3	Transportation efficiency and unit costs are available for material transportation routes and each individual transportation line.
4	The entrances and exits within the logistics facility are not considered, but only the actual PC component loading and erection.

, the center coordinates are shown in Figure 2. In Figure 2, the y-axis and x-axis represent the width and length of a large logistics center, respectively. In addition, the safety distance from the stock yard to the boundary of the logistics center is represented by the x-axis and y-axis, respectively. In addition, the assumptions for this are as shown in Table 1.

Hence, the in-situ production and erection of PC components are affected by each other. The problems can be categorized as follows: (1) space constraints, (2) increased environmental impact: space constraints are the limited PC member stock yard space, which makes stock yard inefficient. When space is insufficient, it becomes difficult to properly arrange the components, which can result in reduced moving distance and time and reduced work efficiency. In addition, misplacement can result in the need for additional component yardage or component movement, which can negatively impact the entire production process. Environmental impact is caused by the increased travel distance of PC components, and inefficient stock yards increase the travel distance between components. This can lead to increased energy consumption and carbon dioxide emissions. In particular, if the components are moved repeatedly, the environmental impact increases significantly. Therefore, it is important to reduce the energy consumption of the equipment and vehicles used in the transportation process and to reduce this environmental impact through efficient layout. Therefore, in this study, it is developed an environmental impact minimization model for the stock yard layout of in-situ produced PC components shown in Figure 1b.

3. Modeling Layout Optimization

3.1. Objective Function

The Paris Agreement, the centerpiece of international action on climate change, was adopted in 2015 [83]. The Paris Agreement includes Article 6, which is the rule underlying the formation of an international carbon market. Article 6 sets out market and non-market approaches for Parties to voluntarily collaborate in implementing their nationally determined contributions (NDCs), making mitigation and adaptation efforts more flexible and cost-effective. Article 6 of the Paris Agreement includes two principles: environmental integrity and the promotion of sustainable development (PA 2015, Article 6.1). This study focuses on the concept of “environmental soundness” as a guiding principle for a collaborative approach.

Environmental soundness has two major meanings. One is that in international greenhouse gas emission reduction projects, the reduction results are not over-credited. Minimizing carbon dioxide emissions during construction site operation is essential to achieving high efficiency and low carbon goals [84]. The arrangement of PC components in the storage yard should be designed to minimize energy usage, carbon dioxide emissions, and resource consumption. The problem of arranging in-situ-produced PC components can be modeled to minimize environmental impact. For this, this study defines objective functions and constraints through mathematical modeling and applies an algorithm to solve them. In this section, it is defined objective functions, constraints, and key variables and parameters for constructing a mathematical model of the arranging problem. Carbon emission calculation is mainly divided into two categories: fixed source carbon dioxide emissions and mobile source carbon dioxide emissions, and the objective function is as in Equation (1).

$$Minimize C=C_F+C_M$$

(1)

where C: carbon dioxide emissions of in-situ produced PC components, C_F: fixed source carbon dioxide emissions, C_M: mobile source carbon dioxide emissions.

① Fixed source carbon dioxide emissions refer to the carbon dioxide emissions generated by the storage yard in the logistics center and increase as the stock yard period increases. Thus, the fixed source carbon dioxide emissions calculation can be related to the number of PC members as well as the space occupied by the stock yard. However, in this study, it is assumed that the fixed source carbon dioxide emissions are calculated by the number of stock yards, which means that the fixed source carbon dioxide emissions can be smaller than the value calculated by the number of PC components due to economies of scale. And the carbon dioxide emissions of labor, electricity, lighting, and heating use are calculated by multiplying the space occupied by storage yard j (m³), the consumption per m³ of space, and the unit fixed source carbon dioxide emission factor. The Equations (2)–(9) are as follows:

$$C=C_L+{C_O+C}_E+C_{LH}$$

(2)

$$C_L=\sum _{j=1}^m\left(M_{jk}{D}_{jk}{L}_j^N{L}_c\right)$$

(3)

$$C_O=\sum _{j=1}^m\left({M_{jk}D}_{jk}{O}_j^N{O}_c\right)$$

(4)

$$C_E=\sum _{j=1}^m\left(M_{jk}{D}_{jk}{E}_j^N{E}_c\right)$$

(5)

$$C_{LH}=\sum _{j=1}^m\left({M_{jk}D}_{jk}{LH}_j^N{LH}_c\right)$$

(6)

$$M_{jk}=\left\{\begin{array}{l}0, there is no flow of goods between j and k.\\ 1, otherwise \end{array}\right.$$

(7)

$$D_{jk}=\left|x_j+x_k\right|+\left|y_j+y_k\right|$$

(8)

$$O_j^N=O_l+O_u$$

(9)

where, C: carbon dioxide emissions, C_L: carbon dioxide emissions of labor, C_O: carbon dioxide emissions of oil, C_E: carbon dioxide emissions of electricity, C_LH: carbon dioxide emissions of lighting and heating use, M_jk: binary variable (0–1) indicating whether there is a movement of PC components between storage yard j and erection area k, D_jk: distance between storage yard j and erection area k calculated using the Manhattan distance formula, $L_j^N$: labor consumption (man/ea) when the number of PC components in storage yard j is N, L_MC: carbon dioxide emission factor (kg/kWh) of labor, $O_j^N$: oil consumption (l/ea) when there are N PCs in storage yard j, O_C: carbon dioxide emission factor (kg/L) of oil, $E_j^N$: electricity consumption (kWh/ea) when there are N PC components in storage yard j, E_C: carbon dioxide emission factor (kg-CO₂/kWh) of electricity, ${LH}_j^N$: Light and heating usage (kWh/ea) when the number of PC components in storage yard j is N, LH_C: carbon dioxide emission factor (kg-CO₂/kWh) of light and heating, $x_j$: x-axis of storage yard j, $x_k$: x-axis of erection zone k$,y_j$: y-axis of storage yard j, $y_k$: y-axis of erection area$,$ O_l: oil use (L/ea) for loading of mobile crane, O_u: oil use (L/ea) for unloading of mobile crane, j: j-th stock yard zone (1, …, m), k: k-th erection zone (1, …, n).

