1 Research Background
Under the background of global climate change and rapid urbanization, the increasing frequency of extreme rainfall events and the expansion of impervious surfaces have become major drivers of urban flood risk
[1–
2]. To mitigate the negative impacts of conventional gray infrastructure, modern stormwater management has introduced a variety of new paradigms and technical measures
[3]. Among these, bio-retention facilities have emerged as common measures for intercepting, infiltrating, and attenuating runoff while reducing pollutant loads
[4–
5]. Bio-retention facilities generally refer to localized depressed areas composed of soil matrix and vegetation, designed to mimic natural hydrological processes in order to reduce surface runoff and delay peak flows. Their primary functions include stormwater storage, runoff regulation, and pollutant load reduction
[6–
8].
In the layout planning of bio-retention facilities, terrain factors play a critical role. The surface elevation directly determines the form and distribution of depression zones within sub-catchments, thereby influencing sink areas, retention volume, and runoff path
[9–
10]. In addition, since changes in surface elevation are associated with earthwork in practice, designers should balance hydrological benefits with the complexity of terrain modification. Previous studies mostly utilize digital terrain and related analytical tools to identify depressions, delineate catchment boundaries, and simulate runoff processes, thus providing a foundation for the layout planning of bio-retention facilities
[11–
13]. However, these approaches tend to focus on static planar identification and lack a systematic consideration of trade-offs among multiple hydrological benefits under complex terrain conditions. Thus, efficient and accurate quantitative planning methods and optimization tools are needed.
This study aims to propose a novel method for layout planning of bio-retention facilities based on the principle of multi-objective optimization. Building upon a preliminary analysis of surface runoff networks, it integrates digital elevation models (DEM) with the Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) to quantitatively assess the impacts of surface elevation modification on multiple layout objectives, thereby supporting rapid identification and optimization of facility layout planning. Using a catchment in Copenhagen, Denmark as the demonstration site, this research 1) investigates how to balance topographic features with hydrological benefits in the layout planning of bio-retention facilities; and 2) provides an operational framework for identifying potential stormwater retention spaces and informing blue–green infrastructure planning.
2 Research Review
2.1 Stormwater Management and Layout Planning of Bio-Retention Facilities
Traditional stormwater management began with the development of urban sewer systems in Europe in the mid-20th century, where curbs, drainage pipes, and other gray infrastructure were employed to achieve centralized pipe-based drainage in order to meet public health and wastewater discharge needs
[2]. Contemporary stormwater management emphasizes climate adaptation and urban resilience, developing concepts and practices such as Low Impact Development and Sustainable Drainage Systems by mimicking natural hydrological processes through diversified stormwater facilities
[3]. Nowadays, many countries and regions are actively promoting stormwater management measures. For instance, the Danish government has advanced climate-adaptive planning pathways for stormwater management and, under the guidance of the EU Water Framework Directive, established municipal stormwater discharge permits and local governance rules, which have driven the demand for layout planning of bio-retention facilities
[14–
16]. In addition, unofficial guidelines such as Sustainable Urban Drainage Systems and Nature-based Solutions provide practical instructions for localized construction practices, though site selection and layout planning of facilities require continuous exploration
[17–
18].
Bio-retention facilities include types of sunken green spaces, bio-retention cells, infiltration trenches, etc. During rainfall events, surface runoff flows along convergence lines toward low-lying area and accumulates in depressions before ultimately spilling over. Therefore, low-lying areas within the natural or built environments are supposed to be suitable sites for implementing bio-retention facilities. How to rationally matching facilities and sites thus becomes one of the essential issues when considering site selection and layout. Previous studies have focused on the type, size, and layout pattern of bio-retention facilities
[19–
20]: 1) the facility type focuses on the compatibility of structural layers and their configuration, such as matrix composition, layer thickness, and vegetation combination; 2) the facility size focuses on the relationship among geometric dimensions, retention capacity, and layout effectiveness; and 3) the layout pattern concentrates on the connectivity among facilities and upstream–downstream linkages
[21–
23]. Among these, facility size is the core factor determining retention capacity and is strongly dependent on the depth and area characteristics of depressions. Therefore, this study takes facility size as the entry point, focusing on the interactions between scale and surface elevation change, in order to support layout planning of facilities.
