Data sources and processing

The experimental data used in this study are derived from the publicly available BuildingNet dataset, which was curated and released by a research team at Stanford University to support deep learning tasks for building analysis. The BuildingNet dataset includes over 2,000 architectural models across various building types—residential, commercial, and mixed-use. It provides semantically labeled 3D mesh data and structural element partitions, making it suitable for component-level optimization modeling and task-driven analysis.

Each architectural model in the dataset includes geometric meshes of structural components, topological connection information, and semantic labels. All models are encoded in the standard OBJ (Object) format with a unified spatial reference system, supplemented by JSON (JavaScript Object Notation) structure description files. Semantic labels cover core building components such as walls, floors, beams, columns, doors, and windows, supporting end-to-end modeling from component recognition to assembly logic mapping.

During preprocessing, defective geometric data were first repaired, including issues such as inconsistent normal vectors, open boundaries, and floating-point errors in small components. The topological structure files were then parsed to extract the inter-component connections and dependency logic, forming the component-connection graph required for subsequent optimization modeling. To eliminate semantic ambiguity in component encoding across models, a unified label mapping was applied to all building models. Only seven key component categories essential for scheduling modeling were retained: floors, walls, beams, columns, stairs, roofs, and openings. Auxiliary or decorative components were excluded from the analysis.

BIM semantic modeling framework

To support the subsequent scheduling and optimization processes, the BIM semantic model was transformed into a computable graph structure that represents the logical relationships and assembly constraints between components. Each architectural instance from the BuildingNet dataset was formally modeled as a directed component graph G= (V, E), where V= {v₁, v₂, …, v_n} denotes all constructible components, and E ⊆ V × V represents directed assembly dependencies between components [28]. Each component node v_i was defined as a structural quintuple: ), where t_i ∈ T denotes the semantic type of the component (e.g., wall, beam, stair), indicates the component’s geometric dimensions, defines its spatial position within the model’s coordinate system, is the estimated mass, and f_i∈{0,1} is a binary flag indicating whether the component belongs to the critical path.

The dependency set E could either be derived from original topological annotations or automatically inferred based on geometric adjacency rules [29]. If , it indicates that component must be installed after in the construction sequence. To map the component graph to a scheduling optimization model, it was converted into a task scheduling graph , where each task node τ_i ∈ V_T corresponds one-to-one with a component node , defined as: , Here, represents the required resource vector, denotes the estimated construction duration, and is the direct construction cost.

The dependency relations are preserved during the conversion process, as shown in Equation (1).

(1)

This task scheduling graph serves as the input for the multi-objective optimization model. For each project instance, the scheduling result is expressed as a decision vector SSS, which includes the start times and resource allocations for all tasks, and is used to compute the multi-objective functions, as defined in Equation (2):

(2)

: Total project duration, : Total construction cost, and : Number of resource conflicts

The scheduling tasks in this study must satisfy the following three types of mathematical constraints:

1. 1. Task Dependency Constraint: If task has a predecessor task , then it must satisfy:

(3)

where is the duration of task .

1. 2. Resource Capacity Constraint: At any time point t, the usage of resource type must not exceed the total available resource :

(4)

1. 3. Scheduling Window Constraint: Each task has a specified earliest start time and latest finish time , which must satisfy:

(5)

All scheduling solutions must simultaneously satisfy the above three constraints to ensure the feasibility of the model results and their practical applicability in engineering.

Multi-Objective optimization framework design

To enable coordinated multi-objective scheduling during the construction process, a comprehensive optimization framework was designed that integrates schedule, cost, and resource conflict control. The optimization targets three critical performance indicators in prefabricated building projects:

• f₁(S): Total project duration
• f₂(S): Direct cost under resource allocation
• f₃(S): Total number of resource conflicts during construction

Let S= {s₁, s₂,..., s_n} denote the scheduling solution vector, containing the start time and assigned resource type for each task. The overall objective vector is defined as shown in Equation (6).

(6)

Given that the priorities of schedule, cost, and resources vary across different construction phases in real-world projects, a set of adjustable weight parameters λ=(λ₁,λ₂,λ₃) was introduced to construct a weighted aggregation function to guide the search process, as shown in Equation (7):

(7)

To preserve the diversity and decision space of the Pareto solution set, the final optimization outcome does not focus on minimizing a single aggregated objective F_agg, but instead constructs a Pareto front based on dominance principles.

