Study on Piping Layout Optimization for Chiller-Plant Rooms Using an Improved A* Algorithm and Building Information Modeling: A Case Study of a Shopping Mall in Qingdao

Abstract

Heating, ventilation, and air-conditioning systems account for 40–60% of the energy consumed in commercial buildings, and much of this load originates from sub-optimal piping layouts in chiller-plant rooms. This study presents an automated routing framework that couples Building Information Modeling (BIM) with an enhanced A* search to produce collision-free, low-resistance pipelines while simultaneously guiding component selection. The algorithm embeds protective buffer zones around equipment, reserves maintenance corridors through an attention-based cost term, and prioritizes 135° elbows to cut local losses. Generated paths are exported as Industry Foundation Classes (IFC) objects for validation in a BIM digital twin, where hydraulic feedback drives iterative reselection of high-efficiency devices—including magnetic-bearing chillers, cartridge filters and tilted-disc valves—until global pressure drop and life-cycle cost are minimized. In a full-scale shopping-mall retrofit, the method significantly reduces pipeline resistance and operating costs, confirming its effectiveness and replicability for sustainable chiller-plant design.

1. Introduction

In urban development, rising living standards coupled with diminishing fossil fuel supplies compels researchers and engineers to focus on energy conservation in buildings. Heating, Ventilation, and Air-Conditioning (HVAC) systems, crucial for ensuring occupant comfort, represent one of the largest energy consumers in buildings. Statistics indicate that 40% to 60% of the energy demand in commercial buildings is allocated to air-conditioning systems [1], with refrigeration plant room energy consumption accounting for approximately 60% to 70% of the HVAC system’s total energy usage [2]. Furthermore, given that most individuals spend over 90% of their time indoors [3], optimizing HVAC systems will play a pivotal role in reducing energy consumption. By incorporating artificial intelligence algorithms to optimize pipeline routing, duct resistance can be effectively reduced, thereby aiding the refrigeration plant room design process, enhancing design efficiency, and simultaneously contributing to lower system energy consumption. This approach holds significant importance for advancing the development of high-efficiency refrigeration plant rooms and achieving building energy efficiency.

1.1. Literature Review

1.1.1. HVAC Piping Network Optimization

Current research on air-conditioning pipe network optimization predominantly focuses on terminal network optimization and hydraulic balance. Huang et al. [4] coupled an energy model, a heat-transfer model, and a genetic algorithm (GA) to optimize Internet Data Center (IDC) terminal parameters, boosting E-ACTE and cutting energy use by ≈20%, with novelty lying in the multi-physics/AI coupling; however, the study omits the plant-room backbone, limiting system-level applicability. Kim et al. [5] studied an Artificial Neural Network (ANN) for real-time Variable Air Volume (VAV) control, trimming energy by 16.7–19.5%, demonstrating ANN’s effectiveness in terminal dynamic control; nevertheless, the water-side hydraulics were ignored, leaving the chiller-plant piping resistance unaddressed. Yu et al. [6] introduced an ADMM-based iterative scheme attaining 28% extra savings via dynamic balance, offering an efficient method for hydraulic balance regulation; yet, the work focuses on control logic, not on the physical layout of pipes. Wang et al. [7] integrated a pipe network hydraulic calculation model with a GA-based pipe impedance calibration model, proposing an optimization method for dynamic hydraulic balance control. Kelvin et al. [8] achieved up to 51% pump savings via an ANN-GA and co-simulation, highlighting the potential of hybrid intelligent algorithms for pump control optimization; however, the hybrid method was restricted to pump control without touching pipe topology. In summary, most studies target terminals or control strategies, and system-wide 3-D plant-room routing capable of collision avoidance, low resistance (minimized path length and optimized elbows), and automation remains under-explored. CAD-based 2-D optimizations cannot avert collisions or high-loss elbows, leaving the core challenge of 3-D machine room piping layout unresolved.

1.1.2. Automatic Pipeline Routing Algorithm

Research on Automatic Pipeline Routing (APR) is not novel, with its conceptual idea having been explored for over 50 years. However, the highly nonlinear nature and innumerable possibilities of pipeline routing result in extreme computational complexity. Today, with exponential computational power growth and advanced algorithms/machine learning, realizing automatic pipeline routing has become feasible [9].

APR commonly employs algorithms categorized into deterministic, stochastic, and hybrid types. Deterministic algorithms include Dijkstra’s algorithm, the A* algorithm, and the Jump Point Search (JPS) algorithm. UIPM et al. [10] applied Dijkstra to courier routing, yet the algorithm fails on graphs with negative weights and oversimplifies geometry. Gunawan et al. [11] utilized it for finding the shortest path in ship engine compartments, validating its basic application in constrained space pathfinding; yet, Dijkstra’s algorithm fails on graphs with negative weights and oversimplifies geometry into dimensionless points, failing to meet practical requirements for pipe dimensions and obstacle avoidance. Liang et al. [12] created a rule-based BIM duct router, completing layouts in <5 min, which is a BIM-integration milestone, but it covers terminals only. Stochastic algorithms encompass Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), among others. For instance, Lu et al. [13] enhanced the ant-colony–dynamic-window algorithm (ACO–DWA), striking a better balance between obstacle avoidance and path convergence and thus improving adaptability in cluttered scenes; however, the added global-update procedure noticeably increases computational load, so runtime still exceeds that of classical Dijkstra and A* methods—a serious drawback for real-time piping design in plant rooms. Zhai et al. [14] combined an improved ant-colony algorithm with the dynamic-window approach to couple global and local planning, balancing search coverage and obstacle avoidance in cluttered environments; yet, validation was confined to 2-D evacuation layouts, leaving its suitability for narrow 3-D pipe spaces untested and limiting generalizability. Yu et al. [15] embedded simulated annealing into particle-swarm optimization (SA-PSO), boosting global optimality and escape from local minima in 3-D planning so that higher-quality UAV paths emerge quickly; nevertheless, repeated annealing cycles impose heavy iteration cost, impeding instant computation on large grids. In summary, hybrid algorithms leverage complementary heuristics to trade off convergence speed and solution quality [16]; however, they seldom integrate pipe-size constraints, local hydraulic losses, and practical constructability, leaving a notable research gap. Among many methods, A*—with its simple cost function and easily tuned heuristics—is widely regarded as one of the most efficient shortest-path searchers on static grids [17]; yet, without domain-specific penalties, it routinely overlooks pipe diameter and maintenance-space requirements.

The A* algorithm is popular for its simplicity and speed, but deeper scrutiny has exposed significant limitations. The classical A* treats entities as point particles, disregarding real pipe dimensions and thus risking clashes with equipment or other lines [18]. Moreover, path smoothness—vital for lowering frictional losses and energy use—is poor in traditional A*, whose routes contain frequent sharp turns [19]. Within complex 3-D plant-room piping, excessively tight bends exacerbate energy penalties, a pressing industrial concern. Consequently, embedding size constraints, turning penalties, and maintenance–access needs—without sacrificing search speed—remain at the heart of ongoing A* debates.