② Mobile source carbon dioxide emissions occur due to electricity or fuel consumption during loading, unloading, and transporting PC members between different storage yards. The electricity or fuel consumption during these stages is affected by various factors such as mobile crane usage, changes in worker behavior, and environmental conditions. Therefore, this study considers the effects of distance and PC member load on carbon dioxide emissions by considering actual field operating conditions. Therefore, mobile source carbon dioxide emissions are calculated as the total travel distance of PC components from the storage yard to the erection area. And the carbon dioxide emissions of labor, electricity, lighting, and heating use are calculated by multiplying the distance calculated using the Manhattan distance formula, a binary variable indicating whether the PC components are moved between the stock yard and the erection area, the consumption per PC component, and the mobile source carbon dioxide emission factor. Equations (2)–(9) for this are the same as for the fixed source.

3.2. Constraint

Layout planning mainly involves the following constraints.

① Boundary constraint

Each storage facility must not extend beyond the boundaries of the planned area and must maintain a specified safety distance from the boundary. In addition, PC components must be placed within the space of a given stock yard, and the coordinates of PC member placement must not exceed the allowed range within each zone. The Equations (10) and (11) are as follows:

$$\left\{\begin{array}{c}{x}_i+a_i+{\displaystyle \frac{l_i}{2}}\le L\\ x_i-a_i-{\displaystyle \frac{l_i}{2}}\ge 0\end{array}\right.$$

(10)

$$x_i \in [x_{min}, x_{max}]$$

(11)

where, $x_i$: x-axis of zone$,$ a_i: x-axis clearance from zone i to the logistics center boundary, l_i: length of zone i, w_i: width of zone i, L: total length of the logistics center, $x_{min}$: x-axis of the minimum boundary of the zone$,x_{max}$: x-axis of the maximum boundary of the zone

② Non-overlapping constraints

Each production area, stock yard area, and erection area of a PC component cannot overlap, and a minimum distance must be maintained between each area, i.e., enough distance must be secured between each area to provide workspace for PC component quality inspection and verification, equipment and material movement, etc. The Equation (12) are as follows: However, the completed erection area can partially overlap with the stock yard area.

$$\left\{\begin{array}{c}{\displaystyle \frac{l_i+l_j}{2}}+h_{ij}\le \left|x_i-x_j\right|\\ {\displaystyle \frac{w_i+w_j}{2}}+v_{ij}\ge \left|y_i-y_j\right|\end{array}\right. , \forall i \ne j$$

(12)

where l_i: length of zone i, w_i: width of stock yard, h_ij: x-axis distance between areas i and j, v_ij: y-axis distance between zones i and j, $x_i$: x-axis of zone$,y_i$: y-axis of zone i

③ Work procedure constraints

PC components must be moved according to the order of work, and the order of placement of certain PC components can be fixed or restricted. This is a constraint to maintain a specific work flow, which is necessary to maximize work efficiency. The Equation (13) for this is as follows:

$$if i precedes j, x_i<x_{i+1} or y_i<y_{i+1}$$

(13)

④ Stacking height constraints

The stacking height of PC components must not exceed the allowed height limit. This model provides the basic mathematical modeling for optimizing the stock yard arrangement of PC components. Based on this model, DBO and IDBO can be applied to solve the optimization issue.

$$H_i<H_{max}$$

(14)

$$H_i={\displaystyle \frac{W_A}{W_l}}{\times H}_{PCj}$$

(15)

where, $H_i$: stacking height of storage yard i, $H_{max}$: maximum allowable height of PC member, $W_A$: allowable weight per area, $W_l$: weight of one layer, $H_{PCj}$: height of PC member j.

4. Solving Algorithms

4.1. DBO Algorithm

The DBO algorithm classifies the population into four subpopulations according to the actions of the dung beetles: rolling, spawning, predation, and stealing. And to increase the efficiency of the algorithm’s search, it implements various search methods and adopts search strategies.

(1)

Rollerball dung beetle

When there are no obstacles along its winding path, the dung beetle uses sunlight as a navigational aid. Therefore, light affects the dung beetle’s path. The location update Equations (16) and (17) for a rolling dung beetle are.

$$X_i^{n+1}=X_i^n+\alpha \times b\times X_i^{n-1}+B\times \Delta x$$

(16)

$$\Delta x=\left|X_i^n-X^W\right|$$

(17)

where, $X_i^n$: location information of the i-th generation of dung beetles after the nth iteration, a: −1 or 1 to represent various effects of nature, b: a random number in [0, 0.2] to represent the defect factor, B: A constant taking values from [1, 0] (used to simulate the change in light intensity), $X^W$: global worst location.