The optimization process is based on an improved MOPSO algorithm. This method retains the standard advantages of particle-based search while incorporating an External Archive (EA) mechanism and non-dominated solution filtering logic [30]. Each particle’s position represents a specific scheduling solution SSS, with position updates defined by Equations (8) and (9):

(8)

(9)

: Current position (solution vector) of particle i. : Velocity of particle i. : Personal best position. : Global best solution selected from the EA. , , : Inertia and learning factors. , ∼U(0,1): Random perturbations.

To align with the task scheduling problem, particle encoding adopts a hybrid representation, including task sequence encoding and resource assignment encoding [31]. Each particle comprises an integer sequence representing task order and a corresponding resource type vector. The fitness function independently evaluates the three objectives. After each update, non-dominance checks are performed: if solution S₁ is no worse than S₂ in all objectives and better in at least one, it is considered a dominating solution.

An EA is introduced in MOPSO to store the current set of non-dominated solutions. After each iteration, new particle solutions are merged with the archive and filtered to retain only the Pareto-optimal set, as described in Equation (10).

(10)

The operator ND(⋅) denotes the non-dominated solution set extraction.

When the archive exceeds its predefined capacity threshold, a crowding distance-based pruning method is applied. This method prioritizes the retention of boundary solutions and solutions in sparse regions, thereby preserving the diversity of the solution distribution [32,33]. The final output represents the approximated Pareto-optimal solution set, from which decision-makers can select a scheduling plan based on practical trade-off requirements.

Reinforcement learning mechanism design

This study employed a DQN as a dynamic feedback mechanism within the MOPSO optimization process. The overall system architecture includes:

• Environment: A multi-objective optimization problem composed of construction scheduling tasks.
• Agent: The DQN model, which is responsible for selecting appropriate optimization strategies based on the current state.
• Action Space: Various resource allocation and task sequencing strategies in the scheduling process.
• State Space: The current status of the scheduling plan, including task progress, resource assignment, and execution status.
• Reward Mechanism: Real-time feedback based on the performance of each scheduling solution in terms of duration, cost, and resource conflicts.

In the context of multi-objective scheduling, the state space S is composed of the current resource allocations, task start times, and the progress of all tasks [34,35]. Formally, the state s_t ∈ S represents global information at the current scheduling time and can be represented as a vector in Equation (11):

(11)

S_t: Progress of each task (e.g., percentage of task completion);

R_t: Current status of resource allocation (e.g., resource availability at a given time);

P_t: Task dependency information (e.g., whether predecessor tasks have been completed).

The action space A consists of all possible scheduling decisions, including adjusting task start times, allocating resources, and modifying task dependencies [36]. For example, an action a_t may represent assigning a specific resource to a selected task or modifying the task’s start time.

The reward function design is a critical component in reinforcement learning, as it determines the optimization direction of the agent’s behavior [37,38]. In this study, the reward function was constructed based on the optimization effectiveness of the scheduling plan, as shown in Equation (12):

(12)

: Total project duration;

: Total construction cost;

: Number of resource conflicts.

α, β, and γ: Adjustment coefficients to balance the influence of schedule, cost, and conflicts. From the perspective of objective function consistency, the formulation of Equation (12) aligns with the three objectives in the optimization function F(S), all of which are designed to be minimized. Therefore, the negative weighted-sum form provides an effective gradient signal during policy updates.

Since the optimization goal is to minimize these values, the reward is defined as the negative of the scheduling metrics. During each iteration of the policy, the agent receives an immediate reward r_t based on the current state s_t and selected action a_t, and updates the Q-value function via the Q-learning algorithm, as shown in Equation (13):

(13)

α denotes the learning rate, and γ is the discount factor, representing the importance of future rewards.

The MOPSO-DQN collaborative mechanism integrates reinforcement learning into the particle swarm optimization process, allowing for adaptive adjustments to the swarm’s search direction. Initially, MOPSO explores the scheduling space using particle swarm search. Then, the DQN module evaluates the performance of the current solution and provides real-time feedback. Based on this feedback, particle search strategies are dynamically refined, guiding the swarm toward more efficient solution regions.