1.1.3. Retrofitting of Existing HVAC Systems

Studies show the Chinese existing building stock has reached 6.96 billion m², over 90% of which performs poorly energetically [20]. In Europe, more than 25% of buildings are over 70 years old [21], while in the United States, 60% of homes are over 30 years of age. Simultaneously, many buildings in developing nations operate at low sustainability levels, underscoring retrofitting urgency [22,23]. Retrofitting existing buildings is deemed pivotal for cutting global energy use and environmental impacts [24]; yet, scholarship still centers on envelopes and control strategies, paying scant attention to integrated optimization of high-resistance plant-room components and piping. In HVAC plant rooms, chillers, filters, and check valves are high-resistance bottlenecks to efficiency gains. Conventional design often ignores resistance variation under differing loads, leading to large pressure drops in service that upset hydraulic balance and degrade efficiency. Dai et al. [25] showed that certain chillers, though thermally efficient at rating, possess intricate heat-exchanger paths that raise water-side resistance, yielding mal-distributed flow and higher pump energy—a clear heat-transfer vs. hydraulic trade-off. Milenković et al. [26] reported that ignoring filter and check-valve resistance coefficients triggers sizeable node pressure drops and system chokepoints; however, they offered no concrete mitigation strategy, limiting practical value. Gobinath et al. [27], using an Australian office case, simulated life-cycle savings of 15–18% via smart controls, yet omitted detailed pipe-network local-loss modeling, reflecting limited focus on plant-room specifics. Scislo et al. [28] developed a cloud-connected distributed IoT sensor grid for continuous monitoring of contaminant migration in dual-heating households, enabling near-real-time alerts for hazardous accumulations and unauthorized access, but its dependency on dense sensor deployment and stable cloud infrastructure may constrain large-scale retrofits.

In summary, the absence of an integrated approach that couples pipe-route optimization with high-resistance component reselection remains a major gap in HVAC retrofit research, and serves as the motivation for this study.

1.2. The Main Aspects and Innovations

Building upon this foundation, this paper develops a holistic pipeline-optimization framework for refrigeration plant rooms that fuses an enhanced A* path-planning algorithm with BIM-based 3-D digital twins and life-cycle cost analysis. The classical A* search is augmented with (i) Protective Buffer Zones (PBZ) that guarantee collision-free clearances, (ii) an attention-weighted heuristic that steers the search through maintenance corridors, and (iii) a turn-penalty term that favors large-radius 135° elbows, lowering local resistance coefficients from ≈ 1.50 to ≈ 1.00. Path nodes are exported directly as IFC entities (Pipe-Segment/Pipe-Fitting) and verified for clashes inside Revit, completing a seamless “Python → IFC → BIM” workflow that eliminates manual model-translation errors. In parallel, high-resistance hardware—screw chillers, Y-strainers, and swing check valves—are systematically reselected as magnetic-bearing chillers, cylindrical strainers, and tilted-disc check valves, cutting individual component pressure drops by 40–75%. Tested in a full-scale shopping-mall retrofit, the combined strategy trims pipe length by 10.43 m, halves equivalent elbow count, and lowers total hydraulic resistance by 239.7 kPa (−47.7%), yielding a ten-year net saving of ¥1.91 million with a 4.25-year payback and 23.5% IRR.

The main contributions of this paper are summarized as follows:

• Path-planning algorithm enhancement: PBZ safety penalties, an attention-weighted heuristic, and a turn-penalty cost enable 98.6% safety-margin compliance on a 120 × 120 × 30 grid while remaining 68% faster than Dijkstra and two orders faster than PSO.
• 3-D modeling and visual clash verification: An automated IFC interface converts algorithmic paths into BIM objects, allowing instant collision checking and intuitive visualization inside Revit.
• Reselection of high-resistance components: Magnetic-bearing chillers, cylindrical strainers, and tilted-disc check valves replace legacy units, reducing local pressure losses by up to 50.8% and synergizing with the smoother pipeline.
• Engineering validation and economic appraisal: In the shopping-mall case, system resistance falls by 239.7 kPa (−47.7%), pump-energy use and maintenance costs drop by 47.7% and 75%, respectively, and a life-cycle cost analysis confirms strong financial viability.

2. Materials and Methods

Optimizing pipeline efficiency within plant rooms is primarily achieved by reducing frictional resistance and local resistance. Path planning to identify the optimal route effectively minimizes pipeline length, thereby reducing frictional resistance. Reselection optimization of high-resistance system components effectively minimizes local resistance. Ultimately, this achieves the goal of reducing energy consumption and operational costs within the plant room.

In the current pipeline design phase, traditional computer-aided design (CAD) methods are predominantly employed. However, CAD designs operate in two dimensions, providing insufficiently intuitive and clear visual representation for three-dimensional building spaces, which significantly increases the likelihood of collision issues [29]. With the gradual proliferation and application of Building Information Modeling (BIM) technology, three-dimensional modeling methodologies are increasingly being integrated into conventional design practices. Creating BIM-based 3-D models from two-dimensional CAD drawings enables the more intuitive identification of pipeline collisions, spatial conflicts, and other critical issues that are difficult to detect in 2-D plans [30].

Currently, the dominant Building Information Modeling (BIM) software in the market includes Autodesk 2025, Bentley 2025, and CATIA V5, among others [31]. Among these, Autodesk’s Revit 2025 is one of the most widely used BIM software applications. In pipeline system design, components such as chillers, filters, and check valves frequently account for the predominant portion of local resistance within plant rooms, approximately 45% to 65%. Optimizing the design and configuration of these high-resistance components is therefore crucial for reducing system resistance and enhancing efficiency. Consequently, the A* algorithm was selected to optimize the pipeline layout. Revit software was employed for the construction and visualization of the 3-D model, ensuring the accuracy and integrity of the design. Additionally, reselecting key components such as chillers, filters, and check valves further reduced the system’s local resistance. This thereby enhances the overall efficiency and reliability of the plant room’s pipeline system.

The framework of the optimization method proposed in this paper is illustrated in Figure 1. The research process comprises two coupled modules: algorithm enhancement and system component optimization. Within the path planning module, an enhanced A* algorithm based on multi-dimensional constraints is first developed: pipeline dimensions and an attention mechanism are integrated into the path planning process to ensure adequate maintenance clearance. The path evaluation function is optimized to effectively minimize path length, reduce the number of turns, and prioritize the selection of large-radius elbows. The optimized A* algorithm enhances the feasibility and smoothness of pipeline path planning, with algorithmic solutions transferring data unidirectionally via IFC file interfaces (Python→Revit). This open-loop configuration without feedback ensures analytical logic remains unaffected by visualization tools, where Autodesk Revit software is utilized exclusively for 3-D visualization rendering, thus enabling feasibility validation of path solutions. The resulting pipeline solutions undergo three-dimensional visual verification on the BIM platform, enabling precise detection of pipeline collision issues. This facilitates the feasibility validation of the path solutions. In the system component optimization module, the three categories of high-resistance components—chillers, filters, and check valves—are reselected to further reduce the local resistance within the plant room. This improves the overall operational efficiency and cost-effectiveness of the entire plant room.