When there is no light in the environment or the road is rough, the direction of travel cannot be identified, and the dung beetles must dance and change direction to find a new path. To determine their next direction of travel, the dung beetles’ position update Equations (18) and (19) are as follows:

$$X_i^{n+1}=X_i^n+\mathrm{t}\mathrm{a}\mathrm{n}\beta \left|X_i^n-X_i^{n-1}\right|$$

(18)

$$0\le \beta \le \pi$$

(19)

where, $X_i^n$: position information of the i-th generation of dung beetles after the n-th iteration, $\left|X_i^n-X_i^{n-1}\right|$: distance between the i-th generation and the (n − 1)th iteration position at the n-th iteration position, $\beta$: Deflection angle belonging to [0,π] (position remains unchanged when 0, ${\displaystyle \frac{\pi }{2}}$).

(2)

Spawning dung beetles

Dung beetles reproduce by rolling balls to a safe space and hiding them. On the other hand, it is important for dung beetles to choose a suitable location in a pile of dung balls to lay eggs. Therefore, the formula for determining the spawning boundary is defined by the following Equations (20) and (21).

$${LB}_1=\mathrm{m}\mathrm{a}\mathrm{x}\left(X^r\times \left(1-T\right),LB\right)$$

(20)

$${UB}_1=\mathrm{m}\mathrm{i}\mathrm{n}\left(X^r\times \left(1+T\right),UB\right)$$

(21)

where, $X^r$: current local optimal position, ${LB}_1$: lower bounds of the optimization issues, ${UB}_1$: upper bounds of the optimization issues, $N_{max}$: Maximum number of repetitions.

When the boundaries of the dung beetle spawning area are determined, females lay eggs only in the area determined by the above formula, and only one egg is laid per generation. When the spawning area changes, female dung beetles can clearly sense the change in boundaries and dynamically adjust their spawning location. The formula for selecting a spawning site for dung beetles is given by the following Equation (22). The spawning area boundary range changes dynamically, mainly depending on the R value. Therefore, the generated ball’s position is dynamic even during the iteration process.

$$X_i^{n+1}=X^r+B_1\times (X_i^n-{LB}_1)+B_2\times (X_i^n-{UB}_1)$$

(22)

where, $X_i^n$: location of the i-th generation after the nth iteration, $B_1$, $B_2$: two random matrices of (1 × Dim), ${LB}_1$: lower bounds of the optimization issues, ${UB}_1$: upper bounds of the optimization issues, Dim: dimensional size of the algorithm.

(3)

Foraging dung beetles

After successful hatching, small dung beetles must forage independently, and the optimal foraging area is shown in Equations (23) and (24).

$${LB}_2=\mathrm{m}\mathrm{a}\mathrm{x}\left(X^{-}\times \left(1-T\right),LB\right)$$

(23)

$${UB}_2=\mathrm{m}\mathrm{i}\mathrm{n}\left(X^{-}\times \left(1+T\right),UB\right)$$

(24)

where, ${LB}_2$: lower boundaries of the dung beetle’s search area for food, ${UB}_2$: upper boundaries of the dung beetle’s search area for food, $X^{-}$: global optimal position, T: boundary selection strategy of dung beetles when laying eggs.

$X^{-}$ denotes the best location globally, ${LB}_2$ and ${UB}_2$ denote the lower and upper bounds of the optimal foraging area, respectively, and the location update of the dung beetles is given by the following Equation (25).

$$X_i^{n+1}=X_i^n+K_1\times (X_i^n-{LB}_2)+K_2\times (X_i^n-{UB}_2)$$

(25)

where, $X_i^n$: position of the i-th generation of small dung beetles at the n-th iteration, $K_1$: a number obeying gaussian distribution, $K_2$: a set belonging to [0, 1].

(4)

Stealing dung beetles

In a colony of dung beetles, there are thieves who steal dung balls from other dung beetles, called theft dung beetles. Theft dung beetles steal dung balls from other dung beetles. The Equation (26) for updating the location of the thief dung beetles is:

$$X_i^{n+1}=X^s+P\times f\times (\left|X_i^n-X^r\right|+\left|X_i^n-X^{-}\right|)$$

(26)

where, $X_i^n$: the position of the i-th burglar at the n-th iteration, f: a stochastic set obeying a normal distribution with size (1 $\times$ Dim), P: a constant value.

4.2. IDBO Algorithm

The initial population of the standard DBO algorithm is randomly generated, but this does not guarantee a high level of chaos. In subsequent iterations, the population of dung beetles will congregate near the current optimal location, and expanding the search can easily lead to a local optimal solution. Therefore, improvements should be made to address these shortcomings.