To further emphasize the uniqueness of this study, the proposed model must be distinguished from existing scheduling optimization approaches. Traditional hybrid MOPSO-based scheduling models typically depend on heuristic rules or static weighting, lacking real-time feedback on scheduling states and thus failing to update strategies effectively in complex dynamic environments. In contrast, this study integrated a DQN module from deep reinforcement learning to enable dynamically adaptive search guidance during the optimization process, improving both solution quality and convergence performance.

Compared with other common reinforcement learning methods, DQN demonstrated superior state-discrete mapping and sample efficiency. In construction scheduling, where decision-making tasks are finite and the state space is well-structured, DQN leveraged experience replay and a fixed target network to reduce policy oscillations and overfitting. Furthermore, its offline training capability made it particularly suitable for synchronous integration with particle swarm iterations, avoiding the instability associated with frequent policy switching.

The inclusion of DQN led to several notable performance improvements: Faster convergence: During multiple particle updates, DQN used historical feedback to guide particles toward high-value regions, accelerating the aggregation of optimal solutions. Enhanced exploration: Policy updates driven by the ε-greedy strategy and Q-value functions allowed DQN to balance exploration and exploitation, reducing the likelihood of becoming trapped in local optima. Improved robustness: In dynamic environments with complex task dependencies and resource constraints, DQN adaptively adjusted strategies to maintain stable scheduling solutions.

The proposed BIM-MOPSO-DQN model effectively integrated semantic modeling, evolutionary optimization, and intelligent feedback, distinguishing it from existing scheduling optimization strategies and making it particularly well-suited for dynamic multi-objective scheduling in complex assembly projects.

BIM-MOPSO-DQN integrated optimization process

To illustrate the integrated workflow of BIM semantic modeling, multi-objective optimization, and deep reinforcement learning developed in this study, a complete scheduling optimization mechanism was designed. The process comprises six steps:

1. Data input and component graph construction: BuildingNet models were loaded, and their geometric and topological relationships were parsed to build directed component and task graphs.
2. Initial population generation: Based on the task graph, scheduling schemes were created using random sequencing and resource allocation as the initial MOPSO particles.
3. MOPSO optimization iteration: During particle updates, the fitness of each solution with respect to the three objectives was calculated and stored in the external archive.
4. Reinforcement learning feedback: DQN learning was run in parallel to generate policy feedback for the current scheduling state, guiding subsequent particle behavior such as position adjustments and resource prioritization.
5. Solution set filtering and non-dominated update: Non-dominated solutions were retained, and pruning based on crowding distance was applied to preserve solution diversity.
6. Pareto solution output: The final external archive (EA) was produced as the recommended set of multi-objective scheduling solutions for decision-makers.

For an intuitive overview of the process, the corresponding pseudocode is presented below:

# Pseudocode: BIM-MOPSO-DQN Framework

Input: BIM task graph G_T, resource profile R, optimization weights λ

Initialize particle population P with random schedule encoding

Initialize External Archive EA ← ∅

Initialize Q-network parameters θ

for iteration = 1 to MaxIter do:

 for each particle i in P:

  Decode Si into schedule solution

  Evaluate objectives f1(Si), f2(Si), f3(Si)

  Update personal and global bests

  Store non-dominated Si into EA

 Update velocity and position of each particle:

  vi ← update_rule(vi, pi*, gi*)

  xi ← xi + vi

 Observe current state st from environment

 Select action at based on ε-greedy(Qθ(st, a))

 Execute action → obtain new solution S′

 Compute reward rt = -(λ1·f1 + λ2·f2 + λ3·f3)

 Update Q-network: θ ← θ - ∇L(Qθ)

 Update archive EA ← ND(EA ∪ {Si})

Return final non-dominated archive EA

This pseudocode combines the position–velocity update mechanism of MOPSO with the state feedback of DQN, creating an adaptive evolutionary optimization loop. This integration balances multi-objective trade-offs and policy learning, enabling more effective exploration of high-quality solution sets and accelerating convergence.

Experimental setup and weight configurations

To assess the performance and feasibility of the proposed optimization method, 100 standardized assembly tasks were selected from a diverse set of construction projects, including residential, commercial, and public buildings. These tasks varied in complexity and covered a broad range of real-world scenarios. Each task included multiple construction components and resource configurations to ensure the results were both reliable and generalizable. Task complexity was evaluated based on project scale, component variety, and resource demands. Component types consisted of key structural elements such as walls, floor slabs, beams, columns, and doors/windows. Resource requirements included equipment (e.g., cranes, hoisting machinery), labor (e.g., workforce size and working hours), and materials (e.g., concrete, rebar).