2.1. Improved A* Algorithm

The A* algorithm is a classic heuristic search algorithm primarily designed to solve the shortest path-finding problem in static grids. Its evaluation function, denoted as $f\left(i\right)$, consists of two components: the actual distance function and the estimated distance function.

$$f\left(i\right)=g\left(i\right)+h\left(i\right)$$

(1)

where $g\left(i\right)$ is the actual distance function from the start node to the current node $i$; $h\left(i\right)$ is the estimated distance function from the current node $i$ to the goal node via the optimal path.

The A* algorithm is widely applied to path-planning problems in two-dimensional planes. However, when applied to the automatic pipeline routing problem within the three-dimensional environment of refrigeration machine rooms, the paths generated by the algorithm often fail to meet pipeline design requirements. The original A* algorithm primarily focuses on finding the shortest path, neglecting considerations of internal building structures or pipeline dimensions. Consequently, path searches often result in issues such as excessive proximity to obstacles and pipeline collisions. As illustrated in Figure 2, the original A* algorithm may plan paths by disregarding dimensional constraints. However, in reality, this proximity between pipelines and obstacles, or between pipelines themselves, leads to collisions. Therefore, when performing pipeline path planning within machine rooms, it is essential to simultaneously account for constraints imposed by both pipeline dimensions and the spatial limitations of the internal building structure.

Currently, optimization efforts for the original A* algorithm predominantly concentrate on enhancing its search efficiency. Consequently, this paper will not address improvements in search efficiency but will instead focus on incorporating the influence of architectural constraints and pipeline dimensions into the algorithm. One aspect primarily involves optimizing the layout concerning building components and pipeline dimensions through obstacle avoidance planning, while incorporating an attention mechanism to reserve necessary maintenance clearance. Simultaneously, the second aspect focuses on optimizing the design by reducing the number of turns in the pipeline path and prioritizing the use of large-radius elbows wherever possible. The following sections elaborate on these two aspects.

2.1.1. Path Planning with Buffer Protection

A 120 × 120 × 30 refrigeration plant room space was constructed and discretized into 1-unit cubic grids. Ten obstacles were placed within the space, with their positional coordinates specified in

Table 1. Obstacle Location Information.

Obstacle Number	Obstacle Coordinates	Equipment Name
1	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[22:40,10:44,0:20]$	Chiller 1
2	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[59:72,10:44,0:20]$	Chiller 2
3	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[86:95,10:38,0:20]$	Plate Type Heat Exchanger 1
4	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[109:117,10:38,0:20]$	Plate Type Heat Exchanger 2
5	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[27:36,87:103,0:20]$	Chilled Water Pumps 1
6	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[45:53,87:103,0:20]$	Chilled Water Pumps 2
7	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[81:88,90:103,0:20]$	Cooling Water Pumps 1
8	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[97:104,90:103,0:20]$	Cooling Water Pumps 2
9	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[$$10:46, 114:120, 0:20]$	Water Separator 1
10	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[$$65:101, 114:120, 0:20]$	Water Separator 2

. Path from $P_s\left(38,\mathrm{44,10}\right)-P_n\left(\mathrm{28,113,5}\right)$.

The original A* algorithm fails to account for dimensional constraints, resulting in planned paths being excessively close to obstacles. As illustrated in Figure 3, the results obtained after running the original A* algorithm are displayed. Here, the white areas represent navigable space, the gray areas denote obstacles, the yellow indicates the start point, the green marks the goal point, and the red path signifies the shortest path. The results indicate that the planned path is positioned too close to the obstacles. However, in a real-world scenario, such proximity could cause the pipeline to collide with obstacles. Therefore, it is essential to incorporate dimensional constraints during the planning process.

The actual distance function $g\left(i\right)$ within the evaluation function of the A* algorithm is a cumulative cost function. It typically considers only the Euclidean distance from the start node to the current node $i$ as the actual movement cost. To effectively incorporate constraints imposed by pipeline dimensions and safety requirements for obstacle avoidance into the path planning process, this paper proposes a method termed Protective Buffer Zones (PBZ), as depicted in Figure 4.

The entire layout space is divided into two distinct zones: the Buffer Zone and the Access Zone. Equipment and an extended surrounding area equivalent to 1.5 times the pipeline diameter are designated as the Buffer Zone. This provides the necessary safety clearance for pipelines, preventing collisions with obstacles. This method redefines the traversal cost evaluation system for nodes. Consequently, it optimizes the actual distance function.

$$g\left(i\right)=g_0\left(i\right)+\gamma ·max\left(0, 1-\delta \right)$$

(2)

where $g_0\left(i\right)$ is the actual path cost from the start node to node $i$ in the traditional A* algorithm (typically the path length); $\gamma$ is the safety cost weighting coefficient; $max\left(0, 1-\delta \right)$ is the safety penalty term, the magnitude of which directly reflects the “depth” of intrusion or the level of hazard posed by the node entering the Buffer Zone. The closer the node is to an obstacle, the larger this value becomes, thus imposing heavier penalties.

The value of $\gamma$ can be defined based on practical requirements, with its significance detailed in

Table 2. The significance of the value of γ.

The Value of γ	Meaning
Large	Extremely prioritizes avoiding the Buffer Zone, even if it requires a significantly longer detour to guarantee safety clearance. Paths will be longer but offer absolute safety.
Medium	Attempts to follow shorter paths. However, if a short path comes too close to obstacles (entering the Buffer Zone), the increased penalty makes it “appear” longer in the cost evaluation. Consequently, it is replaced by a safer alternative path.
Small	Paths resemble those generated by the original A* algorithm. This may result in paths passing close to obstacles (if that path is indeed the shortest). Safety guarantees are weaker.
Infinity	Equivalent to treating the Buffer Zone as an impassable area (hard constraint). The path cost for any path entering the Buffer Zone becomes infinite, effectively prohibiting it entirely.

.

$$max\left(\mathrm{0,1}-\delta \right)=\left\{\begin{array}{c}0, 0>1-\delta \\ 1-\delta , 1-\delta >0\end{array}\right.$$

(3)

where $\delta$ is the safety-margin ratio, representing how “safe” node $i$ is relative to obstacles. When $\delta \ge 1$, the distance from node *i* to the obstacle is greater than or equal to the required safety distance (1.5 times the pipeline diameter). This indicates a highly safe state, placing the node within the “Access Zone”. When $\delta <1$, the distance from node $i$ to the obstacle is less than the required safety distance. This signifies danger, indicating hazardous intrusion into the “Buffer Zone”!

$$\delta ={\displaystyle \frac{{min}_{o\in \Theta }d\left(i,o\right)}{1.5\times r_{pipe}}}$$

(4)

where ${min}_{o\in \Theta }d\left(i,o\right)$ is s the Euclidean distance from the position of node $i$ to its nearest obstacle; $\mathsf{\Theta }$ is the set of obstacles; $i$ is the coordinate of node $i$; $o$ is the coordinate of an obstacle; and $r_{pipe}$ is the pipeline radius.