(1)

Chebyshev Chaos reset population

The quality of the population in the early stages affects the algorithm convergence speed [85]. In order to improve the quality of the initial population, a chaos mapping function should usually be used for initialization. Chebyshev mapping stands out for its excellent chaotic properties and promotes uniform distribution of population within the simulation space. Agrawal et al. [22] compared common chaos mapping functions and proved that Chebyshev chaos mapping is superior to other mapping functions. In addition, Zhang et al. and Pan and Xu [86,87] improved the new optimization algorithm by applying Chebyshev theory. In this paper, Equation (27) is used to integrate Chebyshev chaos mapping into the initialization phase of the DBO algorithm, ensuring a high-quality initial population and facilitating more efficient convergence during the iterative optimization process.

$$x_{n+1}=cos\left(k\times \arccos \left(x_n\right)\right),x_n\in \left[-\mathrm{1,1}\right]$$

(27)

k: order (value 4), $x_n$: the position at the n-th iteration

In evolutionary algorithms, mutation perturbation is essential to enhance population diversity and facilitate exploration of the solution space, helping the algorithm avoid premature convergence to a local optimum. Two common mutation operators, Cauchy mutation and Gaussian mutation, each offer their own unique advantages. Gaussian mutation is effective for fine-tuned searches within a smaller region, yielding controlled and predictable mutation outcomes [88]. On the other hand, Cauchy mutation introduces a broader search range due to its ability to generate larger mutations, but sometimes at the expense of stability. To leverage the advantages of both operators, this study uses an adaptive hybrid mutation perturbation strategy [89] that combines Gaussian and Cauchy mutations to enhance the search capability. This hybrid approach is applied to the optimal individuals, allowing the algorithm to dynamically adjust the mutation behavior according to the search step. After applying this perturbation, the fitness values are evaluated before and after the mutation to maintain the good solution as detailed in Equation (28). The coefficients of ${\delta }_a$ and ${\delta }_b$ are gradually adjusted in a one-dimensional linear fashion to ensure balanced perturbation in each iteration. After tests, the parameter $\sigma$ was selected to derive better results.

$$M^b\left(n\right)=X^b\left(\mathrm{n}\right)\times (1+{\delta }_a\times Gauss(\sigma )+{\delta }_b\times Cauchy(\sigma \left)\right)$$

(28)

where, $X^b\left(\mathrm{n}\right)$: optimal location of individual X at n-th iteration, $M^b\left(n\right)$: position of $X^b\left(\mathrm{n}\right)$ perturbed by Gaussian–Cauchy mutation at n-th iteration, ${\delta }_1$, ${\delta }_2$: mutation operator coefficients, Cauchy(σ) is Cauchy mutation operator, Gauss (σ) is Gaussian mutation operator.

After changing the solution by applying this strategy, the suitability of the changed solution must be re-evaluated by comparing it with the optimal solution. Therefore, a greedy rule is applied to determine whether to improve the optimal solution or not.

$$X^{-}=\left\{\begin{array}{c}{M}^b\left(n\right),f\left[M^b\left(n\right)\right]<f\left[X^{-}\right(n\left)\right]\\ X^b\left(n\right),f\left[M^b\left(n\right)\right]\ge f\left[X^{-}\right(n\left)\right]\end{array}\right.$$

(29)

$X^{-}$: global optimal position, $M^b\left(n\right)$: position of $X^b\left(\mathrm{n}\right)$ perturbed by Gaussian–Cauchy hybrid mutation at the n-th iteration

(2)

IDBO algorithm implementation steps

The framework of the IDBO algorithm is outlined in Algorithm 1. To provide a clear visualization of the process, Figure 3 illustrates the flowchart of the IDBO algorithm. This algorithm aims to enhance search efficiency and convergence speed during optimization by employing a combination of multiple strategies. The IDBO algorithm utilizes the Gaussian-Cauchy strategy to generate mutant solutions by perturbing the optimal solution. Moreover, applying the greedy rule to the current optimal solution to expand the algorithm’s search space and combining it with a dimension-by-dimension optimization strategy to improve the quality of the solution.

Algorithm 1. The framework of the DBO algorithm
Require: The maximum iteration TMAX, the size of the particle’s population N. Ensure: Optimal position Xb and its fitness value fb
1	Initialize the particle’s population i ← 1, 2, …, N and define its relevant parameters
2	while  t ≤ TMAX do
3	for  i = 1 to Number of rollingdung beetles do
4	α = rand(1)
5	if  α ≤ 0.9 then
6	Update Rolling Dung Beetle Location by Equations (16) and (17).
7	Else
8	Rolling the ball in the encounter of obstacles by Equations (18) and (19) to update.
9	end if
10	end for
11	The value of the nonlinear convergence factor is calculated by R = 1 − t∕T MAX.
12	for  i = 1 to Number of dung beetles do
13	Updating of Spawning dung beetles by Equations (20)–(22).
14	end for
15	for  i = 1 to Number of Foraging dung beetles do
16	Update foraging dung beetles by Equations (23)–(25).
17	end for
18	for  i = 1 to Number of Stealing Dung Beetles do
19	Use Equation (26) to update the location of the stealing dung beetle
20	end for
21	end while
22	Return Xb and its fitness value fb

5. Case Project Application

5.1. Case Overview

In order to derive the optimal stock yard layout for minimizing the environmental impact of in-situ production of PC components, a case site was selected, and components for in-situ production were selected. The outline of the case project, a large logistics center building, is shown in

Table 2. Brief description of case project.

Description	Contents
Location	Seoul-si, Republic of Korea
Site area	147,112 m2
Building area	84,413 m2 (491 m long × 497 m width)
Total floor area	420,991 m2
No. of floors	B2–5F (6 buildings, floor height 8.7–12.2 m)
Structure	Columns, Girders, Slabs: Precast concrete structure, Cores: Reinforced concrete structure One building: Steel reinforced concrete structure

. The case project consists of a RC-core, steel-reinforced concrete structure of one building, mainly a PC structure with 5 floors above ground and 2 floors below ground (6 buildings). It should be noted that the case building has a floor height of 8.7–12.2 m and a heavy-loaded building of 2.4 t/m².

