Integrating Grey–Green Infrastructure in Urban Stormwater Management: A Multi–Objective Optimization Framework for Enhanced Resilience and Cost Efficiency

Abstract

Urban stormwater management systems are increasingly strained by rapid urbanization and climate change, yet existing planning approaches often lack holistic optimization frameworks that account for both green and grey infrastructure (GREI) under uncertain future conditions. This study introduces a multi–objective optimization framework for Grey–Green Infrastructure (GGI), which integrates green infrastructure (GI) with GREI to enhance urban flood resilience, cost efficiency, and adaptability. The framework addresses life cycle cost (LCC), technological resilience (Tech-R), and operational resilience (Oper-R), offering a comprehensive approach to navigating the complexities of urban stormwater management. Key findings reveal that: (1) GGI systems optimized for resilience achieve a 33% improvement in Oper-R, with only a marginal increase in LCC of less than 9%, highlighting their robustness under GREI failure scenarios; (2) the integration of bioretention cells (BCs) and porous pavements (PPs) into GGI increases Tech-R by 7.1%, enhancing soil water retention and permeability, particularly in densely urbanized contexts; and (3) decentralized GGI systems exhibit superior adaptability to extreme weather events, with Design D reducing LCC to USD 53.9 M while maintaining no overflow under a 5–year rainfall event. The framework was validated in Zhujiang New Town, Guangzhou, where optimized GGI designs reduced average pipe diameters and manhole depths by 0.2–0.3 m compared to GREI–only systems, demonstrating both cost and resilience advantages. These findings provide decision–makers with a robust tool for evaluating trade–offs in stormwater infrastructure planning, advancing sustainable urban water management.

1. Introduction

Urban stormwater management systems constitute an essential component of urban infrastructure, with their failure potentially triggering significant public health concerns, socio–economic disruptions, and broader implications for societal well–being [1]. Traditionally, these systems have relied predominantly on grey infrastructure (GREI), encompassing networks of urban drainage systems engineered to manage stormwater runoff and mitigate urban flood risks [2,3]. However, GREI is increasingly confronted by multifaceted challenges, including the exacerbating impacts of climate change, rapid urbanization, and, in the context of older urban centers, the declining efficacy of aging infrastructure. These factors underscore the critical need for integrated and optimized design paradigms that not only ensure the reliability of GREI but also enhance its resilience and cost–efficiency, addressing the growing complexities of contemporary urban environments.

The effectiveness of stormwater infrastructure is predicated upon the fulfillment of three core objectives: (a) reliable performance under standard hydrological conditions, (b) minimal failure frequency while adhering to predefined risk thresholds, and (c) robust resilience to extreme hydrometeorological events, such as severe storms and flooding [4]. In this context, the integration of green infrastructure (GI) emerges as a transformative approach, augmenting system resilience, flexibility, and adaptability while simultaneously mitigating environmental impacts [5]. By leveraging GI strategies, including bio–retention cells and green roofs, natural hydrological processes are mimicked, delivering a suite of co–benefits such as flood risk attenuation, the enhancement of water quality, groundwater recharge, and the mitigation of urban heat island effects [6]. However, it is imperative to acknowledge that GI is not a replacement for traditional GREI, but rather a complementary system, reinforcing the overall efficacy and sustainability of urban stormwater management frameworks [7,8].

An optimal paradigm for urban stormwater management likely resides in the adoption of a Grey–Green Infrastructure (GGI) strategy, which synergistically integrates the sustainability and adaptability of GI with the engineering precision and reliability of GREI [9]. However, achieving an ideal equilibrium between GI and GREI represents a highly complex, multi–objective optimization challenge. This endeavor requires a holistic evaluation encompassing technological, economic, and social dimensions, while simultaneously addressing inherent trade–offs and conflicts among competing objectives. The intricacy of this optimization process underscores the need for advanced methodologies capable of navigating these multidimensional constraints to identify resilient and cost–effective solutions [10].

Previous studies have demonstrated the efficacy of multi–objective optimization approaches in evaluating integrated stormwater management systems by accounting for hydrological performance, life cycle costs (LCC), and environmental impacts [11,12]. Leng et al. [13] proposed an enhanced simulation–optimization framework that modifies decision variables to simultaneously consider green and grey infrastructure design, focusing primarily on performance metrics such as flood reduction and cost. Similarly, Jezzini et al. [14] employed agent–based modeling to evaluate the spatial deployment of six GI strategies in Newark, NJ, USA, accounting for social and economic co–benefits across private and public parcels. Nevertheless, these analyses have often overlooked critical factors such as time–dependent performance degradation, evolving maintenance requirements, and environmental variability, which introduce substantial uncertainties into the assessment and operational performance of GGI systems [15,16]. Addressing these complexities is essential to advancing the reliability and robustness of GGI evaluations, ensuring their long–term efficacy under dynamic and uncertain conditions.