Based on the aforementioned PBZ method, the path was recalculated for the same start and goal points as in Figure 3. The buffer zone parameter was set to 4.5 (pipe diameters). The resulting path is depicted in Figure 5.

The accessible area for the pipeline has been reduced. Grid cells within a distance of 4.5 pipe diameters around obstacles are no longer considered accessible nodes. Regardless of the specific pipeline routing, it maintains a greater distance from obstacles. Furthermore, it successfully reaches the goal point.

2.1.2. Introduction of Attention Mechanisms

Incorporating the PBZ into the A* algorithm improves the quality of path planning and effectively prevents pipeline collisions. However, the planned pipeline paths still fail to align with the practical operational requirements of machine rooms. This is because the paths generated by the A* algorithm prioritize minimal distance only, neglecting the requirement to reserve space for personnel access and maintenance activities, as illustrated in Figure 6. Therefore, it is necessary to introduce an attention mechanism into the pipeline path planning process.

The estimated distance function $h\left(i\right)$ within the evaluation function of the A* algorithm is a heuristic function. Heuristic functions typically consider only the Euclidean distance or Manhattan distance as the cost estimate from the current node $i$ to the goal node. To better adapt to the environment of refrigeration machine rooms, a heuristic function based on attention weights is introduced. This function adjusts the cost evaluation for each node, enabling the algorithm to prioritize paths traversing critical areas, thereby optimizing energy utilization and enhancing maintenance accessibility. Consequently, it optimizes the estimated distance function.

$$h\left(i\right)=h_0\left(i\right)·\left(1+\omega \left(i\right)\right)$$

(5)

where $h_0\left(i\right)$ is the Euclidean distance from node $i$ to the goal node in the traditional A* algorithm; $\omega \left(i\right)$ is the attention-weight function for node $i$.

$$\omega \left(i\right)={\displaystyle \frac{1}{1+e^{-k·\left[d\left(i\right)-{ d}_0\right]}}}$$

(6)

where $k$ is the sensitivity coefficient to spatial requirements, which is associated with the machine room space availability. Its value typically ranges from 3 to 5, assigned as 5 for compact machine rooms and 3 for spacious layouts; $d\left(i\right)$ is the Euclidean distance from node $i$ to the centerline of the nearest maintenance access; and $d\left(i\right)$ is the ideal maintenance space radius, related to the dimensions of the required maintenance clearance. It typically ranges from 0.6 to 1.2 m.

Based on the method outlined above, the path generated in Figure 6 was reinforced with the attention mechanism. The resulting path is presented in Figure 7.

As evident from the figure, the path prioritizes traversing critical areas, ensuring ample space for personnel access and maintenance activities.

2.1.3. Turn Optimization

Incorporating an attention mechanism into the A* algorithm, which considers protected buffer zones, reserves space for personnel movement and maintenance, thereby enhancing practicality. However, the actual cost function g(i) in the traditional A* algorithm solely considers path length (or cost), neglecting other physical properties of the path, such as turning. In practical applications, excessive turns increase local resistance and construction costs. This is illustrated in Figure 8.

This paper proposes minimizing the number of path bends and, where bends are necessary, employing large-angle elbows (135°) to reduce the resistance coefficient. This is achieved through an empirical formula for the resistance coefficient.

$$\xi =\left[1.31+1.63{\left({\displaystyle \frac{d}{r}}\right)}^{3.5}\right]{\left({\displaystyle \frac{\theta }{90}}\right)}^{0.5}$$

(7)

where $\xi$ is the local resistance coefficient of the elbow; $\theta$ is the bend angle; $d$ is the pipe diameter; and $r$ is the centerline radius of curvature.

Calculations show that the local resistance coefficient for a 90° elbow is approximately 1.50, while that for a large-angle (135°) elbow is approximately 1.00, as illustrated in Figure 9.

This study proposes an optimization of the actual cost function $g\left(i\right)$ within the evaluation function of the A* algorithm.

$$g\left(i\right)=g\left(parent\left(n\right)\right)+c\left({dir}_{current} ,{dir}_{new}\right)$$

(8)

where $g\left(parent\left(n\right)\right)$ is the cumulative cost from the start point to the parent node of the current node n and $c\left({dir}_{current},{ dir}_{new}\right)$ is the turning cost associated with direction change, and its value is calculated based on the angular difference.

$$c\left({dir}_{current},{ dir}_{new}\right)= \left\{\begin{array}{c}0 if straight\left(0^{\circ }\right)\hfill \\ 1 if {135}^{\circ } turn\hfill \\ 2 if {90}^{\circ } turn\hfill \\ 3 if other sharp turn\hfill \end{array}\right.$$

(9)

where ${dir}_{current}$ is the direction vector from the previous node to the current node and ${dir}_{new}$ is the direction vector from the current node to the next node.

$${dir}_{current}=\left(x_2-x_1, { y}_2-y_1,{ z}_2-z_1 \right)$$

(10)

where $\left(x_1,{ y}_1,{ z}_1\right)$ are the coordinates of the previous point and $\left(x_2,{ y}_2,{ z}_2\right)$ are the coordinates of the current point.

$${dir}_{new}=\left(x_3-x_2,{ y}_3-y_2,{ z}_3-z_2 \right)$$

(11)

where $\left(x_2,{ y}_2,{ z}_2\right)$ are the coordinates of the current point and $\left(x_3,{ y}_3,{ z}_3\right)$ are the coordinates of the next point.

Based on the aforementioned methods, the path between the same origin and destination points as in Figure 8 was recalculated. The resulting path is presented in Figure 10.

As shown in the figure, the original path has been replaced by a route with only four turns, significantly reducing the number of pipe bends. Moreover, all pipe bends employ large-angle (135°) turns, which effectively ensures a reduction in local resistance within the equipment room.

2.1.4. Development of an Automated Interface Between Path Planning and BIM

A significant disconnect exists between traditional path planning algorithms and Building Information Modeling (BIM) workflows: The path points generated by algorithms typically require manual conversion into 3-D models, a process that is not only inefficient but also prone to errors. To ensure the lossless transfer of path planning results to the BIM platform, this study developed an interface that directly outputs Industry Foundation Classes (IFC) files from an enhanced A-star algorithm. This technical solution establishes a unidirectional automated data flow from algorithmic results to standardized BIM models, effectively eliminating manual conversion errors and ensuring the independence of the analysis logic.

Let the path points output by the enhanced A-star algorithm be an ordered set $𝒫$

$$𝒫=\left\{P_1,P_2,\cdots ,P_{n-1},P_n\right\}$$

(12)

where, $P_i=\left(x_i,{ y}_i, { z}_i\right)$ denotes the 3-D spatial coordinates of a path point; $P_1$ denotes the start point of the path; $P_n$ denotes the end point of the path; and $P_2,\cdots ,P_{n-1}$ denotes an intermediate turning point.