2.2 Layout Planning of Bio-Retention Facilities Based on Multi-Objective Optimization Algorithms
Multi-objective optimization has been used for addressing engineering problems that involve multiple conflicting objectives. Since different objectives usually cannot be optimized simultaneously, the results are typically expressed as a set of trade-off solutions, referred to as the Pareto Front Solution Set ("solution set" hereafter)
[24–
25]. The solution set demonstrates the trade-offs among multiple objectives, allowing decision-makers to comprehensively observe and compare results, thereby supporting decision-making. In recent years, multi-objective optimization has been widely applied in research on stormwater facility layout planning, and the combination of optimization algorithms with simulation models has become one of the mainstream approaches
[20]. For instance, studies have constructed various optimization frameworks for facility layout planning using multi-objective algorithms and solved problems of facility configuration under hydrological, ecological, and economic objectives such as runoff volume control, budget constraints, and runoff pollution reduction
[26–
28].
Multi-objective optimization algorithms mainly include simulated annealing, ant colony optimization, strength Pareto evolutionary algorithm, and genetic algorithms
[24,
29]. Among them, simulated annealing is effective at avoiding local extrema but has relatively lower computational efficiency; ant colony optimization is suitable for discrete search spaces; and the strength Pareto evolutionary algorithm can effectively maintain diversity in the solution set, but its computational complexity increases substantially in high-dimensional problems
[24–
25,
30–
31]. By contrast, genetic algorithms represented by NSGA-Ⅱ, owing to their non-dominated sorting strategy and crowding distance calculation mechanism, perform well in terms of convergence speed, diversity, and balance of solutions, and are therefore widely employed
[32–
36].
Multi-objective optimization algorithms are typically combined with hydrological simulation or facility layout tools. Models are primarily implemented through platforms such as SWMM, SWAT, SUSTAIN, and UrbanBEATS, or via secondary development built upon these platforms
[37–
44]. Such studies have revealed the quantitative relationships between bio-retention facility size and evaluation benefits. However, issues such as how facility scale is constrained by terrain conditions and how it matches with surface space remain insufficiently represented in existing models. Meanwhile, DEM-based hydrological analysis methods (e.g., runoff path analysis, depression identification) have already been widely applied
[13,
45–
47]. Using DEM as the analytical object and solving layout problems with multi-objective optimization algorithms provide a more intuitive and operational tool for practitioners in determining facility locations and scale during the planning stage. Nevertheless, few studies have attempted to carry out optimization modeling upon DEM-based hydrological analysis. In summary, this study proposes a DEM-based multi-objective optimization method for the layout planning of bio-retention facilities, in which DEM raster cells are treated as optimization variables for multi-objective operations, thereby providing generative terrain schemes and determining facility size and layout strategies.
3 DEM-Based Multi-Objective Optimization Method for the Layout Planning of Bio-Retention Facilities
3.1 Establishment of the Multi-Objective Optimization Framework
The DEM-based multi-objective optimization for bio-retention facility layout is established by decomposing, abstracting, and refining terrain features and layout problems into optimization variables, objectives, and constraints in a mathematically logic (Fig. 1). First, in the initialization stage, DEMs are encoded to define optimization variables, objectives, and constraints according to the specific problem. Second, in the optimization stage, the solving process is carried out to test the stability under different scenarios. Finally, in the result stage, the solution set is decoded into corresponding schemes, which are presented in visual forms to assist the final decision-making.
3.2 Defining Optimization Variables, Objectives, and Constraints
Optimization variables broadly refer to the adjustable parameters that define the search scope of the problem, i.e., all possible solutions. In this study, the elevation values of DEM raster cells are treated as optimization variables, and data recognition and conversion between DEM and the optimization procedure are achieved through stepwise encoding and decoding.