Highlighting a paradigm shift in infrastructure design and management from traditional reliability–focused frameworks to resilience–oriented planning [17], this study underscores the critical need to address both technological resilience (Tech-R) and operational resilience (Oper-R) in stormwater systems. Technological resilience pertains to the physical robustness of stormwater infrastructure, enabling it to withstand environmental variability and extreme weather phenomena [18]. In contrast, operational resilience encompasses the functional stability of the system, encompassing key dimensions such as equipment durability, structural integrity under extraordinary loads, and the rapidity of post–event recovery [19]. Together, these resilience dimensions provide a comprehensive framework for enhancing the adaptability and reliability of stormwater systems in the face of growing climatic and urbanization challenges.

Previous studies investigating the functional degradation of urban drainage systems have predominantly concentrated on Tech-R [20], largely due to its engineering–oriented parameters, which are more amenable to resolution through targeted investments and management strategies. However, research on Oper-R, particularly regarding secondary functionality losses following structural failures or gradual performance deterioration over time, remains comparatively underexplored [21]. While regression models have been utilized to estimate the likelihood of specific GREI failures [22], the performance of GI is inherently more uncertain due to its dynamic physical properties. Variables such as plant growth, sedimentation, clogging, blockages, and fluctuating surface and subsurface flow resistances contribute to substantial temporal and spatial variability [23]. Failure to account for these complexities risks the significant misrepresentation of GI effectiveness [24]. Consequently, holistic performance assessments must incorporate incremental and cumulative failure mechanisms for both Tech-R and Oper-R to ensure an accurate and comprehensive evaluation of system resilience.

A comprehensive review of the existing literature highlights the pressing need for a robust optimization framework tailored to GGI systems, one that integrates Tech-R, Oper-R, and their synergistic contributions to overall system performance. The complexity of such optimization is compounded by the diverse array of performance metrics, decision–making processes across various developmental phases, and the interplay of technical, environmental, and social constraints. Real–world applications further necessitate the simultaneous optimization of multiple objectives including cost, reliability, Tech-R, and Oper-R, posing a formidable challenge for researchers and practitioners alike. Developing such a framework is critical for advancing the resilience, efficiency, and sustainability of urban stormwater management systems.

This study aims to address critical knowledge gaps by conducting a comprehensive spatial optimization of GGI systems, with a focus on the strategic deployment, placement, scaling, and diversity of GI and GREI components. The analysis incorporates a wide range of potential failure mechanisms throughout the operational lifecycle of the GGI and accounts for the non–linear dynamics of hydrologic and hydraulic constraints, LCC, and multivariate hydrologic risk factors. Specifically, the objectives of this research are to: (1) establish a comprehensive set of hydraulic constraints and modeling parameters for developing optimized GGI configurations, spanning fully centralized to entirely decentralized system layouts; (2) introduce innovative methodologies and algorithms to identify optimal trade–offs among LCC, Tech-R, and Oper-R; and (3) deliver a suite of actionable, feasible solutions to support decision–makers and stakeholders in advancing resilient urban stormwater management. Through these contributions, the study aspires to enhance the design, performance, and sustainability of GGI systems in diverse urban contexts.

2. Materials and Methods

The proposed framework for the multi–objective, multivariate optimization of GGI, integrating Tech-R and Oper-R, is depicted in Figure 1. The framework comprises three sequential task phases, each represented by a distinct column.

Phase 1: GREI Design Optimization (Column 1)

This phase focuses on the design considerations for GREI based on a specified design rainfall event. Key parameters include the physical layout of the drainage network, terrain characteristics, topography, and drainage ancillaries. The primary objective is to minimize the LCC associated with the GREI while establishing a foundational system configuration.

Phase 2: GGI Integration and Baseline Assessment (Column 2)

This phase consists of two interrelated sub–processes, as follows:

(a) Incorporate a selected number and configuration of GI elements into the GREI to form the GGI. The GI is strategically arranged to minimize the overall LCC of the integrated system;

(b) Conduct hydraulic and hydrological simulations using the same design rainfall as in Phase 1, while imposing predefined Tech-R and Oper-R parameters. These simulations establish the baseline peak discharge response and the associated LCC for the GGI.

Phase 3: Resilience Optimization (Column 3)

The final phase seeks to optimize the resilience performance of the GGI under varying Tech-R and Oper-R parameters. This involves evaluating the system’s adaptive capacity to manage uncertainties and stressors, such as operational and environmental variations.

A management matrix is developed to organize the optimized configurations of GGI based on selected Tech-R and Oper-R parameters. The matrix can be structured to rank configurations by increasing LCC, degree of decentralization, or operational efficiency. This reflects the evolving complexity of base infrastructure design, operation, and maintenance as a function of Tech-R and Oper-R interactions. The methodology is further elaborated in the subsequent sections, with a case study of Zhujiang New Town provided to illustrate its application and validate the framework.

