Predictive multi-criteria decision-support framework for urban flyover design: integrating structural, economic, and environmental constraints

1 Introduction

Rapid urbanization in developing economies has precipitated unprecedented demand for grade-separated transportation infrastructure. Indian cities are projected to accommodate an additional 416 million urban residents by 2050 (UN-Habitat, 2022), driving exponential growth in vehicular traffic that overwhelms at-grade intersections and arterial networks. Flyovers—elevated bridge structures that carry traffic streams over intersecting roads, railways, or waterways—represent the primary engineering response to this challenge, offering effective congestion relief without the extensive land acquisition requirements of alternative alignments.

The design of urban flyovers presents multifaceted engineering challenges that resist conventional sequential treatment. Structural configuration decisions affect construction complexity and material requirements; alignment selection impacts land acquisition costs and community displacement; environmental mitigation measures add project costs while satisfying regulatory requirements under the Environment Protection Act, 1986 and subsequent Environmental Impact Assessment notifications. These interdependencies create a complex decision space where modifications to address one constraint inevitably propagate effects across others—a phenomenon inadequately addressed by current practice.

Contemporary infrastructure projects face stringent and often competing constraints from multiple stakeholders: regulatory bodies mandate environmental compliance; funding agencies under the Smart Cities Mission and Atal Mission for Rejuvenation and Urban Transformation (AMRUT) demand cost-effectiveness and value-for-money; communities expect minimal disruption during construction and operation; and engineering safety is governed by Indian Roads Congress standards. This multiplicity of binding constraints necessitates integrated design frameworks that explicitly model constraint interactions rather than treating them as independent considerations amenable to sequential resolution.

Flyover design decisions influence project outcomes across multiple interconnected dimensions. Structural configuration—choice of superstructure type (simply supported PSC girder, continuous box girder, steel composite), pier geometry, and foundation system—determines not only material costs but also construction staging requirements, traffic disruption duration, and long-term maintenance demands. Alignment selection within constrained urban corridors affects right-of-way acquisition, utility relocation, and the extent of heritage or ecologically sensitive areas impacted. Environmental mitigation measures mandated by EIA authorities, including noise barriers, vibration dampening, and air quality monitoring systems, contribute 8%–15% of total project cost in densely populated corridors (National Highways Authority of India, 2023).

Current practice relies heavily on iterative design processes with limited quantitative frameworks for exploring the multidimensional constraint space efficiently. Designers typically employ experience-based heuristics drawn from similar completed projects, conducting rigorous analysis only on a small subset of feasible alternatives identified through professional judgment. This approach risks overlooking superior design configurations and provides limited systematic insight into trade-off relationships among competing objectives. Furthermore, the absence of rapid screening tools forces critical early-stage decisions—which fundamentally shape project trajectory—to be made with incomplete understanding of the solution space.

While substantial research exists on structural optimization of individual flyover components (Martinez et al., 2021; Johnson et al., 2023) and environmental impact assessment methodologies (Patel et al., 2024; Kumar and Sharma, 2023), integrated frameworks addressing the complete constraint landscape for urban flyovers remain limited. Existing studies typically suffer from one or more of the following limitations:

• Single-objective optimization prioritizing either cost minimization or structural performance, without concurrent treatment of environmental objectives
• Post-design environmental assessment rather than embedding EIA metrics as active constraints within the optimization problem formulation
• Discrete scenario comparison of a limited alternative set without comprehensive parametric modeling of the continuous design space
• Reliance on linear surrogate models that inadequately capture the non-linear relationships and constraint boundary discontinuities characteristic of infrastructure design problems
• Limited incorporation of site-specific constraints from diverse geographical and geotechnical contexts representative of the Indian subcontinent

The non-linear, high-dimensional nature of the flyover design problem—where structural, economic, and environmental responses interact in complex ways across a continuous parameter space—renders conventional linear regression models and discrete scenario analysis fundamentally inadequate. Multivariate radial basis function (MRBF) networks offer a methodological pathway to address this gap, providing smooth non-linear approximation capabilities demonstrated in analogous engineering applications (Zhou et al., 2023; Nakamura and Tanaka, 2024), yet their systematic application to integrated infrastructure design optimization remains unexplored in published literature.