Optimization objectives refer to the outcome indicators that are improved by changing the optimization variables. There is a linkage between the modified surface elevation and the objectives of bio-retention facility layout (Fig. 2). Layout objectives usually include retention volume, sink area, pollutant reduction, earthwork volume, and facility cost
[5,
10].
Optimization constraints refer to restrictions imposed on the range of values for optimization variables or objectives. For example, constraints can be applied to the locations of DEM raster cells that are allowed to vary, or to the thresholds of permissible elevation changes—both of which limit the spatial extent and depth of terrain modification. It can be anticipated that looser constraints yield higher upper limits for optimization results. Therefore, to produce more practical and targeted optimization results, constraints should be set based on specific factors such as existing sink areas, land-use types, or cut-and-fill limitations of the terrain.
3.3 Data Preprocessing
The DEM provides essential spatial and hydrological information of the given site and forms the data basis for the optimization procedure. Data preprocessing mainly focuses on the basic attributes and characteristics of the DEM, including resolution, catchment delineation, runoff path, overflow volume, and the initial values of layout objectives. It is worth noting that, since the DEM generalizes terrain into a matrix of raster cells, the total number of raster cells directly affects optimization efficiency. Too low a resolution will lose terrain details and reduce result reliability, whereas too high a resolution will produce excessive raster counts and lower computational efficiency. Therefore, the input DEM resolution should be reasonably determined based on site scale and the precision requirements of optimization.
4 Demonstration Site and Results
To verify the DEM-based multi-objective optimization for bio-retention facility layout planning proposed in this study, an area in Copenhagen, Denmark, was selected as the demonstration site.
4.1 Demonstration Site
The demonstration site covers approximately 89 hm2. The overall terrain slopes gently from west to east, with elevations ranging from 24.04 m to 38.19 m (Fig. 3). The reasons for selecting this site include 1) the area lies in an independent upstream catchment within the local watershed, which largely eliminates external inflow during rainfall events; 2) the underlying surface is predominantly farmland and grassland, with only a few buildings and roads, allowing it to be approximated as green space composed of natural pervious soils and minimizing interference from initial soil saturation, hydraulic conductivity, and land-cover heterogeneity; and 3) the area already contains local depressions, providing favorable conditions for facility layout. The DEM of the study area was obtained from the open database of the Danish Agency for Data Supply and Infrastructure, with an original resolution of 0.4 m. Considering the spatial scale of the study, computational efficiency, and the effect of different resolutions on hydrological convergence analysis, the DEM was resampled to 5 m resolution after multiple pre-tests to balance model complexity and result accuracy. After resampling, a total of 33, 930 raster cells were obtained; the initial retention volume was 26, 270 m3 and the depression area was 97, 400 m2.
Local government encourages the use of regenerative agriculture and grassland restoration to enhance the retention and detention capacities of agricultural and public green spaces. Accordingly, the optimization objectives were set as follows: 1) maximum retention volume, to increase stormwater storage capacity during extreme rainfall events and reduce flood risk downstream; 2) maximum sink area, to improve spatial capacity for capturing and retaining runoff; and 3) minimum total earthwork, to reduce construction costs and environmental disturbance.
In this case study, the Malstroem bluespot tool was employed to conduct a preliminary runoff network analysis of the demonstration site (Fig. 4). Based on DEM data, this tool identifies surface depressions, pour points, and runoff paths, and simulates spillover processes, thereby quantifying spillover volumes and runoff connectivity between depressions
[48]. Preprocessed results indicate that runoff in the study area primarily converges from west to east, successively accumulating in multiple depressions, spilling over, and eventually discharging toward the downstream eastern region. Considering that green spaces and water bodies are easier to modify and already possess relatively higher retention potential, these land-cover types were overlaid with depression areas, and a 20 m buffer zone was applied to obtain the optimization area
①, comprising a total of 4, 386 raster cells. Finally, four scenarios were defined according to different ranges of terrain elevation modification as constraints: 1) Scenario 1: elevation variation ranging from 0 to 0.5 m; 2) Scenario 2: elevation variation ranging from 0 to 1.0 m; 3) Scenario 3: elevation variation ranging from 0 to 1.5 m; and 4) Scenario 4: elevation variation ranging from 0 to 2.0 m. Each scenario was run 10 times to test program stability and average computation time. The specific program settings are provided in Table 1
[30–
31,
49].