2.1. Case Study: Zhujiang New Town

Guangzhou, identified as the most flood–prone city among 136 global coastal cities, experiences a subtropical monsoon climate with a substantial annual average rainfall of 1890 mm [25]. This study focuses on Zhujiang New Town, a prominent urban business district in Guangzhou, as the case study area. The catchment spans 102 hectares, characterized by relatively flat topography and a drainage network comprising 43 sub–catchments, 119 conduits, and 11 potential flow outlets (Figure 2). The Storm Water Management Model 5 (SWMM 5) was employed to simulate the rainfall–runoff processes within this catchment. Rainfall losses were modeled using the Horton infiltration method, while surface flow was routed using the dynamic wave approach [26]. Detailed descriptions of the sub–catchment characteristics and the corresponding hydrological and hydraulic parameters are provided in Table S1. The hydrological model was calibrated using observed rainfall–runoff data from 2013–2014, in accordance with the methodology of Zhu et al. [27]. Calibration focused on optimizing key parameters such as hydraulic conductivity, impervious area fraction, and infiltration rates using a trial–and–error approach supported by sensitivity analysis. Validation was conducted using 10 independent rainfall events not used in the calibration phase, covering a wide range of intensities and durations. Model performance was evaluated using the Nash–Sutcliffe Efficiency (NSE) and Kling–Gupta Efficiency (KGE), with results exceeding 0.75 and 0.70, respectively, indicating good to excellent model accuracy across diverse storm conditions [28,29]. The validation results demonstrate high congruence between observed and simulated data, consistently achieving strong efficiency scores and maintaining relative errors well below 10% across various rainfall scenarios. These results affirm the model’s accuracy and reliability for simulating stormwater dynamics in urban settings. Furthermore, this study builds upon insights and methodologies from prior research conducted by the same group of authors [30] on a comparable urban catchment. The integration of these prior experiences underscores the robustness of the methodological framework and enhances the credibility of the findings presented.

2.2. Optimization of GREI Networks and Management Trade–off

The design and optimization of the spatial configuration of GREI were founded on combinatorial optimization within graph theory. The Hanging Gardens Algorithm (HGA) [31] was used here to determine an optimal GREI network featuring various degrees of decentralization of layout (DDL). The HGA algorithm commences with the identification of candidate flow outlets (N_CO), corresponding to a centralized layout. DDL are then introduced progressively through the selection of other feasible outlets. Subsequent tiers of DDL are then introduced through the selection of other viable outlets. A total of 2 × NL decision variables, where NL corresponds to the number of loops in the baseline drainage pipes, were required by the HGA algorithm to generate one feasible layout corresponding to a set of DDL. Further details on HGA can be found in Bakhshipour et al. [29].

The degree of decentralization of a GREI network can be quantified as follows:

$$DDL={\displaystyle \frac{N_{SO}-1}{N_{CO}-1}}\times 100\%$$

(1)

where N_SO represents the number of selected outlets, and N_CO denotes the total number of viable candidate outlets. A fully decentralized layout (DDL = 100%) occurs when all viable outlets are utilized, whereas a completely centralized layout (DDL = 0%) consolidates drainage to a single outlet (N_SO = 1).

The GREI network design adheres to flow requirements, hydraulic criteria, and standard design specifications, ensuring compliance with urban drainage best practices. Key parameters include telescopic pipe diameter patterns, minimum and maximum cover depths, slopes, flow velocities, and hydraulic reliability. To meet these requirements, the adaptive pipe flow design algorithm proposed by Haghighi and Bakhshipour [32] was implemented, guaranteeing that no flooding occurred under a specified design storm. Each potential network configuration involved 2 × NP decision variables in the genetic algorithm, where NP represents the total number of pipes. Two variables—diameter and longitudinal slope—were considered for each pipe. The design storm adopted was a continuous 6 h precipitation event with a 5-year recurrence interval, generating a total rainfall of 121 mm. The rainfall profile followed the Chicago Hyetograph, as prescribed in the urban drainage design standards by the Ministry of Housing and Urban–Rural Development [33]. This ensured the hydraulic and structural reliability of all generated GREI layouts, balancing operational efficiency and resilience across varying degrees of decentralization.

2.3. Optimization of Grey–Green Infrastructure (GGI) Networks

2.3.1. Formulation of Multi-Objective Optimization Problem

Building upon the optimal design and generation of GREI networks with varying degrees of decentralization, as detailed in the section Optimization of GREI Networks and Management Trade-offs, GI was subsequently introduced and integrated to form GGI systems. Multiple stormwater management scenarios were incorporated to assess the performances of these integrated systems under diverse conditions. To address the technical and cost trade–offs—specifically between Tech-R and Oper-R—a multi–objective optimization framework was employed. The primary goal of this framework was to identify configurations that minimized LCC while satisfying the resilience and performance criteria. The mathematical formulation of the multi–objective optimization problem for GGI systems is expressed as

$$d_{\mathit{opt}}=\mathit{arg}\underset{d\in D}{\mathit{max}}\left[〈f_{\mathit{LCC}}〉, 〈f_{\mathit{Tech}-R}〉, 〈f_{\mathit{Oper}-R}〉\right]$$

(2)

where d_opt represents the optimal vector of decision variables defining the GGI system; d is the vector of decision variables, which are elaborated in the subsequent section.