Based on the path point set $𝒫$, we can construct the straight pipe-segment sequence $S_{pipe}$ for the entire pipeline path.

$$S_{pipe}=\left\{〈P_1,P_2〉,〈P_2,P_3〉,\cdots ,〈P_{n-2},P_{n-1}〉,〈P_{n-1},P_n〉\right\}$$

(13)

where $〈P_i,P_{i+1},〉$ represents the straight pipe segment connecting $P_i$ and $P_{i+1}$.

For each turning point $P_j\left(j=\mathrm{2,3},\cdots ,n-1\right)$ along the path, the required elbow angle ${\theta }_j$ is determined by the angle between the direction vectors of the adjacent pipe segments.

$${\theta }_j=arccos\left({\displaystyle \frac{\overrightarrow{P_{j-1}{P}_j}·\overrightarrow{P_j{P}_{j+1}}}{‖\overrightarrow{P_{j-1}{P}_j}‖·‖\overrightarrow{P_j{P}_{j+1}}‖}}\right), j=\mathrm{2,3},\cdots ,n-1$$

(14)

where $\overrightarrow{P_{j-1}{P}_j}$ denotes the direction vector of the pipe segment entering point $P_j$; $\overrightarrow{P_j{P}_{j+1}}$ denotes the direction vector of the pipe segment leaving point $P_j$; $‖\overrightarrow{P_{j-1}{P}_j}‖$ denotes the magnitude (length) of the direction vector of the pipe segment entering point $P_j;$ and $‖\overrightarrow{P_j{P}_{j+1}}‖$ denotes the magnitude (length) of the direction vector of the pipe segment leaving point $P_j$.

Based on the calculated elbow angles, construct the set $𝒥$ of elbow locations along the entire pipeline path.

$$𝒥=\left\{P_j\left|\left\{\begin{array}{c}{\theta }_j=90°\\ {\theta }_j=135°\end{array}\right.\right.\right\}, j=\mathrm{2,3},\cdots ,n-1$$

(15)

Convert the generated straight pipe segments into IFC-compliant geometric entities ${\Gamma }_{pipe}$.

$$\begin{array}{c}{\Gamma }_{pipe}=Cylinder\left(axis=\overrightarrow{P_i{P}_{i+1}},radius={\displaystyle \frac{D}{2}},Length=‖P_i-P_{i+1}‖\right), i\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =\mathrm{1,2},\dots ,n-1,n\hfill \end{array}$$

(16)

where $axis$ denotes the direction of the linear extension from turning point $P_i$ to turning point $P_{i+1}$; $radius$ denotes the design radius of the pipe; and $Length$ denotes the length of the pipe segment.

Convert the generated elbows into IFC-compliant geometric entities ${\Gamma }_{elbow}$

$${\Gamma }_{elbow}=\left\{\begin{array}{c}90° Standard Elbow, if {\theta }_j=90° \\ 135° Standard Elbow, if {\theta }_j=135°\end{array}\right.$$

(17)

where, if ${\theta }_j=90°$, a standard 90° elbow is selected; if ${\theta }_j=135°$, a standard 135° elbow is selected.

Finally, organize the generated pipeline entities into a BIM-compliant hierarchical topological structure, as detailed in

Table 3. Comparison of resistance of common chiller with cooling capacity of 1750 kw.

Level	IFC Entity Type	Purpose
Root Node	Project	Global container for the entire project.
Spatial Positioning	Site	Defines the project site/land parcel.
	Building	Defines the target building.
	Building-Storey	Defines the specific building storey (floor) where the components are located.
Component Entity	Pipe-Segment	Carries the geometric data of the straight pipe segments.
Connector	Pipe-Fitting	Carries the type parameters (e.g., angle) of the elbows.

and illustrated in Figure 11. This ensures that the model can be parsed and displayed correctly within BIM software. This structure has Project as its root node, establishes spatial positioning through Site, Building, and Building Storey, has Pipe-Segment carrying the geometric data of straight pipe segments, and has Pipe-Fitting carrying the type parameters of elbows.

Finally, integrate all pipeline components and output them as an IFC file using the IFC serialization operator $\psi$

$$F_{IFC}=\psi \left(\bigcup _{k=1}^{\left|S_{pipe}\right|}{Pipe-Segment}_k\cup \bigcup _{m=1}^{\left|𝒥\right|}{Pipe-Fitting}_m\right)$$

(18)

where $\psi$ denotes the IFC serialization operator, which converts the geometric and attribute data of the pipeline into IFC entities compliant with the standard (i.e., the IFC STEP file format).

Based on the aforementioned automated interface, the path planning results from the enhanced A-star algorithm are losslessly converted into an IFC-compliant model, as shown in Figure 12.

Visualization verification within the BIM platform demonstrates that the generated pipeline system fully replicates the spatial coordinates and topological relationships from the path planning and achieves zero-collision interference in the obstacle environment. This validates the effectiveness of the interface in terms of geometric fidelity and safety.

2.1.5. Computational Complexity Analysis

To address computational efficiency concerns, we provide theoretical complexity analysis and empirical benchmarks for the improved A* algorithm. The core framework retains the classical A* complexity of $O\left(b^d\right)$ where $b$ is the branching factor (26 for 3-D 26-connectivity grids) and $d$ is the solution depth. Our enhancements introduce three constant-time operations per node: PBZ Safety Check via precomputed obstacle distance field; attention weight, using spatial hashing for nearest maintenance passage; Turn Penalty, a direction vector comparison.

Empirical validation confirms this analysis, with

Table 4. Computational benchmarks (Intel i7-12700H, 32 GB RAM).

Grid Size	Classical A* (s)	Improved A* (s)	Overhead
50 × 50 × 30	0.41	0.48	+17%
100 × 100 × 30	1.92	2.28	+19%
150 × 150 × 30	4.37	5.32	+22%
200 × 200 × 30	8.76	10.71	+22%

showing only 15–25% runtime increase versus classical A* across grid scales.

Memory consumption is dominated by Grid Node Storage: $O\left(N\right)$ for $N$ grid cells, and Priority Queue: $O\left(bd\right)$ for open-list nodes.

For a 200 × 200 × 30 grid ($1.2\times {10}^6$ cells), peak memory usage was 412 MB (vs. 338 MB for classical A*), attributable to storing auxiliary data (e.g., δ, ω per node). This remains feasible for modern workstations.

2.1.6. Parametric Sensitivity Analysis

A controlled-variable experiment on Path $P_s\left(38, 44, 10\right)-P_n\left(28, 113, 5\right)$ evaluates parameter robustness.

To comprehensively evaluate the influence of parameters on algorithm performance, this study sets the PBZ weight $\gamma$ (Equation (2)) to 0.1, 0.5, 1, 5, and 10, thereby covering all strategies listed in Table 1. The attention sensitivity $k$ (Equation (6)) is assigned values of 2, 3, 4, 5, and 6 to accommodate both compact and spacious plant-room scenarios. For different design pipe diameters, $r_{pipe}$ (Equation (4)) is set to 1.125, 1.5, and 1.875, corresponding to DN150, DN200, and DN250, respectively.

To quantify the impact of parameter adjustments on system performance, this study conducts an evaluation from four perspectives.