In this study, the case sites applied in this study are columns, girders, and slabs that are manufactured and constructed with PC. However, the components that can be in-situ produced are limited to columns and girders, which require less production area. In other words, columns and girders are long and thin, so the production space is narrow, but slabs require a large production and stock yard space, so it is difficult to produce in-situ in a limited area. Therefore, this study calculates the quantity of columns and girders that are subject to optimal stock yard layout. The actual project layout is modified for the efficiency of the stock yard layout simulation, which is defined as the original layout and the applied layout as shown in Figure 4. Figure 4a 84,413 m², Figure 4b 84,140 m², and divided into A, B, and C zones according to the number of cranes used. According to the functional attributes, PC components can be divided into four zones: production zone (1), stock yard zone (2), erection zone (3), and other work zone (4), and the other work area is not separately indicated because it is an area to be calculated. In this case, the stock yard area is the total site area excluding production, erection, and other work zones (including free space for transportation, etc.). This can be expressed as Equation (30).

$$A_{Sij}=\sum \sum (A_{Tij}-A_{Pij}-A_{Eij}-A_{Oij})$$

(30)

where, $A_{Sij}$: stock yard area of i-zone j-period, $A_{Tij}$: total site area of i-zone j-period, $A_{Pij}$: production area of i-zone j-period, $A_{Eij}$: erection area of i-zone j-period, $A_{Oij}$: other operations area of i-zone j-period, i: i-th zone (1, …, n), j: j-th period (1, …, m).

5.2. Optimization Result

It is necessary to calculate the movement distance of the crane used in the stacking stage of the in-situ production PC components and the erection stage of the stacked components. The crane movement distance can be calculated as the rotation distance. The rotation distance can be divided into the crane horizontal (Figure 5a) and vertical (Figure 5b) rotation distances and is calculated by calculating each distance and adding them up [90]. That is, the horizontal rotation of the crane means the movement from ⓐ to ⓑ in Figure 5a, and the vertical rotation means the movement from ⓑ to ⓒ in Figure 5b. The horizontal rotation angle of the boom is calculated as the relative coordinate value of the installation part with the crane position coordinate as the origin, as in Equation (31). The horizontal distance of the crane can be calculated as in Equation (32) using the distance from the crane to the trailer and the horizontal rotation angle of the boom. The boom head position must be defined to calculate the horizontal rotation distance. The vertical rotation angle of the boom is calculated using the boom length and the straight-line distance during vertical rotation, as in Equation (33). The vertical distance of the crane can be calculated using the boom length and the vertical rotation angle, as in Equation (34). Finally, the boom trajectory distance $D_t$ is calculated as the sum of the horizontal rotation distance and the vertical rotation distance, as in Equation (35). The vertical rotation angle of the boom is calculated using Equations (31)–(35), and the vertical rotation distance of the crane is derived.

$${\theta }_i=\pi -\arctan \left({\displaystyle \frac{\left|x_i-0\right|}{\left|y_i-0\right|}}\right)$$

(31)

$$r\left({\theta }_i\right)=l_T\times {\theta }_i$$

(32)

$${\phi }_i=2\times \arcsin \left({\displaystyle \frac{A/2}{L_B}}\right)$$

(33)

$$r\left({\phi }_i\right)=L_B\times {\phi }_i$$

(34)

$$D_t=\sum _{i=1}^n\left(r\right({\theta }_i)+r\left({\phi }_i\right))$$

(35)

where, $M_{ci}$: column member position coordinate, $x_{ci}$: erection column member x-axis, $y_{ci}$: erection column member y-axis, $z_{ci}$: erection column member z-axis, C: crane position axis, T: trailer position axis, $x_t$: x-axis of the trailer, $y_t$: y-axis of the trailer, $z_t$: z- axis of the trailer, ${\theta }_i$: horizontal rotation angle of the boom in radians, r(${\theta }_i)$: horizontal rotation distance, $l_T$: distance from the crane to the trailer, $l_{cmci}$: distance from the crane to the erection member, $L_B$: boom length, A: straight line distance in vertical rotation, ${\phi }_i$: vertical rotation angle of the boom in radians, r(${\phi }_i)$: vertical rotation distance, $D_t$: boom trajectory distance, i: number of i-th erection member at crane position (1, …, n).

Create rules utilizing the queue and stack methods to stack PC components. The simulation is performed accordingly, and if there is an error in the order of utilization of the storage yard and the order of loading in the stock yard, the simulation is corrected (feedback routine). If there are no errors, the simulation is completed. Since the order of erection in three-layer yarding is different from the order of in-situ production, stock yard rules are required for simulation. To manage the order of erection and production, Rule 1 is established as shown in Figure 6. PC components in all stock yards are based on sequentially loading from the 1st storage yard to the n-th storage yard.