To analyze the effect of different optimization objectives, three distinct weight configurations were designed:

1. Profit-Priority: The optimization objective focuses on maximizing the economic benefit of the project. The weight configuration is λ=(0.3,0.6,0.1), with λ₂ = 0.6 emphasizing cost minimization.
2. Time-Priority: The optimization objective emphasizes minimizing the construction duration. The weight configuration is λ=(0.7,0.2,0.1), where λ₁ = 0.7 highlights schedule compression.
3. Resource-Priority: The optimization objective aims to reduce resource conflicts and improve resource utilization efficiency. The weight configuration is λ=(0.3,0.2,0.5), in which λ₃ = 0.5 focuses on resource conflict control.

Optimization performance analysis

The optimization was carried out under three distinct weight configurations: Profit-Priority, Time-Priority, and Resource-Priority. Each scenario emphasized a different project goal, leading to varied outcomes in terms of project duration, budget, and resource conflicts. Fig 1 displays the results for each configuration, highlighting differences in total construction time, estimated cost, and the frequency of resource conflicts. These findings illustrate the trade-offs between competing objectives and demonstrate the flexibility of the MOPSO-DQN framework in adapting to different project priorities.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Project duration, cost, and resource conflict counts under different weight configurations.

https://doi.org/10.1371/journal.pone.0333354.g001

As shown in Fig 1, the Profit-Priority scenario focuses on minimizing costs. As a result, the project duration is relatively long at 90.3 days, and resource conflicts occur slightly more frequently (2.1 times). However, the budget is effectively controlled at $1.456 million. In the Time-Priority scenario, the goal is to shorten the project duration. This leads to the shortest schedule—85.2 days—among all scenarios. Although the cost rises to $1.486 million, resource conflicts are minimized to just 1.7 occurrences, indicating more efficient resource coordination. In the Resource-Priority scenario, the emphasis is on reducing resource conflicts. The outcome is a balanced solution with a duration of 88.5 days, a cost of $1.462 million, and the lowest number of resource conflicts overall (1.3 times).

The optimization model generated multiple feasible scheduling solutions under different weight configurations. Table 2 presents a detailed comparison of three representative construction schedules.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Detailed analysis of representative construction schedules.

https://doi.org/10.1371/journal.pone.0333354.t002

A comparison of the generated schedules reveals clear differences across optimization objectives. These differences are not limited to trade-offs between time and cost, but also include variations in task sequencing and resource allocation strategies.

Performance comparison with baseline models

To further evaluate the proposed optimization approach, it was benchmarked against five baseline models: the Rule-Based Scheduling Model, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Static MOPSO (without reinforcement feedback), a Heuristic Scheduling Algorithm, and a Greedy Algorithm. Performance was assessed by comparing the mean and standard deviation of three key metrics—project duration, cost, and the number of resource conflicts. The comparative results are shown in Fig 2.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Comparison of project duration, cost, and resource conflicts across six models.

https://doi.org/10.1371/journal.pone.0333354.g002

As shown in Fig 2, the proposed method outperforms all five baseline models in terms of project duration, achieving the shortest schedule of 85.2 days. In contrast, the rule-based scheduling and greedy algorithms result in the longest durations, highlighting significant weaknesses in time optimization. Regarding budget cost, the proposed method (USD 1.486 million) performs similarly to NSGA-II and static MOPSO, but offers notable cost reductions compared to the rule-based, heuristic, and greedy algorithms. This demonstrates the method’s superior economic efficiency. In terms of resource conflict management, the proposed approach results in the fewest conflicts (1.7 occurrences), significantly outperforming the other models. Specifically, the rule-based and greedy algorithms experience higher conflict frequencies, suggesting that traditional methods struggle with effective resource coordination.