This research addresses the identified methodological gaps through the following specific objectives:

• Develop a comprehensive constraint taxonomy for urban flyover design encompassing structural, economic, environmental, and socio-political dimensions, grounded in Indian regulatory requirements and engineering standards
• Establish quantitative parametric relationships between independent design variables and dependent performance metrics using multivariate radial basis function modeling calibrated on 47 completed flyover projects
• Validate the proposed predictive decision-support framework through case studies in Delhi, Mumbai, and Bengaluru, representing diverse urban density, geotechnical, and climatological contexts
• Quantify trade-off relationships among competing objectives through sensitivity analysis and Pareto frontier characterization to support multi-criteria decision-making
• Demonstrate practical applicability for rapid preliminary design evaluation, benchmarking computational efficiency against conventional iterative approaches

While the present study primarily develops MRBF surrogate models for predictive evaluation and trade-off visualization, the framework is positioned as a decision-support tool rather than a complete optimization algorithm. Future work will integrate evolutionary optimization procedures (e.g., NSGA-II, MOEA/D) with the surrogate models to generate Pareto-optimal solutions. Accordingly, the current contribution should be interpreted as a predictive multi-criteria decision-support framework enabling rapid evaluation of design alternatives under multiple constraints. This research makes the following distinct contributions to infrastructure design methodology:

Methodological Innovation: First comprehensive application of MRBF modeling with Gaussian kernel functions to integrated flyover design optimization in the Indian urban context, enabling efficient exploration of a seven-dimensional constraint space exhibiting strongly non-linear interdependencies.

Theoretical Advancement: Development of a unified constraint taxonomy integrating traditionally siloed design considerations—IRC structural standards, MoEFCC environmental norms, and urban planning regulations—revealing previously unquantified coupling effects between soil bearing capacity and noise impact predictions.

Empirical Contribution: Quantification of constraint sensitivity metrics from 47 real-world projects spanning diverse Indian urban contexts, providing evidence-based guidance for design prioritization under varying site conditions.

Practical Application: Creation of rapid evaluation tools achieving 63% reduction in preliminary design time while maintaining compliance with IRC:6-2017 and IRC:78-2014 safety standards, directly applicable to resource-constrained infrastructure planning environments.

Section 2 reviews relevant literature on flyover design optimization, environmental impact assessment, and radial basis function modeling. Section 3 presents the research methodology including constraint identification, data collection from 47 projects, and MRBF model development. Section 4 details three case studies validating the framework across diverse Indian urban contexts. Section 5 presents and discusses results including sensitivity analysis, Pareto trade-off characterization, and practical implications. Section 6 concludes with research contributions and future research directions. Despite advances in structural optimization and environmental assessment, most studies treat constraints sequentially, provide limited quantitative metrics, and focus on contexts outside India. This study addresses these gaps by applying multivariate radial basis function modeling to develop an integrated, quantitatively validated, and context-appropriate predictive decision-support framework for urban flyover design.

2 Literature review

2.1 Flyover and bridge design optimization

Research on infrastructure optimization has evolved from single-component structural analysis toward integrated system-level approaches. Foundational work by Frangopol and Maute (2003) established the basis for multi-objective bridge optimization under uncertainty, highlighting trade-offs between initial construction cost and long-term reliability. More recent studies have focused on material efficiency and structural performance. For example, Martinez et al. (2021) optimized PSC girder configurations using particle swarm algorithms, achieving 12%–18% cost reductions, while Wang and Chen (2022) developed pier spacing algorithms that minimized foundation costs under variable soil profiles.

Multi-objective predictive decision-support frameworks have gained prominence. Thompson et al. (2023) applied NSGA-II for simultaneous cost and construction time optimization of flyover corridors, reporting 8%–15% improvements over sequential approaches. However, environmental considerations were excluded. Liu et al. (2024) integrated life-cycle cost analysis with structural optimization but treated environmental compliance as binary constraints, limiting optimization potential. In the Indian context, Rao and Krishnamurthy (2022) applied evolutionary algorithms under IRC loading combinations, reporting material savings but neglecting urban constraints such as right-of-way and noise standards.

2.2 Environmental impact assessment in transportation infrastructure

Environmental considerations have shifted from post-design compliance checks to integrated design factors. Kumar and Sharma (2023) proposed a hierarchical EIA framework categorizing impacts across construction, operational, and decommissioning phases, showing that construction methods account for 40%–55% of total environmental burden. Garcia et al. (2024) developed parametric EIA models correlating project characteristics with environmental footprint metrics, achieving 87% prediction accuracy using gradient boosted regression trees. Their work revealed strong non-linearities, particularly between urban density and noise impact.

Regulatory frameworks such as the MoEFCC Environmental Impact Assessment Notification (2006, amended 2020) mandate comprehensive EIA for urban flyovers exceeding 500 m, with binding thresholds for noise, air quality, and ecosystem preservation. Incorporating these thresholds as active constraints within predictive decision-support frameworks represents a methodological advancement over sequential compliance approaches.

2.3 Multi-criteria decision making in infrastructure projects

Multi-criteria decision making (MCDM) techniques have been widely applied to infrastructure planning. Rahman et al. (2023) used AHP to structure stakeholder preferences for highway alignment selection, demonstrating sensitivity to weight assignment. Vaidya and Kumar (2006) reviewed AHP applications, noting reproducibility limitations due to subjective matrices. Anderson and Wong (2024) applied TOPSIS to bridge design alternatives, offering objective rankings but limited to discrete scenarios. Similarly, Singh and Sharma (2023) applied the VIKOR method to metro infrastructure, balancing group utility and individual regret but again constrained by discrete alternatives.

