Optimization of urban stormwater systems: a multi-criteria approach to sustainable and cost-effective LID implementation

Changes in the hydrological regime due to climate change and increasing extreme rainfalls as well as increased impervious areas due to rapid urbanization can lead to higher flood hazards across cities worldwide that cause a threat to both life and the built environment (Hettiarachchi et al. 2018; Zhou et al. 2019). Realizing that pipe-based drainage systems alone cannot meet these challenges, communities have started to look for other measures that can simultaneously manage stormwater and accomplish other sustainability objectives (Liu & Jensen 2018). While these measures are referred to by different names around the world – such as Sponge City in China, Sustainable Urban Drainage Systems in Britain, low-impact development (LID), and green infrastructure (GI) in North America, and nature-based solutions (NBS) in Europe (Roghani et al. 2024) – they all embody the same core concept of sustainable stormwater management.

By definition, these solutions are nature-inspired and nature-supported, offering cost-effective strategies that deliver environmental, social, and economic benefits while enhancing resilience (Senes et al. 2021). However, despite their advantages, LIDs cannot entirely supplant grey infrastructures owing to their restricted capacity during significant storm events (Xu et al. 2019). Instead, they should be integrated with grey infrastructures. Integrating green and grey infrastructures has been shown to enhance urban flood resilience effectively, particularly under changing climatic and urban conditions (Park et al. 2024). These coupled systems offer complementary benefits that address both hydrological and infrastructure challenges. The primary concern, though, is how to obtain the optimal green–grey infrastructures in terms of implementation cost and performance.

LID optimization planning has gained an abundance of momentum over the past decade, as an extensive number of pioneering studies have shown the benefits of using optimization techniques (Zhang & Jia 2023; Xie et al. 2024). Among them, some studies developed simulation–optimization frameworks that combine multi-objective optimization algorithms with hydrological models to aid in the decision-making process when implementing LIDs in combination with pipe systems. For instance, Saadatpour et al. (2020) developed the multi-objective, multi-circuit Electimize (MOMCE) optimization algorithm, combined with the stormwater management model (SWMM), and presented a comprehensive tool for restoring pre-development hydrological conditions while enhancing stormwater quality. Liu et al. (2019) paired a physically based model, the Markov chain, with the multi-objective shuffled frog leaping algorithm (MOSFLA) to determine the optimal design of LID practices.

In order to assess LID strategies, Eckart et al. (2018) developed a coupled model by connecting the Borg multi-objective evolutionary algorithm (Borg MOEA) to the SWMM. Macro et al. (2019) linked the SWMM with the Optimization Software Toolkit for Research Involving Computational Heuristics (OSTRICH) to create an open-source multi-objective SWMM optimization tool.

Nevertheless, previous studies have employed narrow objectives in evaluating the performance of integrated systems within their optimization frameworks. These objectives typically focus on metrics such as the number and volume of combined sewer overflows, runoff peak reduction, runoff volume reduction, and pollutant load reduction (Lee et al. 2012; Giacomoni & Joseph 2017; Eckart et al. 2018; Macro et al. 2019; Saadatpour et al. 2020; Gao et al. 2022; Tansar et al. 2022; Nazari et al. 2023). In addition to system performance indicators, other criteria should also be considered when deciding on enhancing the current drainage system with LIDs, as these systems offer multiple additional service functions, such as promoting biodiversity, improving aesthetics, and enhancing air quality (Sowińska-Świerkosz & García 2022). According to the International Union for Conservation of Nature (IUCN 2020), any intervention that qualifies as a LID should not only address environmental concerns but also safeguard biodiversity and prioritize human well-being. Therefore, the integration of LIDs must reflect both ecological and societal benefits.

Accordingly, the main contribution of this study is the introduction and integration of a comprehensive set of criteria including cost, sustainability index, and vegetated LID coverage for evaluating the performance of integrated stormwater systems with LID elements regarding stormwater quantity control and promoting other service functions of these sustainable measures within the multi-objective optimization framework. For this purpose, comprehensive modelling comprising SWMM, SUSTAIN, and MCDM models has been utilized. This approach aims to address various critical aspects and provide a more holistic basis for decision-making regarding the selection of LID measures. The following sections contain a detailed description of the proposed methodology and the results obtained.

Environmental Protection Agency's (EPA) SWMM is a dynamic rainfall-runoff simulation model designed for both single-event and long-term rainfall scenarios in urban watersheds, enabling the simulation of both the quantity and quality of runoff. It is extensively used for the planning, analysis, and design of urban stormwater systems. Recent advancements, such as those by Farina et al. (2023), have further demonstrated its effectiveness for simulating urban drainage systems, supporting its application in this study. The model can simulate runoff from sub-watersheds, pipe and channel flow rates, and stormwater runoff quality at specified time intervals. Additionally, the SWMM includes modules that allow for the simulation of LID methods.