2.3.2. Green Infrastructure Area Allocation

Porous pavement (PP) and bioretention cells (BCs) were selected as representative GI components due to their suitability for areas with limited land availability and high urban density [34]. Considering the spatial limitations common in high–density urban catchments [35], the total area allocated for GI, including PPs and BCs, was limited to 10% of the total sub–catchment area. This upper bound reflects realistic design constraints and follows the approach recommended by Eckart et al. [36]. The specific parameters for the PP and BCs modules used in the SWMM are detailed in Table S2. The integration of GI into the GREI network to form GGI systems plays a critical role in mitigating peak stormwater runoff. This reduction in runoff allows for smaller pipe diameters within the GREI network, thereby decreasing LCC while preserving hydraulic reliability. The optimization process incorporates these benefits into a framework that evaluates the trade–offs among key objective functions: LCC, Tech-R, and Oper-R.

2.3.3. Life Cycle Cost

The comparison of various GGI configurations was conducted based on their respective LCC, which served as a key metric for evaluating investments in stormwater management systems. LCC encompassed both initial capital expenditures and subsequent operation and maintenance (O&M) costs, expressed as present values (PV). This comprehensive approach ensured a holistic assessment of the economic feasibility of different GGI designs (Equations (3) and (4)),

$$LCC={\mathit{Capital}}_{GGI}+P{V}_{O\&M-GI}+P{V}_{O\&M-GREI}$$

(3)

$$P{V}_{O\&M}={\displaystyle {\sum }_1^{n}O\&M}{\displaystyle \frac{1}{{(1+i)}^n}}$$

(4)

where n is the expected service life, set at 30 years [8]; i represents the annual discount rate in China, fixed at 2% [37]; PV denotes the present value of capital costs; PV_O&M signifies the PV of cumulative O&M costs over the service life.

Capital costs were estimated based on locally sourced materials and construction/project costs [38]. Annual O&M costs for PP, BCs, and GREI were approximated at 4%, 8%, and 10%, respectively, of their initial capital cost, in accordance with findings by Houle et al. [39] and adjusted for the Guangzhou context.

2.3.4. Resilience Assessment

Resilience to overflow load (Res) was defined as the capacity of the infrastructure to maintain functionality following an extreme event, and was quantified using Equation (5) [40],

$$R{\mathit{es}}_i=\left(1-{\displaystyle \frac{V_{\mathit{flooding}\left(i\right)}}{V_{\mathit{precipitation}\left(i\right)}}}\right)\cdot 100\%$$

(5)

where V_flooding(i) and V_{precipitation(i)} represent the volume of overflow and precipitation for a given rainfall event i, respectively. Res values range from 0% (indicating worst performance, where the overflow volume equals precipitation) to 100% (indicating full functionality, with no overflow).

Four optimized GGI configurations—spanning fully centralized to fully decentralized network structures—were analyzed to evaluate Tech-R and Oper-R under extreme environmental conditions, including intense rainfall events, storm profiles, and long–term functional degradation due to wear, maintenance, and system restoration measures. Tech-R reflects the percentage of functionality of the primary, as–built infrastructure, while Oper-R measures the residual functionality during the service life, incorporating factors such as degradation, maintenance, and failure mitigation. Both metrics were evaluated using Equation (5) and analyzed in relation to global resilience indicators, failure probabilities, and infrastructure serviceability over time [41]. The Tech-R assessment employed a storm model characterized by a 50–year return interval, 6 h duration, and cumulative rainfall depth of 161 mm, with a peak runoff rate of 6.1 mm/min. This setup aimed to establish the maximum attainable resilience levels for both Tech-R and Oper-R. Tech-R was interpreted as the structural functionality of the primary infrastructure, while Oper-R captured residual performance amidst potential degradation and failures over the system’s operational lifespan.

To simulate failure scenarios, this study formulated cases where the GREI network experienced impairment, blockages, or structural collapse due to exceptional damage. In the absence of long–term monitoring data on urban drainage system failures, failure probability analyses employed a single–parameter exponential distribution function to estimate monthly incremental probabilities and cumulative failure distributions [42].

For GI, the mean effectiveness of bioretention cells (BCs_mean) was assumed to follow a normal distribution over its service life, accounting for seasonal variations such as reduced efficiency during spring and winter due to vegetation growth and increased soil organism activity. Similarly, the mean effectiveness of porous pavement (PP_mean) was modeled to exhibit a linear decline over time, reflecting structural degradation, increased clogging, and sediment accumulation. Detailed calculations and parameter estimates were derived from prior studies [43].

3. Results and Discussion

3.1. Trade–Offs Between DDL and LCC in a GREI Context

The trade–offs between centralized (0 ≤ DDL < 50%) and decentralized (50% < DDL ≤ 100%) GREI systems arise primarily from variations in discharge outlet configurations, pipe specifications, and fluid flow distribution within the network. These factors directly influence the capital expenditure associated with construction. Construction costs encompass excavation for manholes, trenching between nodes, pipe installation, backfilling, and leveling, all of which vary with the DDL.

To streamline material costing and accounting, a uniform “mean” pipe diameter was adopted across all configurations. Manhole depth, a critical factor in GREI design, significantly impacts overall construction costs. Manhole depth determines pipe–laying complexity and flow capacity, with deeper manholes requiring more extensive excavation, structural support, and associated costs. Flow capacity is calculated as the product of pipe flow velocity and cross–sectional area (assuming full–pipe flow), and manhole depth directly reflects the excavation effort and cost. As such, manhole depth serves as a reliable indicator of construction costs.