Path length $L$ characterizes the dominant effect of distributed friction losses

$$L=\sum ‖P_i-P_{i+1}‖$$

(19)

where $P_i$ denotes path points (Equation (12)); $‖P_i-P_{i+1}‖$ denotes Euclidean distances between consecutive path points $P_i$ and $P_{i+1}$.

The equivalent number of elbows $N_{eq}$ quantifies local resistance

$$N_{eq}=\sum {\displaystyle \frac{{\xi }_j}{{\xi }_{90°}}}$$

(20)

where $\xi$ denotes resistance coefficient (Equation (7)).

The safety-margin compliance rate $\eta$ reflects the probability of collision risk

$$\eta ={\displaystyle \frac{count\left(\delta \ge 1\right)}{N_{nodes}}}$$

(21)

where count (condition) denotes the number of nodes satisfying the given condition; $\delta$ denotes safety-margin ratio (Equation (4)); $N_{nodes}$ denotes total nodes in discretized path.

The proportion of maintenance passages $\mu$ gauges maintainability assurance.

$$\mu ={\displaystyle \frac{count\left(\omega \left(i\right)<0.2\right)}{N_{nodes}}}$$

(22)

where $\omega \left(i\right)$ denotes attention weight (Equation (6)).

The results obtained by the above method are shown in

Table 5. Results.

Param	Value	L/m	${\mathit{N}}_{\mathit{e}\mathit{q}}$	$\mathit{\eta }$/%	$\mathit{\mu }$/%	Dominant Constraint Shift
$\gamma$	0.1	104.2	3.8	63.7	71.2	$\mathrm{Safety} \mathrm{failure} (\eta \downarrow )$
	0.5	107.5	3.5	82.1	73.5	Path close to obstacles
	1	112.3	3.2	98.6	72.8	Baseline
	5	118.7	3.0	100	70.1	$\mathrm{Path} \mathrm{redundancy} \uparrow$
	10	121.9	2.9	100	68.3	Over-conservative
$k$	2	110.1	3.4	97.8	61.3	$\mathrm{Inadequate} \mathrm{access} (\mu \downarrow )$
	3	111.2	3.3	98.1	68.7	Moderate maintenance
	4	112.3	3.2	98.6	72.8	Baseline
	5	115.8	3.1	98.9	79.4	Priority to access
	6	119.2	3.0	99.2	85.6	Path detour
$r_{pipe}$	1.125	108.7	3.6	99.1	74.2	Smaller buffer
	1.5	112.3	3.2	98.6	72.8	Baseline
	1.8	117.4	2.9	96.3	70.5	$\mathrm{Buffer} \mathrm{encroachment} (\eta \downarrow )$

as follows.

To conclude, adopting a medium-safety strategy with $\gamma =1$ effectively balances efficiency and safety, achieving $\eta >98\%$ while keeping the equivalent elbow count $N_{eq}$ to a minimum. Setting the attention sensitivity to $k=4$(moderate compactness) guarantees a maintenance passage ratio $\mu >70\%$, thereby satisfying maintainability requirements. However, when the design pipe diameter $r_{pipe}$ further increases, a fixed buffer coefficient causes a marked decline in the safety margin η, necessitating an adaptive buffer adjustment mechanism.

2.1.7. Algorithm Benchmarking

To address reviewer feedback and validate the superiority of the improved A* algorithm, comparative experiments were conducted against two classical path planning methods: Dijkstra’s algorithm and Particle Swarm Optimization (PSO). The identical experimental environment from Section 2.1.1 was adopted: a 120 × 120 × 30 discretized grid space with obstacles defined in Table 1, and the test path from $P_s\left(\mathrm{38,44,10}\right)-P_n\left(\mathrm{28,113,5}\right)$. Pipe radius was set to $r_{pipe} = 1.5$ units. Evaluation metrics included path length ($L$, Equation (19)); equivalent elbow count ($N_{eq}$, Equation (20)); safety-margin compliance rate ($\eta$, Equation (21)); and computation time ($T$, seconds).

Implementation details: For Dijkstra’s algorithm, 26-connectivity was used in 3-D space with no added constraints such as protective buffer zones (PBZ) or turn-penalty terms; for the PSO algorithm, 50 particles, and 100 iterations were set, and its fitness function minimized only total path length, omitting safety margins and turn optimization; The improved A* algorithm employed $\gamma = 1$ in Equation (2), $k = 4$ in Equation (6), and incorporated turn-penalty weights defined in Equation (9). The comparative results can be obtained as shown in

Table 6. Path planning performance under identical conditions (120 × 120 × 30 grid).

Algorithm	L/Units	${\mathit{N}}_{\mathit{e}\mathit{q}}$	$\mathit{\eta }$/%	$\mathit{T}$/s
Dijkstra	105.9	6.1	61.3	8.97
PSO	116.7	4.8	91.2	127.6
Improved A*	112.3	3.2	98.6	2.84

.

Dijkstra’s algorithm achieved the shortest path $(L=105.9 units)$, but exhibiting critical limitations. The absence of dimensional awareness resulted in 38.7% of nodes violating safety margins $(\eta =61.3\%)$, while unrestricted turns generated 6.1 equivalent elbows that significantly increase flow resistance.

PSO generated paths with erratic turns $(N_{eq}=4.8)$ and sub-optimal safety $(\eta =91.2\%)$. Its computational efficiency proved severely limited, requiring 127.6 s due to the inherent cost of iterative population evaluation.

$$T\propto N_{particles}\times N_{iterations}\times C_{constraint}$$

(23)

where $C_{constraint}$ represents collision detection (Equation (4)) and turn penalty (Equation (9)) calculations per path.

In contrast, the improved A* algorithm demonstrated balanced optimization. The PBZ mechanism (Section 2.1.1) ensured 98.6% safety compliance ($\eta$) by enforcing minimum clearance distances $(\delta \ge 1)$, while turn optimization (Section 2.1.3) reduced elbows to 3.2 equivalents through strategic 135° bend prioritization. Heuristic guidance via the attention mechanism (Equation (5)) enabled efficient node exploration, achieving computation times of 2.84 s—45 faster than PSO and 68% faster than Dijkstra—despite additional constraints.

2.2. Optimizing Local Resistance in Chiller-Plant Rooms

2.2.1. Optimization of Chiller-Plant Selection

Traditional projects commonly employ evaporative chillers and screw chillers, whose evaporators and condensers exhibit relatively high hydraulic resistance. In contrast, magnetic-bearing chillers utilize more advanced structural designs for their evaporators and condensers, resulting in smoother water-side flow paths and consequently lower resistance. Taking chillers with a cooling capacity of approximately 1750 kW as an example, for a conventional evaporative chiller, the evaporator resistance is about 90 kPa, and the condenser resistance is about 80 kPa. For a screw chiller, the evaporator resistance is about 80 kPa, and the condenser resistance is about 90 kPa. For a magnetic-bearing chiller, the evaporator resistance is about 50 kPa, and the condenser resistance is about 40 kPa.