The SUSTAIN model, developed by the U.S. EPA as an ArcGIS tool, is designed to analyse and manage urban stormwater flow and its contamination (U.S. EPA 2009). It is applicable at various scales, ranging from small local areas to larger watersheds, and can simulate both single-event and continuous rainfall scenarios (Lee et al. 2012). This tool consists of a set of algorithms that provide accurate technical and theoretical calculations, enabling effective cost and performance analyses for real-world operations (U.S. EPA 2009). Additionally, SUSTAIN includes an optimization module that can be used to optimize and compare different LID scenarios (Chen et al. 2014). It should be noted that SUSTAIN has been utilized successfully by previous studies to perform cost-effectiveness and optimization of LID scenarios (e.g. Hou & Yuan 2020; Nazari et al. 2023). This model has four main modules: land simulation, LID simulation, cost, and optimization.

The land simulation module in SUSTAIN utilizes the SWMM simulation algorithms to calculate the hydrograph, a process referred to as internal simulation. However, SUSTAIN also allows the importation of results from other models, known as external simulation, which is the approach used in this study to import SWMM results. The LID simulation module is a process-based simulator for stormwater and pollution transport, encompassing a wide range of LID solutions. It allows for the selection and combination of LID solutions, enabling the configuration and evaluation of systems based on physical characteristics such as size and soil parameters.

The SUSTAIN model offers two primary methods for simulating LID implementation: 1 – aggregate method (lumped approach) and 2 – individual representation method (distributed approach). In this research, the aggregate method has been implemented, which provides a simplified approach for modelling LID practices in stormwater management systems. Instead of representing each LID practice individually, the aggregate method combines multiple LIDs within a catchment into a single unit, streamlining the computational process. This approach minimizes complexity and is particularly advantageous for large-scale analyses where individual modelling of LIDs is impractical.

Additionally, SUSTAIN includes a dataset that tracks the cost of each LID element, which can be utilized within the cost module. This module estimates the total cost based on the fundamental construction components (FCCs) of each LID. The cost formulation used in this study is further elaborated in Section 2.4. The optimization module in SUSTAIN is designed to identify cost-effective strategies for both quantitative and qualitative stormwater control using LID methods. It employs evolutionary optimization techniques to determine the optimal combination of LIDs based on predefined decision-making criteria (U.S. EPA 2009). This study utilizes the NSGA-II optimization module within SUSTAIN, and the objective functions are runoff volume and cost reduction. The optimized solutions were imported into the SWMM to evaluate the performance criteria for urban stormwater management (i.e., reliability, resiliency, and vulnerability), accounting for both the existing conventional stormwater network and the proposed LID scenarios distributed across all smaller sub-catchments. This distribution was implemented using the SWMM through the aggregate method, utilizing the optimized results derived from SUSTAIN.

In high-density metropolitan locations, decision-makers generally have restricted options when choosing feasible LIDs because of spatial constraints. In this research, after investigating several scenarios and consulting with relevant experts in the municipality, four final scenarios were developed. These scenarios involve different combinations of LID methods, including green roofs (GR), rain barrels (RB), bio-retention cells (BC), porous pavements (PP), and vegetated swales (VS), as shown in Table 1. The rationale for selecting these LID measures stems from technical reports, indicating that 56% of the study area is covered by roofs, making runoff control from these surfaces critical (Zistab Consulting Engineers 2015). Consequently, GR and RB are appropriate alternatives for managing roof-generated runoff. The remaining 44%, comprising roads, sidewalks, and urban spaces, can benefit from BC and PP for runoff control. Additionally, VS offers a cost-effective complement for further reducing and managing stormwater runoff.

In the current study, scenarios were compared to each other using different indices, including the sustainability index, which consists of reliability, vulnerability, resilience indices, costs, and vegetated LID coverage. Below, these criteria are defined.

This index, which is an indicator for determining the risk level, has a value between 0 and 1, and the more it is, the lower the risk the system has. In this research, for the first time, this indicator has been used to evaluate the performance of LID implementation in conventional stormwater systems (pipeline systems). Its three components and their formula are given below.

While all LID strategies are beneficial for managing stormwater, vegetated LID options, such as GR, BS, and VS, provide additional ecosystem services beyond runoff control. These systems can improve air quality by capturing airborne pollutants, enhance biodiversity by offering habitats for a variety of species, and contribute to aesthetic value, which can have positive effects on mental well-being. Moreover, vegetated LIDs play a key role in urban cooling by mitigating the urban heat island effect through evapotranspiration, thereby improving local climate conditions.