This rule utilizes the queue method to produce and load first in first out (FIFO) from left to right and the stack method to produce and load first in last out (FILO) from top to bottom [91,92]. In-situ produced PCs are stacked in the order of white circles 1, 2, 3, …, 20, and erection is performed in the order of blue circles 1, 2, 3, …, 20. In addition, since the loading of PC beams and the loading of the 4th floor are single-layer loading, no separate loading plan is required. Storage yard consisting of a n × m matrix can be represented as the following Equation (36), and the stock yard rule 1 can be formulated as the following Equation (37). The total number of components in the storage yard is given by the product of the rows and columns of the stock yard. If the storage yard is organized as a n × m matrix with rows in the stack method and columns in the queue method, the positions of the stacking order and production order can be expressed as a matrix.

$$f\left(x\right)=n\times m$$

(36)

$$\begin{array}{cc}X\left(a_{ij},b_{ij}\right)& =\left(\begin{array}{ccc}(a_{11},b_{11})& \cdots & (a_{1j},b_{1j})\\ ⋮& \ddots & ⋮\\ (a_{i1},b_{i1})& \cdots & (a_{ij},b_{ij})\end{array}\right)\hfill \\ & =\left(\begin{array}{ccc}(n,1)& \cdots & (nm-(n-n),nm-(n-1\left)\right)\\ ⋮& \ddots & ⋮\\ (1,n)& \cdots & (nm-(n-1),nm-(n-n\left)\right)\end{array}\right)\hfill \end{array}$$

(37)

where, $\mathrm{f}\left(\mathrm{x}\right)$: Total number of components in 1 storage yard, $\mathrm{X}({\mathrm{a}}_{ij},{\mathrm{b}}_{ij})$: production rule of the 1st stock yard rule, ${\mathrm{a}}_{ij}$: production order of the member in the i-th row, column j-th, and ${\mathrm{b}}_{ij}$: stock yard order of the member in the i-th row, column j-th.

PC columns are based on stacking 10 PC columns in 3 tiers, and an area of 125.5 m² is required for PC columns as shown in Figure 7. In addition, if it is stacked on the bottom floor of the 5th floor, it will be stacked in one layer, so an area of 376.5 m² is required for 30 pieces. The production and stock yard area for PC beams can be calculated in the same way. In addition, the following rules have been established to minimize the risk of PC components when loading and unloading, as shown in

Table 3. PC member yard storage rules.

No.	Assumption
1	In-situ-produced components in each zone are basically stacked outside the building of each zone.
2	PC components are stacked within the crane working radius.
3	When the construction of the 5th floor is completed, the 5th floor is prioritized as the stock yard space.
4	In-situ produced components are based on the erection of steel plates at + GL (ground level) and stacked in 3 columns and 2 beams.
5	As the load of the building is designed to be 2.4 tons/m2, the PC components are stacked in 1-layer on the 2nd, 3rd, 4th, and 5th floors.
6	i-th storage yard is divided by zone and member.
7	i-th storage yard is based on sequential loading.
8	Each storage yard is based on stacking 30 components.

.

After in-situ production of PC components, the details of the loading rules are as follows:

① PC components are in-situ produced and erected by driving cranes in each zone. Therefore, the basic rule is that the in-situ produced components are stacked outside the building, corresponding to the area of each zone. However, if the space is limited, it is possible to utilize the site of a neighboring zone, a site outside the zone, or a building slab.

② PC components should be stacked in consideration of the erection location, i.e., stacked close to the erection location so that the travel distance of the components is short. The components must be stacked within the crane working radius.

③ To minimize the risk, it is important to ensure that the loading plan is not affected by the erection schedule of PC components. Therefore, in this project, which is a PC structure up to the 5th floor, the 5th floor can be utilized as stock yard space after the construction of the 5th floor is completed. In other words, the 5th floor is the roof level of the building, and there is no interference with the erection of PC components, so there is no need to move the stock yard space.

④ The in-situ produced components are basically stacked in three columns and one beam after installing steel plates at GL. The reason for installing steel plates is that there is a problem of damage to the components due to ground subsidence caused by the weight of the components due to insufficient compaction. In addition, the number of loading units is based on the characteristics of the components, and columns that can be loaded in multiple units are loaded in three units, and beams that cannot be loaded in multiple units are loaded in one unit.

⑤ This case project is a logistics center facility, and the building is designed with a load of 2.4 tons/m² to reflect the movement of large vehicles transporting loaded cargo. Therefore, when the bottom floors of the 2nd–5th floors of the building are utilized as stock yard space, the number of stacks of components is limited to one in consideration of the load of the components.

⑥ When stacking components, establish a stacking plan by zone, by type of column and beam member, and by the nth stock yard.

⑦ Storage yard is based on sequential loading. However, if the space is limited, the stock yard and erection can be carried out simultaneously at one stock yard.

⑧ Each storage yard is based on loading 30 components for the convenience of stock yard management. In addition, the stock yard area is calculated by considering the basic unit of the stock yard.

The total construction time was 20 months, and the erection time was 12 months. Through time series analysis, the area derived by each zone corresponding to the erection time is as shown in

Table 4. PC absence area for 12 months by time series analysis (unit: m²).

Area	M + 1	M + 2	M + 3	M + 4	M + 5	M + 6	M + 7	M + 8	M + 9	M + 10	M + 11	M + 12
Erection	36,603	35,574	36,058	37,994	30,976	15,972	19,844	12,100	7502	2420	2420	2178
Other work	4350	4682	3025	3120	2925	2543	2432	2210	2100	1468	1055	831
Production	3220	3220	3220	2240	2240	1120	1120	1120	0	0	0	0
Stock	49,581	49,168	43,454	37,626	33,421	29,660	16,915	10,753	9702	9580	8883	0

. It is necessary to calculate the stock yard area corresponding to the number of stock yard components per zone and per member type. This should be calculated on a weekly or monthly basis during the period of simultaneous production and erection. To perform the production and erection simulation, the production and stock yard area is calculated according to the calculated number of molds and the number of stock yard components.