① Adding the 20 m (four-cell) buffer was accounted for the reasonable expansion and adjustment during terrain modification. This value may be adjusted according to the specific conditions of the given site.
4.2 Solution Sets and Visualization Analysis
According to the four scenarios, four groups of solution sets were obtained, all of which exhibited convergence (Table 2, Fig. 5). The average computation time across the four scenarios was around 20 min, with constraints having little effect on calculation speed, indicating overall high computational efficiency. The results show that 1) under different scenarios, the optimization results consistently produced solution sets, proving the feasibility and stability of the proposed framework; 2) as the elevation modification threshold increased, the distribution ranges of the three optimization objectives expanded, with maximum retention volume and maximum sink area corresponding to larger earthwork volume and showing a simultaneous growth; and 3) under conditions of similar maximum sink area, higher-threshold scenarios could achieve greater retention volume at the cost of larger earthwork, and vice versa for similar maximum retention volume. Decision-makers are able to thus select suitable solution sets according to specific engineering requirements.
Each of the four solution sets contained 100 solutions, and any solution could be decoded to generate corresponding DEMs. It is impossible to present all solutions individually in this study; instead, Fig. 6 shows the mean DEM results of the solution sets under the four scenarios—average retention depth map and sink probability map. The former was obtained by averaging the retention depths across all DEM raster cells, while the latter was calculated by overlaying all sink area maps of DEM solutions and counting the frequency at which each raster was identified as a sink.
Spatial distribution patterns indicate that, in all four scenarios, continuous depression areas formed along the north–south drainage route on the western side of the site and in the northeast. This suggests that these locations have a higher probability of being selected for implementing bio-retention facilities. As the constraint threshold increased, these high-probability areas generally expand and connect on the basis of the existing depressions, exhibiting a more "aggressive" areal pattern. However, in Scenario 4, the depressions around certain locations in the northeastern part shrunk. This is because the enlarged threshold broadened the feasible solution space and altered the objective trade-offs. The nonlinear response of the local terrain structure consequently led to a decline in local connectivity. Changes in retention depth were reflected mainly in two aspects: 1) as constraints increased, average retention depth of depressions rose from 1.2 m to about 2 m, while local peaks increased from 2 m to 3 m, indicating larger scales of terrain excavation; and 2) high-depth areas strongly overlapped with high-probability sink areas, whereas low-depth areas were markedly reduced in Scenarios 3 and 4, reflecting that the additional earthwork operations were concentrated in existing sink areas rather than randomly dispersed.
The visualization of optimization results provides quantitative spatial references for hierarchical strategies for bio-retention facility layout planning. Specific strategies include 1) if terrain modification is limited, Scenarios 1 and 2 may be preferred, as depressions are more concentrated and depths moderate, making them suitable for embedding bio-retention facilities in a "point–strip" pattern with minimal disturbance to existing land-cover texture; and 2) if the goal is to substantially increase retention capacity and expand sink areas, Scenarios 3 and 4 offer larger and more spatially continuous potential depressions, allowing for an "areal" systematic layout of bio-retention facility networks. Overall, high-probability areas may be defined as priority terrain modification units, while medium- and low-probability areas can be regarded as alternatives.
It should be noted that in all four scenarios, some solutions produced maximum retention volume or maximum depression area values lower than the existing baseline. Theoretically, these solutions are mathematically valid within the optimization process; but in this study, such solutions do not provide practical improvement and can be regarded as invalid solutions.