Due to the lack of data to separately quantify each of these benefits in this study, all these aspects have been integrated into a single criterion, which is the percentage of the study area covered by vegetated LIDs. This approach allows us to capture the combined environmental and social benefits of these systems, such as improved air quality, enhanced biodiversity, urban cooling, and aesthetic value, without the complexity of addressing each benefit individually. By considering vegetated LID coverage as a single, integrated criterion, it becomes possible to evaluate the broader, holistic impact of these systems, providing a comprehensive metric for comparing the potential of different LID scenarios in contributing to urban sustainability.

The Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) technique is used to determine the best LID scenario. To calculate the relative importance of each criterion described in the previous section, criteria weights are first calculated using the AHP method (Saaty 1980) based on expert opinion extraction and the pairwise comparison matrix. To do so, a questionnaire was created and circulated among a group of experts with extensive experience in stormwater management, LIDs, and green–grey infrastructure. The experts were instructed to use a scale from 1 (equally important) to 9 (extremely important) to compare the two criteria and assess their relative importance. To ensure the robustness and objectivity of the process, the consistency ratio (CR) for the AHP was calculated, and the CR values were kept within acceptable limits, ensuring the reliability of the expert judgments.

Next, the SUSTAIN-derived data, which included the optimal LID measure sizes and numbers as well as the non-LID scenario (current state), were fed into the SWMM to assess the urban stormwater system's performance. The model was run under rainfall with a 10-year return period for each scenario. Based on the model outputs, the indices of resiliency, reliability, vulnerability, and sustainability were calculated to assess the stormwater system's performance both with and without the use of LID techniques. These values along with cost and vegetated LID coverage are presented in Table 3. As mentioned before, the weights in this study were calculated using the AHP technique based on the pairwise comparison matrices, ensuring a systematic and validated approach. To reduce subjectivity, a CR was computed, confirming the reliability of the weights. Additionally, the criteria in the decision matrix (Table 3) were derived objectively from simulation outputs, eliminating subjective bias in the decision-making process.

According to the table, Scenario S3 notably improved the system's performance over the baseline scenario without LID (S0). It enhanced the system's reliability by 18% and resiliency by 10% (relative values), while decreasing its vulnerability by 38%. In this regard, there is a possibility to increase the sustainability index up to 11.33% for S3, but this scenario is very costly due to GR used in large areas.

Regarding the vegetated LID coverage, Scenarios 3 and 1 outperform the others, demonstrating their potential to provide additional ecosystem services such as air quality improvement, biodiversity enhancement, and aesthetic value to the area. However, these two scenarios are extremely more expensive than S2 and S4. All in all, selecting the best scenario is not straightforward, given the range of factors to consider. Therefore, employing MCDM analysis can be highly beneficial in weighing the trade-offs between different objectives, helping to identify the most suitable option for this region.

As outlined in the method section, we prepared a questionnaire and distributed it to expert team members to determine the relative weights of each criterion. After analysing the responses using the AHP method, the weights for the sustainability index, cost, and vegetated LID coverage were found to be 0.258, 0.637, and 0.105, respectively, with a CR of 4.0%, which is a promising result. Using these weights and normalized values, scenario scores were calculated using WSM and WPM methods, as presented in Table 4. For sensitivity analysis of WASPAS results, three λ values (0.25, 0.5, and 0.75) were assumed. In all cases, S2 ranked highest, followed by S4, S3, and S1. Moreover, considering the cost associated with improving the sustainability index by 1% (as presented in Table 3), Scenario S2 outperforms the others, offering the most cost-effective solution. In contrast, scenarios with GRs (S1 and S3) are significantly more expensive, being approximately 19 and 16 times more costly, respectively, than S2. While scenarios such as S1 and S3 may offer potential long-term benefits, including improved social safety and disaster resilience, these benefits must be weighed carefully against their higher initial costs. This study underscores the importance of using a multi-criteria approach to balance these trade-offs, with cost remaining a central factor in the decision-making process.

Regarding the overall proposed methodology, it should be indicated that although the optimization process in SUSTAIN is hydrological, the inputs to SUSTAIN are derived from the SWMM, which incorporates the hydraulic properties of the stormwater network, such as conduit properties, imperviousness, and rainfall data. This ensures that the optimization in SUSTAIN reflects the hydraulic characteristics of the system. Furthermore, after the optimization, the output LID scenarios are imported back into the SWMM for performance evaluation, where hydraulic criteria such as reliability, resiliency, and vulnerability are assessed based on the network's hydraulic properties. This integration allows for a holistic evaluation, combining hydrological optimization with hydraulic performance metrics, bridging the two approaches and ensuring the relevance of the results.