To further assess the solution quality, the Pareto fronts generated by each model were mapped and compared in Fig 3, revealing differences in solution diversity, convergence, and coverage of the objective space.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Comparison of Pareto front diversity (spread) and crowding metrics.

https://doi.org/10.1371/journal.pone.0333354.g003

As shown in Fig 3, the proposed method achieves the highest performance in terms of the hypervolume (HV) indicator, with a score of 0.683. This demonstrates superior coverage and diversity of the Pareto front. In comparison, other models, such as the greedy algorithm and rule-based scheduling, exhibit lower HV values, indicating a more concentrated and less diverse distribution of solutions. The proposed method also achieves the best spread (0.227) across the objective space, highlighting its ability to generate widely distributed solutions and maintain an effective balance among competing objectives. Furthermore, it records the lowest inverted generational distance (IGD = 0.017), signifying the best convergence toward the true Pareto front and a higher proportion of high-quality solutions. Additionally, the proposed method outperforms the baseline models in terms of uniformity and crowding.

To further verify the performance advantages of the proposed method, five key performance indicators were analyzed. These indicators included HV, spread, IGD, convergence rate, and diversity index. For both the proposed model and five comparative models, the mean and standard deviation of these metrics were calculated. The results are shown in Table 3.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Multi-algorithm performance comparison and statistical analysis.

https://doi.org/10.1371/journal.pone.0333354.t003

As shown in Table 3, the BIM-MOPSO-DQN method achieved the highest HV value (0.683), significantly outperforming all comparative models, indicating superior coverage of the objective space. Its spread value (0.227) was also lower than that of other models, reflecting a more uniform distribution of solutions across the Pareto front. A smaller IGD indicates closer proximity to the true Pareto front; the proposed method reached 0.017, demonstrating excellent convergence. In terms of convergence rate, the proposed model reached a stable solution set with fewer iterations, showing an average convergence improvement of approximately 18.5% compared to NSGA-II and static MOPSO. For diversity index, BIM-MOPSO-DQN maintained highly consistent solution spacing, enabling a more diverse set of high-quality scheduling solutions. Overall, the proposed method demonstrated superior solution quality, search efficiency, and distribution stability, confirming its multi-objective optimization capability in complex construction scheduling scenarios.

To validate the statistical significance of the proposed method’s performance, non-parametric tests were conducted to compare solution sets across models for the key performance indicators. Table 4 presents the results of the Wilcoxon rank-sum tests and Friedman analysis of variance.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Statistical test results.

https://doi.org/10.1371/journal.pone.0333354.t004

Based on Table 4, BIM-MOPSO-DQN showed statistically significant differences (p < 0.05) compared with three representative algorithms in HV, spread, and IGD. These results confirm its advantages in solution diversity, coverage, and proximity to the true Pareto front. Friedman tests on convergence rate and diversity index further revealed statistically significant differences among all models (p < 0.01), demonstrating improvements in global search capability and solution set balance. These findings statistically confirm the effectiveness and stability of BIM-MOPSO-DQN in multi-objective scheduling optimization.

Robustness and generalization analysis

To further analyze the impact of key model parameters on scheduling optimization results, three sets of sensitivity experiments were conducted. These experiments tested the effects of multi-objective weight coefficients (λ), DQN hyperparameters (learning rate α and discount factor γ), and task complexity (number of tasks n) on optimization performance. Each experiment maintained fixed initial conditions while varying the target parameter, recording the resulting duration, cost, resource conflicts, and other indicators. The results are summarized in Table 5.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 5. Parameter sensitivity experiment results.

https://doi.org/10.1371/journal.pone.0333354.t005

As shown in Table 5, variations in the objective weight λ directly influenced the optimization focus and outcomes. When λ₁ was higher (time-priority), the model achieved the shortest duration (85.2 days). When λ₂ was higher (profit-priority), the cost was minimized (1.456 million USD), but duration and resource conflicts slightly increased. DQN hyperparameters also significantly affected model performance. A higher learning rate (α = 0.10) accelerated early convergence but increased solution set volatility and resource conflicts (2.0 times). The balanced setting with α = 0.05 and γ = 0.90 achieved more stable performance (HV = 0.683, IGD = 0.017). Task number had a notable impact on performance. When the number of tasks increased to 140, duration and conflict counts rose substantially, indicating that higher complexity requires handling a larger search space. Nevertheless, solution set coverage and convergence remained acceptable (HV = 0.641).

A sensitivity analysis was conducted to assess the model’s robustness under varying initial conditions. The two primary adjustments included:

• Initial Resource Configuration: Varying the number of workers, equipment, and materials to simulate surplus or shortage conditions.
• Initial Task Sequence: Altering the task start order to evaluate the impact of dependency variations on final outcomes.