5.3. Result Comparison

In this study, IDBO and DBO algorithms were simulated to minimize the environmental impact of in-situ produced PC components. To ensure the fairness of the experiment, the initial population size of all algorithms is set to 30, and the number of repetitions is set to a maximum of 300. The number of ball rolling, spawning, and stealing of dung beetles is 6, 6, 7, and 11, respectively. As each algorithm produces different results each time, to eliminate the influence of randomness in the experiment, each algorithm is run independently 30 times and the results are analyzed. This study compares the optimization solutions derived from the two algorithms and plots the average fitness iteration curve of one of the results in Figure 8. All fitness iteration curves are listed in Figure A1.

Figure 5 shows that the DBO algorithm reached a plateau at the optimum point at the 45th iteration. However, at the beginning stage, due to the application of Chebyshev mapping, the IDBO algorithm can be seen to converge faster than the DBO algorithm at first. As the iterations progress, the DBO algorithm gets stuck in a local optimum, while the IDBO algorithm shows superior search capability and eventually finds a better solution. In this study, there was still room for improvement even after 300 iterations of the algorithm. This suggests that the Gaussian–Cauchy strategy is effective in improving the search ability of the algorithm. In other words, in the convergence curve, the IDBO algorithm shows superior optimization capability, which is characterized by improved exploration ability, greater stability, accelerated convergence speed, and improved convergence accuracy than the DBO algorithm. This trend continues even when the iterations increase to 300 because the IDBO algorithm continues to show commendable performance in solving high-dimensional optimization problems.

Figure 9 shows the optimal layout derived from the two algorithms. Figure 8 shows that the DBO layout is analyzed to show inefficient placement. On the other hand, the IDBO optimized layout ensures more efficient construction site operation by making the stock yards and crane movement path more rational. Therefore, it was concluded that the IDBO algorithm is more suitable than the DBO algorithm for the environmental impact optimization problem for the stock yard of in-situ produced PC components.

Table 5. Carbon emission calculation of DBO and IDBO algorithm (T-CO₂).

Item	DBO Layout		IDBO Layout
	Fixed Source	Mobile Source	Fixed Source	Mobile Source
Labor	7	36	3	25
Oil use	0	2610	0	2152
Electricity use	32	55	17	48
Lighting, and heating use	10	15	4	9
Total	49	2716	24	2234

shows the carbon emission calculation results for each layout method using Equations (2)–(9). Except for oil use, the mobile source was found to be 2–8 times larger than the fixed source in terms of labor, electricity use, lighting, and heating use. In other words, the carbon dioxide emissions generated from transportation, loading, and unloading activities between storage yards were found to be significantly larger than the carbon dioxide emissions generated in the storage yards within the logistics center. Therefore, although it is necessary to reduce unnecessary carbon dioxide emissions from fixed sources, it is also important to reduce carbon dioxide emissions from transportation, loading, and unloading activities. In addition, in terms of oil use, the DBO and IDBO layout showed high CO₂ emission rates, accounting for 94% and 95%, respectively.

The optimization effect of each layout method on the random simulation results is compared as shown in

Table 6. Layout optimization comparison of DBO and IDBO algorithm.

Layout Plan	Adjacent Correlation	Carbon Dioxide Emissions (T-CO2)
DBO optimization layout	29.93	2765
IDBO optimization layout	36.75	2258

. This table shows that the DBO algorithm reduces the overall cost by 14.46%. The adjacent correlations of the DBO and IDBO algorithms are 29.93 and 36.75, respectively, and the carbon dioxide emissions are 2765 and 2258. In other words, the IDBO algorithm improves the adjacent correlation by 22.79% and reduces the carbon dioxide emissions by 18.33% compared to the DBO algorithm. This confirms that the IDBO algorithm can improve neighbor correlation and the DBO algorithm can reduce carbon dioxide emissions.

The DBO algorithm applied in this study solves the stock yard layout optimization problem through the basic exploration and exploitation mechanism. The DBO algorithm can generally perform adequately in optimization problems, especially in the initial exploration, which has a good global exploration ability and can explore a variety of solutions. In the initial stage of this study, the environmental impact optimization for the stock yard of in-situ produced PC components was simulated in two parts because the convergence speed was slowed down during the simulation process and the final solution was not close to the optimal solution. The reason for the slow convergence was that the DBO algorithm was likely to fall into a local optimum due to the large number of complex constraints and the large problem space. In other words, the DBO algorithm can have poor solution quality for problems with complex constraints.

The IDBO algorithm, on the other hand, is designed to improve the performance of the DBO algorithm. By introducing chaos mapping and mutation strategies, the IDBO algorithm was able to enhance its exploration capabilities and better balance global exploration and local exploitation. It was found that the IDBO algorithm is more likely to outperform the DBO algorithm in problems with complex constraints or multi-objective optimization problems, which means that the IDBO algorithm is more likely to outperform the DBO algorithm. It was also found that the IDBO algorithm produces higher-quality solutions compared to the DBO algorithm. This is because the IDBO algorithm is able to use different search strategies to search for the global optimum and converge more precisely. Therefore, the solution produced by IDBO is more likely to be an optimal arrangement that satisfies the constraints while minimizing the environmental footprint.