Furthermore, this study included five LID types, GR, RB, BC, PP, and VS, evaluated through four predefined scenarios. While these scenarios reflect practical and implementable options for the dense and crowded study area, the exclusion of other possible scenarios limited the potential to explore more diverse combinations of LIDs. Expanding the analysis to include all possible combinations would have provided deeper insights into optimal trade-offs but would also have significantly increased computational demands, as the SUSTAIN engine with NSGA-II optimization requires extensive run times for large-scale scenarios.

It is also worth mentioning that a significant limitation of this study is the exclusion of water quality aspects from the multi-criteria analysis, despite its importance in evaluating LID benefits. Water quality enhancement plays a crucial role in protecting downstream ecosystems, supporting recreational uses, and reducing the public health risks associated with stormwater pollution. However, due to the absence of observed water quality data in the study area, incorporating a water quality index would have required a qualitative assessment. To maintain a quantitative focus and minimize uncertainty in the evaluation process, this aspect was excluded from the present analysis. This decision reflects the need to balance comprehensiveness and methodological rigour when reliable data are unavailable.

In this study, only cost and runoff reduction were directly optimized from a multi-objective perspective due to the limitations of the SUSTAIN engine, which supports the simultaneous optimization of only two objective functions using the NSGA-II algorithm. Expanding the analysis to optimize additional parameters, such as resilience, sustainability, reliability, vulnerability, and vegetated LID coverage, would have significantly increased computational time and complexity, which is a key consideration in urban stormwater management models. The focus on cost and runoff reduction was chosen to align with practical stormwater management goals, especially in dense urban environments, where these factors are crucial. The other parameters were evaluated based on the optimized solutions and incorporated into the MCDM framework to explore trade-offs, although not through simultaneous optimization. Future work could explore alternative optimization tools or frameworks capable of handling multiple objectives at once, which would allow for a more comprehensive analysis of trade-offs across all relevant criteria. Additionally, improvements in computational resources could facilitate the inclusion of more parameters for a more detailed evaluation of urban water system management strategies.

This study presents a comprehensive framework for optimizing urban stormwater systems through the integration of LID measures using a combination of simulation–optimization and MCDM modules. By introducing a sustainability index – derived from reliability, resiliency, and vulnerability indices – and a novel criterion of vegetated LID coverage, the framework offers a holistic approach that balances environmental, economic, and social considerations. Applied to the case study of Tehran's District 11, the framework demonstrated its capability to identify the most cost-effective LID solutions, with Scenario 2 (RB, BC, and VS) emerging as the optimal choice. This scenario, while not maximizing vegetated LID coverage, provides the best trade-off between cost and performance.

The results emphasize the importance of incorporating multiple criteria, such as sustainability and ecosystem benefits, into the decision-making process for stormwater management. This approach not only facilitates informed decision-making but also promotes sustainable urban development by providing a tool for integrating GI into urban stormwater systems.

Future research could enhance this approach by incorporating additional benefits of LIDs, such as water quality improvements, social benefits, biodiversity, and urban cooling, as highlighted in previous studies. Introducing a water quality index would enable a more comprehensive evaluation of LID benefits, particularly when calibration and validation data are available. This enhancement would facilitate more informed decision-making by accounting for the health and ecological cost-savings associated with improved stormwater quality.

Additionally, future studies could explore a broader range of LID scenarios, especially in areas with fewer spatial constraints and greater computational resources. Such an approach could uncover additional balanced solutions and strengthen the robustness of scenario-based decision-making for LID implementation.

The absence of real-world observations in this study limits the reliability of the simulation results, as model outputs rely on hypothetical scenarios. Future research should apply this methodology to urban stormwater systems with observed discharge and water quality data for calibration and validation. This would improve the accuracy of the model and provide stronger support for LID implementation decisions. Sensitivity analyses of key SWMM parameters, such as infiltration rates and roughness coefficients, are also recommended to ensure the robustness of the outputs.

Exploring well-known alternative MCDM methods, such as Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) or Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), is suggested to evaluate their suitability for LID scenario selection and establish a basis for comparative analysis. These efforts would further refine decision-making frameworks and contribute to a more holistic and robust assessment of LID implementation.

The authors sincerely extend their gratitude to Mr Amirhossein Nazari for his support in providing some of the necessary data and analysis for this research.

A.R. was responsible for conceptualization, supervision, validation, and writing the original draft. B.R. contributed by writing the original draft and conducting visualization and data analysis. V.N. handled validation and participated in writing, reviewing, and editing the manuscript. K.P. also conducted validation and contributed to writing, reviewing, and editing the manuscript. U.R. was involved in writing, reviewing, and editing the manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.