Table 1. Mean pipe diameter, mean manhole depth, and associated unit material and construction costs of the pipe network for optimized GREI systems across various degrees of decentralization (DDL).

DDL (%)	Max. Pipe Diameter (m)	Mean Pipe Diameter (m)	Max. Manhole Depth (m)	Mean Manhole Depth (m)	LCC of Pipes (USD M)	LCC of Manholes (USD M)	Total LCC (USD M)	DDL (%)
0	2.0	0.9	7.1	2.3	91.7	5.0	96.7	0
20	2.0	0.9	6.6	2.4	81.9	4.9	86.8	20
40	2.0	0.9	6.1	2.3	80.1	4.8	85.0	40
60	1.5	0.9	6.0	2.3	76.2	4.5	80.7	60
80	1.5	0.9	5.1	2.2	70.9	4.2	75.2	80
100	1.5	0.9	5.8	2.4	70.2	4.5	74.7	100

Note: The mean manhole depth serves as an indicator of construction costs.

presents data on pipe diameters, manhole depths, and their associated material and construction costs.

The optimization of GREI networks across various DDL levels focused on minimizing LCC by reducing pipe diameters and excavation depths while maintaining flow rate requirements. The optimization aimed for the smallest feasible pipe diameter, the shallowest possible manholes, and minimal longitudinal gradients to achieve cost–efficient designs.

For practical classification, threshold DDL levels of 40% and 60% were established to distinguish primarily centralized (DDL ≤ 40%) from significantly decentralized (DDL ≥ 60%) drainage networks. Table 1 highlights a consistent decrease in LCC with increasing DDL levels. Decentralized networks (DDL ≥ 60%) were characterized by smaller pipe diameters and shallower manholes, aligning with findings by Bakhshipour et al. [44] and corroborating recent research by Hesarkazzazi et al. [45]. Conversely, centralized networks (DDL ≤ 40%) exhibited larger collectors and deeper manholes, typical of conventional stormwater infrastructure, as illustrated in Figure 3.

Interestingly, a fully decentralized network (DDL = 100%) and a network with DDL = 80%, when designed with the same manhole depth, showed only marginal fiscal benefits from reduced pipe diameters, yielding a modest 0.7% reduction in total LCC. This observation underscores the intricate balance in GREI design and highlights the nuanced economic feasibility of decentralized stormwater management solutions [46]. These findings emphasize the importance of a comprehensive evaluation framework for optimizing the cost and performance of GREI systems across varying levels of decentralization.

3.2. Optimized GREI–Only and GGI Frameworks with Varying DDL and Resilience Goals

GGI offers the potential to enhance system performance by streamlining O&M procedures. The associated costs, expressed as a percentage of the total LCC of the GGI, exhibit variability depending on the network’s targeted goals and anticipated outcomes. Estimating O&M costs requires the application of localized unit price indices, encompassing activities such as routine cleaning and the inspection of network components. As ancillary operations to primary construction, O&M activities contribute significantly to LCC, particularly for GGI systems in highly centralized districts, as illustrated in Figure 4. Figure 4 presents a multi–objective trade–off matrix plotting LCC, Tech-R, and Oper-R across various DDL. Each point represents a GGI configuration, forming a Pareto front where no single objective can be improved without compromising another. The chart reveals that higher resilience tends to increase cost, while decentralized layouts (higher DDL) yield better Tech-R and Oper-R performance, particularly under failure scenarios.

The complexity of LCC arises from its coupling with diverse GGI objectives, including efficient drainage, aesthetic enhancements, structural integrity, Tech-R, and Oper-R, along with maintenance, restoration, replacement, inspection, and surveillance requirements. This multidimensional LCC matrix integrates considerations of service lifespan, physical infrastructure integrity, and various levels of Tech-R and Oper-R implementation. Each cell in the matrix corresponds to a specific objective and the associated LCC, forming a comprehensive framework for decision–making.

The optimization of GGI configurations relies on the Pareto front, which represents a set of non–dominated solutions balancing multiple cost contributors. The Pareto front encapsulates the trade–offs between competing objectives, reflecting optimal configurations that maximize Tech-R and Oper-R while minimizing LCC. Figure 5 illustrates the optimized solutions for 24 GREI–only and GGI configurations, each optimized for a specific DDL to achieve resilience goals. Figure 5 shows the LCC values for each DDL under different decision preferences (e.g., maximizing Tech-R, Oper-R, or a balanced approach). The steep rise in LCC under resilience–focused preferences highlights the financial trade–offs of robustness. For instance, at DDL = 100%, the LCC increases to USD 44.7 million when both Tech-R and Oper-R are maximized.

The findings underscore the economic advantages of decentralized systems in achieving superior resilience performance. These results align with previous studies demonstrating the cost–effectiveness of decentralized GGI across diverse urban and climatic contexts [47]. For example, research indicates that GGI can fulfill essential urban drainage requirements under varying rainfall scenarios [48]. This reinforces the multifunctionality of decentralized GGI systems in addressing the growing complexities of urban water resource management, particularly in the face of climate change challenges [45].