6. Discussion

When stock yard space is limited, it is sometimes necessary to move stacked components to storage yard in a different space. This is the same as the default for odd-order reloading, but different for even-order reloading. This is defined as yard storage rule 2 and is illustrated in Figure 10. In the 1st storage yard of Figure 9a, the PCs produced in-situ are stacked in the order of white circles 1, 2, 3, …, 20, and the erection is performed in the order of blue circles 1, 2, 3, …, 20. After that, when the storage yard is moved, the order of the PCs produced and stacked in-situ and the PCs being erected are stacked in the opposite order, as in the 2nd storage yard of Figure 9b. In other words, the PCs must be stacked considering the erection order at the end. If a PC member needs to be installed in a storage yard that is stacked with components on the ground floor, the storage yard must be moved to another room for erection. The calculation of the number of storage yard movements is expressed as Equation (38). However, it is assumed that reloading is not done because it increases environmental impact, cost, and time.

$$N_S=Min\sum f\left(x_i\right)$$

(38)

where, N_s: Total number of storage yard moves for PC components, x_i: storage yard moves.

Modern societies are facing a variety of environmental challenges due to rapid industrialization and urbanization. These challenges can be described by the concept of environmental impact, which refers to the negative impact of human activities on the natural environment. Environmental impact is primarily related to resource consumption, energy use, emissions generation, and waste disposal, which can lead to a number of environmental problems such as air pollution, water pollution, ecosystem degradation, and climate change.

Effective management of environmental footprints in construction projects is an essential component of realizing sustainable construction. It goes beyond simply complying with legal regulations and extends to a strategic approach related to corporate social responsibility. Reducing environmental footprint can also provide economic benefits in the long run, leading to cost savings and efficiency gains. For these reasons, innovative methodologies are needed to minimize the environmental footprint and enhance sustainability. Optimizing stock yard layout in PC member in-situ production is part of this effort and is an important strategy to minimize the environmental impact of construction sites and promote sustainable development.

In this study, an optimized layout model for in-situ production was applied to PC columns and beams. In other words, the in-situ production in this study was targeted at slender parts such as columns and beams. However, PC slabs such as RPS (Rib-Plus Slab) and double T (double T) slabs occupy a large space during production, so additional conditions should be considered when applying in-situ production. In addition, this study applied the increased number of mold reuses considering the cost and assumed that the size of the parts and the details of the reinforcement were similar and that in-situ production was performed with one mold type. However, real in-situ production produces PC members of various sizes, so different results may be derived. In addition, this study assumed that the lead time was secured, production was performed in advance, and production management time was limited, so the yard stock area increased. However, if the number of molds is increased and production is performed just in time and the number of exclusive uses is not considered, the storage area will not occupy more than 5 times the production area. In other words, this issue is a matter of focusing on the work space or on the cost. Additionally, this study has limitations in that it was conducted on a small data set with only 300 repetitions and an early population size of 30. However, repeating the optimization with different population sizes and multiple runs may lead to different results from the results of this study.

7. Conclusions

In this study, the DBO algorithm and the IDBO algorithm were applied to develop an environmental impact minimization model for in-situ production of PC components. For this, after analyzing the existing in-situ production process of PC components, the problems of in-situ production were identified, and the objective function and constraints of in-situ production were presented to build the optimization model. And the DBO algorithm and IDBO algorithm were compared and analyzed. The following conclusions were derived from this study.

(1)

Considering the impact of characteristics of the large logistics center and internal layout on carbon emissions, a carbon dioxide emission factor was introduced. And the layout optimization model was formulated with the goal of maximizing adjacency correlation and minimizing carbon dioxide emissions. The DBO algorithm layout was found to show unnecessary paths and overlaps for efficient operation. On the other hand, the IDBO algorithm layout ensures more reasonable stock yards and crane movement paths and ensures efficient field operation. In other words, it was confirmed that the IDBO algorithm is more suitable than the DBO algorithm for the environmental impact optimization problem.

(2)

Based on the DBO algorithm, Chebyshev chaos mapping was introduced in the early stage to improve the initial population quality. The Gaussian-Cauchy hybrid strategy was introduced in the subsequent iterations to improve the exploration ability of the population algorithm. The IDBO algorithm was utilized to solve the layout issue of the distribution center. The results showed that the IDBO algorithm reduces carbon dioxide emissions by 18.33% compared to the DBO algorithm while increasing the adjacent correlation by 22.79%, making the layout of the distribution center more rational.

(3)

For the environmental impact optimization for the stock yard of in-situ produced PC components, the DBO algorithm slowed down the convergence speed during the simulation process, and the final solution was not close to the optimal solution. However, the IDBO algorithm performed well even when the number of complex constraints and the problem space of the stock yard optimization problem increased. It was analyzed that IDBO has the potential for faster convergence speed and higher quality solutions, which is especially advantageous in complex constraints and multi-objective optimization problems. Therefore, IDBO is more suitable than DBO in terms of practical applicability and optimization performance.

The IDBO algorithm of this study can be used to easily and quickly arrange stock yard space by applying frequently changing site conditions. In addition, it can be used academically to calculate the minimum environmental load of in-situ production and build an environmental risk management model based on this study. And the proposed IDBO algorithm can provide reference material for actual logistics center field operations or yard storage planning. The proposed environmental impact minimization model can support the construction, reconstruction, and functional upgrade of logistics centers, contributing to the low-carbon development of the logistics industry. The results of this study can be used as a basis for further research on stock yards, stock yard area, and supply chain management of various materials in limited construction sites. Furthermore, it is necessary to apply the results to various meta-heuristic algorithms and compare the results in the future.