Under identical cooling capacities, the evaporator resistance of the magnetic-bearing chiller is only 55% that of the evaporative chiller and 63% that of the screw chiller; its condenser resistance is only 50% that of the evaporative chiller and 44% that of the screw chiller. This effectively reduces the overall resistance of the water system, enhancing system operational efficiency and lowering energy consumption. A comparison of the resistance values is provided in

Table 7. Comparison of resistance of common chiller with cooling capacity of 1750 kw.

Equipment Name	Evaporator Pressure Drop/ kPa	Condenser Pressure Drop/ kPa
Evaporative chiller	90	80
Screw chiller	80	90
Magnetic levitation chiller	50	40

.

2.2.2. Optimization of Filter Selection

Traditional projects typically employ Y-strainers, which are characterized by a small filtration area and high resistance, with a typical resistance coefficient of around 6.5. However, for air-conditioning systems, particles smaller than 2 mm in diameter circulating within the system do not adversely affect the chiller, terminal units, or the overall system operation. Consequently, filters with larger pore sizes and greater filtration areas can be adopted to further reduce the resistance imposed by the filter. For instance, the hydraulic resistance coefficient of cartridge-type filters is typically no higher than five.

The optimized design exclusively selected cartridge-type filters. Under identical conditions, the resistance offered by the cartridge-type filter is approximately 76.9% of that of the Y-strainer, thereby reducing the resistance in the piping network. Physical photographs of both filter types are shown in Figure 13.

2.2.3. Optimization of Check Valve Selection

Conventional projects commonly utilize swing check valves that operate via a disc rotating on a hinged arm, exhibiting high-resistance coefficients (typically 1.3–2.5) and susceptibility to jamming from viscous media or impurities. In air-conditioning water systems, however, maintaining unidirectional flow stability takes higher priority than absolute sealing integrity, while the system features low impurity content and moderate flow velocities. This permits the adoption of streamlined check valves to reduce flow resistance.

The optimized design replaces these with tilted disc check valves, where the disc aligns parallel to the pipeline axis when fully open, resulting in flow path geometry closely resembling a straight pipe section, with hydraulic resistance coefficients reducible to 0.18–0.6. For instance, in DN200 pipelines, the head loss across tilted disc valves is only 13.8% to 24% of that across swing check valves, significantly reducing pumping energy consumption. Physical specimens of both valve types are shown in Figure 14.

2.2.4. Life-Cycle Cost Analysis Framework

Assuming the annual energy cost and annual maintenance cost remain constant throughout the analysis period, to holistically evaluate the economic impact of the equipment reselection, a 10-year Life-Cycle Cost Analysis (LCCA) model was established in accordance withthe standard:

$$LCC=C_{cap}-{\displaystyle \frac{S}{{\left(1+r\right)}^T}}+\left(C_{energy}+C_{maint}\right){\displaystyle \frac{1-{\left(1+r\right)}^{-T}}{r}}$$

(24)

where $C_{cap}$ denotes initial investment (equipment + installation); $C_{energy}$ denotes annual energy cost (pump operation); $C_{maint}$ denotes annual maintenance cost; $S$ denotes residual value (10% of $C_{cap}$ per the standard); $r$ denotes discount rate = 5% (China HVAC industry benchmark); and $T$ denotes analysis an period of 10 years.

$$C_{energy}=W\times H\times P_{elec}$$

(25)

where $W$ denotes pressure drop; $H$ denotes Annual operating hours; and $P_{elec}$ denotes electricity price.

$$W={\displaystyle \frac{P·Q}{3.6\times {10}^6·\eta }}$$

(26)

where $P$ denotes pressure drop; $Q$ denotes Pump flow rate; and $\eta$ denotes Pump efficiency.

3. Case Study

3.1. Project Background

To validate the effectiveness of the pipeline path planning method based on the improved A* algorithm, an experimental analysis was conducted using a shopping mall as a case study. The building has a floor area of approximately 44,000 m² and was completed and put into operation in 2001. The building comprises three stories above ground and three basement levels. The above-ground section primarily houses retail stores and a supermarket, while the basement levels are mainly allocated for parking and dining facilities. The mall’s original air-conditioning system employed two variable-frequency screw-type water chillers, each with a cooling capacity of 1737 kW. The system incorporated ten Y-strainers and six swing check valves.

The building’s mechanical room was selected as the experimental subject. The original BIM model of the mechanical room is shown in Figure 15.

While this project focuses on a shopping mall, the methodology’s parametric design and physics-based principles ensure applicability across diverse building types, as further discussed in Section 4.

3.2. Pipeline Path Planning

Modeling was performed using Python software 3.1.3 in a Windows environment. A 110 × 88 × 30 refrigeration plant room space was constructed in the Python environment and discretized into 1-unit cubic grids. Eight obstacles were placed within the space, with their positional coordinates specified in

Table 8. Obstacle location information.

Obstacle Number	Obstacle Coordinates	Equipment Name
1	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[10:33,16:53,0:20]$	Chiller 1
2	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[44:67,16:53,0:20]$	Chiller 2
3	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:92,6:13,0:10]$	Chilled water pumps 1
4	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:\mathrm{92,17}:24,0:10]$	Chilled water pumps 2
5	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:92,28:35,0:10]$	Chilled water pumps 3
6	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:\mathrm{92,39}:46,0:10]$	Cooling water pumps 1
7	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:\mathrm{92,50}:57,0:10]$	Cooling water pumps 2
8	$\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}[78:92,61:68,0:10]$	Cooling water pumps 3

. The spatial layout is illustrated in Figure 16 below.

Given a maximum pipe diameter of 3 units, the buffer zone was set to 4.5 units. Two distinct pipeline routes with different starting points were defined: Route I from $P_{s1}\left(\mathrm{27,52,6}\right)-P_{n1}\left(\mathrm{78,9},6\right)$, and Route II from $P_{s2}\left(\mathrm{27,52,6}\right)-P_{n2}\left(\mathrm{15,52,6}\right)$. Route I connects the chiller to the chilled water pump, while Route II links the cooling water pump to the chiller. These routes exhibit the longest pipeline lengths and highest elbow counts; thus, all other pipelines can be aligned with Routes I and II. The optimized A* algorithm was executed to compute the optimal paths from start to end points. The generated pipelines for Routes I and II are illustrated in Figure 17 below.

The final pipeline layout for the refrigeration plant room is illustrated in Figure 18. Based on this layout, a BIM model was developed for visualization. The resulting BIM model of the refrigeration plant room is shown in Figure 19. The model demonstrates alignment with standard refrigeration plant room designs, with no pipeline collisions occurring. Pipelines are arranged compactly and orderly, meeting all design specifications. The total pipeline length was reduced by 10.43 m. Fourteen 135° wide-angle elbows replaced right-angle elbows. Post-optimization pipeline resistance decreased by 16 kPa compared to the original design. This represents a 25.8% reduction in resistance.