Finally, the solution with the largest retention volume was selected for an example of decoding and visualization (Figs. 7, 8). In this solution, the three objective values were maximum retention volume of 122, 153 m3, maximum sink area of 154, 125 m2, and minimum total earthwork volume of 134, 027 m3. Compared with the baseline, new depressions were mainly located within existing green spaces and open areas, with local depths reaching up to 3 m. Retention volume was significantly improved, and spillover analysis revealed that overflow at 5 typical pour points decreased by 63% ~ 100% (Fig. 9). This solution represents a high-cost extreme case under benefit-prioritized conditions, illustrating the upper limit of retention potential and the spatial configuration characteristics in an extreme scenario.
5 Discussion and Conclusions
This study proposed a DEM-based multi-objective optimization method for the layout planning of bio-retention facilities, achieving optimization objectives of maximum retention volume, maximum sink area, and minimum total earthwork. The method demonstrates rapid operability, flexible scalability, and application potential. It is applicable to nature-based terrain modification practices and has shown feasibility and stability in framework construction and solution set generation. However, due to the high uncertainty of terrain variables, further validation under different conditions is required to refine parameter settings and evaluate application effects. The limitations of this study include 1) constrained by computing hardware, the upper limits for the scale of optimization variables and objectives that can be processed are not yet fully clear; 2) facility parameters such as initial saturation, hydraulic conductivity, and vegetation type were not incorporated into this study; 3) the terrain-modification-based approach to enhancing retention volume and area is limited in applicability to sites with complex hydrological connectivity; and 4) the demonstration site selected in this paper contains relatively abundant green and open spaces, which differ substantially from high-density built environments, making it inappropriate to directly apply the optimization parameters and technical pathways presented herein.
To advance research and practice in the layout planning of bio-retention facilities, this study proposes the following recommendations.
1) Explore computational efficiency limits and effective constraint conditions. The number of optimization variables determines the dimensionality of the algorithm's population, thereby affecting resource consumption in encoding/decoding, objective function calculation, and memory allocation. During testing, it was observed that increasing DEM resolution or the number of variables led to a significant decline in computational efficiency. Therefore, for high-resolution DEMs or larger-scale applications, users should improve computational efficiency by enhancing computing resources or splitting data objects.
2) Adopt more diverse optimization objectives. The number of optimization variables and objectives in this study still has room for improvement. The approximately linear distribution of solutions suggests that some objective functions may be strongly correlated or coupled in optimization trends. Future research should consider incorporating objectives with stronger independence or broader representativeness to enhance the diversity of solutions and the scientific validity of optimization dimensions. Moreover, recent advances in many-objective optimization algorithms make it increasingly feasible to simultaneously address a larger number of objectives while further improving computational efficiency
[50].
3) Expand the scale and hierarchy of research objects. By generalizing the depression characteristics of lakes, ponds, and constructed wetlands as large-scale blue–green infrastructure, this optimization framework has the potential to be extended to the city or watershed scale. Designing urban runoff conveyance through DEMs and strategically embedding retention spaces can enhance spatial retention capacity and improve the city's overall resilience to extreme rainfall events.
4) Consider multiple impacts of terrain optimization. Large-scale terrain modifications may lead to localized surface damage, soil structure disturbance, and rainfall-induced erosion, thereby affecting vegetation cover and ecological stability. Future studies could incorporate surface stability models, water pollution diffusion models, and vegetation restoration strategies to conduct integrated optimization under multi-dimensional constraints, ensuring the site's ecological sustainability.
Admittedly, interpretable multi-objective optimization methods provide a foundation of instrumental rationality② for the layout planning practice of bio-retention facilities. However, beyond engineering and technical considerations, urban stormwater management also involves multiple social and cultural factors. Future research should deepen the understanding of the "chaotic" nature and "pain points" in planning and design, thereby offering valuable guidance for practical decision-making.
② "Instrumental rationality" is a concept proposed by sociologist Max Weber, also known as "efficiency rationality" or "purposive rationality." It refers to the use of precise calculations to select the most effective means for achieving predetermined goals, focusing on minimizing costs, maximizing benefits, and realizing utilitarian purposes in the most optimal way. In contrast, "value rationality" emphasizes choices guided by values or beliefs rather than utility (source: Ref. [
51]).
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