Urban environmental constraints, such as limited open space availability and the finite capacity of soil water storage, present significant challenges to the effective implementation of GI [25]. Enhanced drainage capacity through expanded GREI designs offers a robust, albeit costlier, solution for managing extreme rainfall events [48]. For example, Solutions 1 and 4, which prioritize resilience within combined strategies, yield substantial Oper-R improvements of 33%, accompanied by a modest increase in LCC of less than 9% (

Table 2. Comparison of 24 optimized solutions for GREI–only and GGI systems, categorized by decentralization degree and optimized for maximum operational resilience (Oper-R), maximum technological resilience (Tech-R), and minimum life cycle cost (LCC).

DDL (%)	Optimized GREI–Only Solutions				GGI Solutions with Maximum Oper-R				GGI Solutions with Maximum Tech-R				GGI Solutions with Minimum LCC
	No.	LCC (USD M)	Tech-R (%)	Oper-R (%)	No.	LCC (USD M)	Tech-R (%)	Oper-R (%)	No.	LCC (USD M)	Tech-R (%)	Oper-R (%)	No.	LCC (USD M)	Tech-R (%)	Oper-R (%)
0	1	96.7	92.4	45.2	2	65.5	90.6	66.3	3	105.8	99.9	76.8	4	104.8	99.5	78.2
20	5	86.8	97.0	40.6	6	61.7	93.8	65.4	7	90.9	99.9	75.0	8	90.4	99.8	75.6
40	9	85.0	97.2	38.8	10	58.9	92.3	64.4	11	92.0	99.9	72.4	12	89.6	99.5	73.9
60	13	80.7	97.4	40.7	14	56.2	94.1	64.7	15	85.6	99.9	72.9	16	84.7	99.9	73.9
80	17	75.2	96.8	36.7	18	55.1	94.4	63.1	19	80.0	100.0	72.0	20	80.8	99.9	72.0
100	21	74.7	96.3	37.9	22	53.9	92.6	61.5	23	80.8	99.9	69.4	24	81.2	99.8	70.5

). This demonstrates the ability of GI to provide reliable resilience under specific GREI failure scenarios, even when accounting for long–term performance degradation.

Furthermore, integrating cost–effective BCs and PP into GGI systems results in modest improvements in Tech-R, enhancing soil water storage and permeability. For instance, the inclusion of BCs and PP in optimized configurations yields a Tech-R increase of 7.1% (Table 2) [49]. These improvements underscore the complementary roles of GI and GREI in augmenting system performance, even within the spatial and hydrological limitations typical of urban environments.

All optimized configurations demonstrate exemplary Tech-R performance. Hydraulic reliability—defined as the ability to meet design standards under severe rainfall events (peak flow up to 4.6 m³/s)—is a fundamental requirement. Achieving this reliability often necessitates larger–scale GREI designs that increase the capacity and redundancy of drainage networks. For example, Solution 19 achieves a Tech-R of 100%, signifying the complete elimination of flooding—an essential feature for flood–prone urban regions. This result underscores the critical role of expanded drainage capacity in GREI systems to address extreme rainfall scenarios [48].

The optimization strategies also highlight the importance of integrating sufficient quantities of BCs and PP to bolster Tech-R in GGI systems, aligning with recommendations by Li et al. [49]. However, the inherent challenges in urban areas, such as constrained soil pore water storage and limited open space, necessitate the adoption of combined strategies and more comprehensive GREI solutions. These findings reinforce the need for a balanced and context—sensitive approach to urban stormwater management, combining innovative GI measures with robust GREI designs to ensure long–term system resilience and cost efficiency.

3.3. Advancing GGI: Interrelationship Among DDL, LCC, and Resilience

Advancing the resilience of GGI systems requires a nuanced understanding of the interrelationships among DDL, LCC, and resilience. Figure 6a presents the Pareto non–dominated solutions, illustrating GGI configurations across various DDL. Four distinct design alternatives emerge, each balancing diverse management objectives with differing LCC, Oper-R, and Tech-R values (

Table 3. Design parameters, life cycle costs (LCC), and green infrastructure (GI) allocations for optimal GGI schemes at varying degrees of decentralization (DDL).

Optimal GGI Design	DDL (%)	GREI Design Parameters				GI Design Parameters		LCC of GREI (USD M)		LCC of GI (USD M)		Total LCC (USD M)
		Max. Pipe Diameter (m)	Mean Pipe Diameter (m)	Max. Manhole Depth (m)	Mean Manhole Depth (m)	Total BCs Area (ha)	Total PP Area (ha)	Pipes	Manholes	BCs	PP
A	60	1.5	0.7	5.7	2.1	2.20	7.91	56.1	3.1	4.7	5.2	69.1
B	60	1.5	0.7	5.7	2.1	1.62	8.28	57.0	3.9	3.4	5.5	69.8
C	80	1.5	0.7	4.8	2.0	1.50	8.57	57.3	3.8	3.2	5.7	70.0
D	100	1.0	0.6	5.6	2.1	2.56	5.49	41.3	3.4	5.4	3.7	53.9

Note: The mean manhole depth is used as an indicator of construction costs.

). This study focuses on solutions meeting the criteria of Tech-R ≥ 95%, Oper-R ≥ 70%, and minimal LCC.