The optimization results under these differing initial conditions are presented in Fig 4.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Comparison of optimization results under different initial conditions.

https://doi.org/10.1371/journal.pone.0333354.g004

As shown in Fig 4, the variation in project duration across different initial resource configurations is minimal, ranging from 85.5 to 87.0 days. This demonstrates the model’s robustness in handling fluctuations in resource availability. Similarly, budget costs remain stable under varying initial conditions, highlighting the model’s ability to adaptively reallocate resources and maintain cost efficiency. While resource conflicts exhibit some variation, the total number consistently stays low, ranging from 1.7 to 2.0 occurrences. This further confirms the model’s resilience and effectiveness in managing resources.

To evaluate its generalization capability, the model was tested on a variety of large-scale construction projects, including residential, commercial, and public buildings. The performance results for these project types are presented in Fig 5:

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Optimization performance on large-scale construction samples.

https://doi.org/10.1371/journal.pone.0333354.g005

As shown in Fig 5, the model demonstrates minimal variation in project duration across different building types, highlighting its adaptability to construction projects of varying scale and complexity. While the budget increases slightly with project size—ranging from USD 1.53 million to 1.60 million—the overall cost control remains effective, indicating the model’s stability in large-scale construction projects. Public and commercial buildings, however, experience more frequent resource conflicts, reflecting the increased complexity and tighter resource constraints of these project types. This underscores the need for efficient scheduling and resource coordination in complex construction environments.

To validate the rationality of the designed reward function and the effectiveness of the dynamic feedback mechanism, a statistical analysis was conducted on the iteration behavior and convergence trends during the optimization process. Key indicators recorded throughout training included the objective values of the global best solution, average reward values, and the number of non-dominated solutions. These metrics were used to assess whether the DQN-guided search improved solution quality and convergence speed. Fig 6 illustrates the changes in average reward and HV of the Pareto front across iterations under a typical weight configuration (λ₁ = 0.7, λ₂ = 0.2, λ₃ = 0.1).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. Changes in reward and solution set performance over iterations (typical time-priority scenario).

https://doi.org/10.1371/journal.pone.0333354.g006

As shown in Fig 6, the average reward increased significantly over the iterations, rising from −178.3 to −123.4. This indicates that the DQN effectively identified resource allocation and task sequencing strategies that improved scheduling quality. At the same time, the optimal duration and resource conflict metrics steadily improved. The HV of the Pareto solution set grew consistently from 0.421 to 0.683, demonstrating enhanced global convergence and solution diversity. Empirically, the reward function successfully guided the learning process under multi-objective trade-offs. It steered particles toward high-quality scheduling regions and accelerated the evolution of the non-dominated solution set. These results confirm the strong positive impact of the reward design and policy iteration mechanism on search performance.

To further validate the model’s applicability and coordination ability in a real BIM scenario, a complex multi-component building sample from the BuildingNet dataset was used. This case involved 162 prefabricated components—including slabs, beams, columns, and openings—with multiple initial construction logic dependencies and spatial conflicts, representing high modeling complexity. Scheduling was performed using the proposed method alongside three comparative algorithms: NSGA-II, rule-driven scheduling, and static MOPSO. Key construction indicators were recorded, as shown in Table 6.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 6. Comparison of Construction Coordination Indicators in a Real BIM Case.

https://doi.org/10.1371/journal.pone.0333354.t006

As shown in Table 6, the proposed method excelled in controlling conflict detections, identifying only 1.5 spatial or resource conflicts. This was significantly fewer than the other methods, which detected 3.2 conflicts for NSGA-II and 5.7 for the rule-driven model. In terms of construction coordination rate—which reflects task dependency satisfaction and spatial/resource consistency—the proposed method achieved 92.4%, substantially higher than traditional approaches. Regarding task parallelism, the model supported a maximum of six concurrent tasks, outperforming the other methods. This demonstrates its ability to efficiently schedule parallel construction stages under resource constraints, thereby enhancing overall efficiency. These results show that the BIM-MOPSO-DQN method not only delivers superior objective values in simulations but also performs strongly on practical construction metrics, validating its coordination capabilities and applicability in real BIM projects.