3.3. Optimization of Refrigeration System Components

Following the methodology described in Section 2.2, high-resistance components in the existing system were optimized. Two variable-frequency screw-type water chillers (cooling capacity: 1737 kW) were replaced with two magnetic-bearing chillers (cooling capacity: 1759 kW). A comparative analysis of chiller optimization parameters is provided in

Table 9. Comparison of chiller performance parameters before and after optimization.

	Name	Number of Units/ Units	Cooling Capacity/ kW	Evaporator Pressure Drop/ kPa	Condenser Pressure Drop/ kPa
Original Program	Screw Chiller	2	1737	87.5	77
Optimized Program	Magnetic Levitation Chiller	2	1759	46	35

below. Ten Y-strainers were substituted with ten cylindrical strainers. Six swing check valves at pump outlets were replaced with six tilted disc check valves. Pipeline component resistance comparisons are shown in

Table 10. Comparison of resistance of piping components before and after optimization.

	Name	Number of Individuals/ Individual	Drag Coefficient	Resistance/ kPa
Original Program	Y-filter	10	6.5	9.39
Optimized Program	Cylindrical Filter	10	5	5.06
Original Program	Swing Check Valves	6	2	2.89
Optimized Program	Swashplate Check Valves	6	0.45	0.65

. Post-optimization pipeline resistance decreased by 223.74 kPa compared to the original design. This constitutes a 50.8% reduction in resistance.

3.4. Life-Cycle Cost Analysis of Equipment Replacement

The LCCA framework introduced in Section 2.2.4 is used here to quantify the economic effect of replacing the main pumping equipment and associated components. The calculation results are summarized in

Table 11. Life-Cycle Cost (LCC) comparison: conventional vs. optimized scheme.

Parameter	Conventional	Optimized	Delta
${\mathrm{C}}_{\mathrm{c}\mathrm{a}\mathrm{p}}/\mathrm{\yen }$	3,344,000	5,522,000	+2,178,000
${\mathrm{C}}_{\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}}/\mathrm{\yen }$	600,320	313,958	−286,362
${\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{t}}/\mathrm{\yen }$	300,800	75,000	−225,800
$\mathrm{S}/\mathrm{\yen }$	334,400	552,200	+217,800
$\mathrm{r}/\%$	5	5	0
$\mathrm{T}/\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}$	10	10	0
$\mathrm{L}\mathrm{C}\mathrm{C}/\mathrm{\yen }$	10,096,917	8,186,428	−1,910,489

and illustrated in Figure 20.

Although the optimized scheme requires an additional upfront investment of ¥2.178 million, a 47.7% reduction in energy costs and a 75% cut in maintenance expenses enable it to surpass the conventional option by the fifth year and ultimately generate a net saving of ¥1.91 million. Its 4.25-year payback period and 23.5% internal rate of return (IRR) confirm the scheme’s superior life-cycle economics.

3.5. Comparison of Piping Resistance in the Server Room Before and After Optimization

The optimized water system pipelines exhibit enhanced simplicity. Low-resistance components—including 135° elbows, oblique tees, magnetic-bearing chillers, T-shaped right-angle strainers, and tilted disc check valves—were substituted for traditional piping elements and equipment. This resulted in a substantial reduction in pipeline system resistance. Post-optimization pipeline resistance decreased by 239.7 kPa compared to the original design. This represents a 47.7% reduction. These findings demonstrate that the proposed optimization strategy significantly reduces hydraulic resistance in water systems.

4. Discussion and Conclusions

This paper proposes an efficient pipeline planning method for refrigeration plant rooms that integrates an optimized A* algorithm with BIM modeling. It aims to address the problems inherent in traditional path planning methods—such as irrational paths, elevated hydraulic resistance and sub-optimal life-cycle costs—which stem from overlooking critical factors like building dimensions, pipe sizes, and the layout of high-resistance components.

The advantages of this method lie not only in the accuracy and rationality of the path planning, but also in its systematic integration of building 3-D modeling, intelligent path generation, and equipment selection optimization. Field application reduced total pipeline resistance by 47.7% and, according to a 10-year LCCA, yielded a net saving of ¥1.91 million. This provides a practical, visualizable, and high-efficiency comprehensive optimization solution for the pipeline network systems in refrigeration plant rooms.

Unlike previous A* algorithm improvement studies that focused primarily on enhancing computational efficiency, this paper centers its research focus on the impact of building structure and the actual spatial constraints of equipment rooms on path feasibility, safety, and energy efficiency. Specifically, the optimized A* algorithm:

• Introduces Protective Buffer Zones (PBZ) to prevent collisions, a strategy applicable to any confined equipment room layout;
• Employs an attention mechanism to reserve maintenance space, addressing a universal need for operational accessibility;
• Prioritizes 135° large-angle elbows to minimize flow resistance, a hydraulic optimization principle transferable to all piping systems.

Furthermore, in equipment room systems, components such as chillers, filters, and check valves frequently contribute to excessive overall system pressure drops. The reselection strategy for low-resistance components (e.g., magnetic-bearing chillers, cartridge filters, swashplate check valves) is based on intrinsic fluid dynamics principles, making it independent of building typology. For instance, magnetic-bearing chillers reduce hydraulic resistance by 45% versus conventional units a physics-based improvement universally beneficial regardless of building function.

4.1. Method Generalizability and Limitations

While validated in a shopping-mall case study, the methodology’s core framework exhibits inherent generalizability:

• Algorithmic adaptability: PBZ safety margins ($\gamma$), attention weights ($k$, $d\left(i\right)$), and turn penalties are user-configurable parameters, enabling adaptation to spatial constraints in hospitals (strict clearance needs), data centers (high-density layouts), or retrofits (legacy space limitations);
• Component optimization universality: Resistance reduction via equipment reselection (Section 2.2) relies on standard hydraulic properties, not building-specific factors.

Although the proposed method demonstrates promising results in practical applications, several limitations warrant further improvement:

• Computational efficiency of the improved A* algorithm was validated for a 110 × 88 × 30 grid space with ten obstacles, but its performance in hyper-complex systems (e.g., multi-chiller plants with 50+ obstacles or irregular geometries) remains untested;
• Current research focuses primarily on path optimization for standard refrigeration systems, where computational efficiency for complex system path generation requires further enhancement;

While the cost function modifications were grounded in mechanical and hydraulic principles, direct empirical validation of its isolated impact remains a future task. Current validation relies on system-level outcomes (e.g., collision-free BIM models and aggregated resistance reduction). Future studies will incorporate sensor-based pressure measurements to decouple the algorithm’s contribution from component reselection effects.

4.2. Future Work

Future work will focus on the following aspects:

• Cross-building validation demonstrates its adaptability by implementing the method across diverse critical infrastructures: hospitals, data centers, retrofit projects, etc.;
• Significantly improving computational efficiency, particularly processing speed, for hyper-complex systems;
• To enhance credibility, we are committed to conducting field measurements by installing pressure sensors at pump inlets/outlets and critical nodes within the retrofitted mall system. This will enable a direct comparison of pump power consumption before and after optimization (scheduled completion: December 2025);
• Develop self-adaptive learning algorithms for parameters $\gamma , k, d₀$ to enhance generalizability.