Figure 6a presents Pareto–optimal solutions categorized by management priorities. Four optimal design types are highlighted: Design A (balanced), Design B (Oper-R priority), Design C (Tech-R priority), and Design D (LCC priority). These offer tailored options based on stakeholder goals. Design A is identified as the optimal solution, achieving a Tech-R of 99.2%, Oper-R of 70.4%, and an LCC of USD 69.8M at a DDL of 60%. This configuration represents a balanced trade–off between cost efficiency and resilience (Figure 6a). When an LCC cap is imposed (e.g., USD 70.0M) (Figure 6c,d), Designs B (DDL = 60%) and C (DDL = 80%) emerge as alternatives optimized for Oper-R and Tech-R, respectively. Design B demonstrates robust resilience against significant GREI failures and GI degradation, while Design C excels in managing extreme weather conditions. Thus, the selection of a specific design should depend on budget constraints, local conditions, and desired GGI configurations.

The findings reveal that Oper-R remains relatively stable across varying DDL for a fixed LCC. Decentralized systems (green points in Figure 6c) outperform centralized systems (blue points) marginally, reflecting better adaptability to diverse stressors. Furthermore, the distribution of Tech-R highlights the superior performance of decentralized designs (Figure 6d), attributed to their inherent flexibility and enhanced resilience to extreme storm events, even in the face of significant GREI damage [31].

Design D, representing a fully decentralized network, achieves the lowest LCC. While its resilience is slightly lower than those of Designs A, B, or C, it reliably prevents overflow under a 5–year design rainfall scenario. These findings align with the work of Bakhshipour et al. [44] and emphasize the importance of multi–objective optimization in infrastructure design. They underscore the necessity of data–driven decision–making, balancing cost minimization, functionality, and resilience in the development of sustainable and robust GGI systems.

3.4. Allocating Space for Green Infrastructure Development

Figure 7 compares the spatial allocation of GI at the sub–catchment level across four optimal GGI designs (Designs A, B, C, and D). Each design integrates a unique combination of location, scale, and types of grey and green infrastructure, illustrating the effectiveness of GI integration in reducing the scale of GREI through peak runoff mitigation. Figure 7 visualizes the spatial configuration of GREI and GI elements for the four design types. GI types are distinguished by color and size. Pipe thicknesses reflect diameter, and manhole size reflects depth, enabling the visual comparison of system complexity and investment scale. This integration results in a more cost–effective GGI system compared to GREI–only designs with equivalent DDL (Figure 3). Notably, average pipe diameters and manhole depths in GGI designs decrease by 0.2–0.3 m compared to GREI–only systems (Table 3). Among the designs, Design D achieves the smallest main trunk pipe diameter of 1 m, underscoring its cost efficiency.

Optimization–driven solutions (Designs A, B, and C) predominantly allocate space to PPs over BCs (Figure 7a–c), largely due to the lower cost per unit area of PPs (Table 3). This strategic allocation enhances hydraulic and hydrologic resilience by effectively pairing appropriately scaled GREI with cost–efficient PPs. In contrast, Design D incorporates a larger proportion of BCs while maintaining the lowest total LCC (Figure 7d). Design D allocates 2.56 hectares to BCs, approximately 48% more than the other optimized designs (Table 3). In scenarios where GI implementation is capped at 10% of each sub–catchment, BCs outperform PPs in mitigating surface runoff, making them particularly advantageous in densely urbanized areas. Designs A, B, and C, with their emphasis on PPs, are particularly suited for high–density urban areas where space constraints and cost efficiency are critical considerations. On the other hand, Design D minimizes LCC, favoring decentralized systems with a higher proportion of BCs. While this design requires more land, it is optimal for newly developed or low–density areas where land availability is not a constraint and ecological co–benefits are valued.

These findings reinforce the value of a balanced urban stormwater management strategy. By integrating GI to complement GREI, GGI systems demonstrate superior performance in both cost efficiency and resilience. The results align with existing literature, underscoring the indispensable role of integrated GGI in enhancing flood resilience and presenting GGI as a viable, economical solution for urban stormwater management [41,50].

3.5. Evaluating Operational Resilience: A Comparative Discourse

This study utilized Critical Component Analysis (CCA) to evaluate the average Oper-R under hypothetical failure scenarios of key infrastructure components throughout their service life. Centralized networks exhibited an 8% higher Oper-R when the optimization process prioritized minimizing LCC (Table 2). However, a contrasting perspective is offered by Wang et al. [24], whose global resilience analysis suggested that decentralized strategies require fewer resources while achieving superior Oper-R. This discrepancy may arise from global resilience analysis accounting for the aggregate effects of network failures. While holistic, the computational complexity of this approach limits the number of random failure scenarios analyzed at each level to several hundred, potentially reducing the comprehensiveness of its findings [15].

Decentralized schemes have been favored in other studies, likely due to the interdependence of critical components in decentralized networks, such as outlets and downstream pipelines, which may not be easily separable or discernible. This interdependence can lead to their omission from assessments, thereby biasing results against decentralized schemes. Similarly, CCA–based analyses may fail to capture the adaptability advantages inherent in decentralized layouts [20]. As a result, conclusions may disproportionately favor centralized schemes due to their higher retention capacity and more comprehensive GREI and GI integration [45]. However, this does not imply that centralized systems consistently outperform in terms of Oper-R. For designs with LCC below USD 77.4M, the highest Oper-R is observed at a moderate DDL of 60% (Figure 6c).

While global resilience analysis is claimed to provide a more comprehensive and realistic perspective, its integration into optimization processes poses significant challenges due to the unpredictability of GREI failure distributions (e.g., location and frequency). Within this study’s CCA framework, Oper-R assessments were limited to simulations of three typical years, underscoring a practical limitation. Bakhshipour et al. [44] introduced a structural resilience index to identify critical components and assess system Oper-R, offering computational feasibility and efficiency compared to global resilience analysis or CCA. However, this index assumes uniform sub–catchment areas per outlet, which may limit its applicability in densely urbanized areas with complex land use and limited open spaces.

Failures in critical components of both GREI and GGI systems can lead to catastrophic flooding in densely populated areas [51,52]. Enhancing reliability and resilience requires prioritizing severe threats and their potential impacts over the service life of the infrastructure, even if the perceived threats are of low probability [53]. In this study, an exponential distribution function was employed to estimate GREI failure probabilities. However, real–world scenarios are inherently more complex. Long–term monitoring data could enable the development of more robust statistical models, such as Weibull distributions [54], or serve as the basis for machine learning models to predict network failures [55]. Similarly, empirical data could support the development of long–term efficiency distribution functions for GI, enabling more comprehensive multi–dimensional assessments and validation in future studies [56].

3.6. Limitations and Future Work

In urbanized regions, implementing a robust stormwater management system is critical to mitigating hydrological risks. The proposed framework, founded on an optimized multi–criteria decision–making platform, offers a significant advancement by harmonizing economic, reliability, and resilience factors throughout the infrastructure lifecycle. Notably, it addresses uncertainties associated with hydrological resilience, enhancing urban flood resilience evaluation and adaptability to climate change. This framework represents a valuable tool in designing resilient and sustainable urban stormwater management systems.

However, several limitations warrant acknowledgment. The resilience assessment employed in this study relies on a simplistic exponential distribution function to approximate the failure probability of GREI. While this approach provides a foundational baseline for analysis, it cannot capture the complexity of real–world scenarios involving numerous parameters and dynamic interactions. Similarly, the design storms used in this study ensure consistency and control over variables, but may not reflect the variability of actual rainfall and runoff patterns. Future research should incorporate empirical rainfall and runoff data to improve the accuracy and applicability of the framework under diverse conditions.

The current framework primarily considers BCs and PPs as representative examples of GI. While suitable for the study context, this limited selection may restrict the framework’s generalizability to other urban environments with diverse GI options. Expanding the framework to include additional GI types, tailored to varying local contexts, would enhance its versatility and applicability.

Furthermore, the optimization process leverages a genetic algorithm with a predominant focus on economic performance. Although effective in balancing costs and resilience, this approach may not fully address multifaceted real–world challenges, such as non–point source pollution or additional environmental and social indicators. Future work should explore more sophisticated optimization algorithms capable of addressing complex multi–objective problems, integrating factors such as water quality, ecosystem services, and community well–being.

4. Conclusions

This study highlights the effectiveness of a multi–objective optimization framework that integrates LCC with technological and operational resilience. The proposed approach provides a valuable decision–making tool for addressing extreme hydrological events in densely populated urban areas. The key findings of this research are as follows:

(1)

Integration of GREI and GI. Coupled strategies that optimize the integration of GREI and GI outperform standalone GREI solutions. These integrated systems offer enhanced economic viability and resilience, particularly in mitigating the impacts of hydrological adversities;

(2)

Performance gains in GGI. While implementing GGI with selected resilience preferences may slightly increase LCC, the enhanced Oper-R provided by GGI significantly improves overall system performance compared to GREI–only networks;

(3)

Resilience of decentralized systems. Decentralized GGI systems demonstrate superior flexibility and resilience to extreme storm events, even when substantial damage occurs to GREI components. This highlights their robustness and adaptability in addressing severe climatic challenges;

(4)

Effectiveness of bioretention cells. For equivalent footprint areas, BCs outperform PPs in attenuating surface runoff, making them particularly suitable for densely urbanized areas. Their application has high potential for increasing pervious surface areas, contributing to improved stormwater management;

(5)

Critical component analysis for enhanced reliability. The failure of critical drainage system components can lead to severe flooding. To ensure long–term system reliability and resilience, it is essential to assess the most severe threats and their consequences throughout the infrastructure’s lifespan using critical component analysis, even for low–probability extreme events.

This research contributes a comprehensive and adaptable optimization approach that supports resilient, cost–effective, and context–sensitive urban stormwater management planning. It provides a valuable decision–making tool for city planners, engineers, and policymakers seeking to navigate the increasing complexity of stormwater management under climate change. Future studies could further refine this framework by incorporating broader environmental indicators, additional GI types, and more advanced optimization techniques to address the multifaceted challenges of urban stormwater systems.