Emerging approaches integrate surrogate modeling with MCDM to address continuous design spaces. Surrogate models trained on design-of-experiment samples enable efficient Pareto frontier exploration, a paradigm well established in aerospace engineering (Jin, 2011) but rarely applied in civil infrastructure.

2.4 Radial basis function modeling in engineering

Radial basis function (RBF) networks provide smooth non-linear approximation capabilities, making them suitable for constraint boundary modeling. The theoretical foundation was established by Powell (1987) and systematized by Buhmann (2003). Engineering applications have demonstrated their efficacy: Zhou et al. (2023) used MRBF for finite element validation of suspension bridges, achieving sub-1% error; Nakamura and Tanaka (2024) applied RBF surrogate models for vibration-based damage detection in highway bridges; and Mollahasani et al. (2011) predicted soil bearing capacity using RBF networks, outperforming regression methods.

Gaussian kernels, with infinite differentiability, are particularly effective for smooth response functions, while multiquadric kernels offer better extrapolation properties. Despite proven success in structural and geotechnical engineering, systematic application of MRBF modeling to integrated infrastructure design optimization—combining structural, economic, and environmental responses—remains unexplored, representing the central methodological gap addressed in this study recent advances in infrastructure optimization and sustainability have been highlighted in several studies (Bošnjak and Jajac, 2023; Chen et al., 2023; Das and Mukherjee, 2024; Garcia and Lopez, 2023; Gupta and Rao, 2023; Huang and Wang, 2024; Huang and Wu, 2025; IEMA, 2023; Jain and Sharma, 2023; Kim and Lee, 2024; Lee and Kim, 2025; Liu and Zhou, 2023; Mehta and Patil, 2024; MoEFCC, 2024; Rahman and Chowdhury, 2023; Singh and Patel, 2023; Wang and Zhou, 2024; Zhang and Chen, 2024; Zhang et al., 2025).

2.5 Research gaps

From this review, several gaps emerge:

• Limited integration: Most studies treat structural, economic, and environmental constraints sequentially rather than simultaneously.
• Insufficient quantification: Few frameworks provide quantitative performance metrics comparing parametric versus conventional approaches.
• Context specificity: Existing research often focuses on developed nations, with limited applicability to Indian urban contexts.
• Implementation complexity: Advanced optimization techniques require computational resources often unavailable to municipal engineering departments.

This study addresses these gaps by applying MRBF modeling to develop an integrated, quantitatively validated, and context-appropriate predictive decision-support framework for urban flyover design.

3 Methodology

3.1 Research framework overview

The research methodology comprises five sequential phases organized within an iterative validation loop: (1) constraint identification and taxonomy development through systematic literature review and expert consultation; (2) parametric data collection from completed flyover projects; (3) MRBF model development, hyperparameter optimization, and validation; (4) case study implementation in three Indian cities; and (5) sensitivity analysis and trade-off quantification through Pareto frontier characterization. Figure 1 presents the methodological framework adopted in this study. The process begins with site characterization, incorporating geological surveys, land use analysis, and regulatory constraints. Alternatives evaluation compares flyover and tunnel options using lifecycle costing and multi-criteria decision analysis. Parametric optimization employs MRBF modeling to explore design variables and sensitivity analysis. Numerical validation through finite element analysis ensures structural adequacy and performance metrics. Finally, sustainability assessment integrates environmental impact, noise, air quality, and policy compliance. Feedback loops from validation and sustainability stages reinforce iterative refinement of design decisions.

The framework is designed for use during the preliminary design stage—after project scope and corridor definition but before detailed engineering—where rapid evaluation of multiple design configurations can most effectively reduce total project cost and duration. At this stage, independent design variables are determined by site and traffic studies, enabling parametric evaluation of dependent structural and environmental outcomes.

3.2 Constraint taxonomy development

Through systematic literature review and structured consultations with 23 infrastructure professionals (average experience: 17.4 years; range: 8–31 years) including IRC technical committee members, NHAI project directors, and MoEFCC environmental assessors, we developed a hierarchical constraint taxonomy organized into four primary categories aligned with the project evaluation framework of NITI Aayog Infrastructure Working Group (2023).

Structural Constraints: Load-bearing capacity per IRC:6-2017 Class A and 70R loading; maximum vertical deflection limits per IRC:24-2010 Section 510.4 (L/800 for main girders, L/300 for cantilevers; L/600 assumed in this study for case-specific modeling); pier foundation adequacy per IRC:78-2014; seismic design per IS:1893 Zone II–V; minimum vertical clearance 5.5 m for national highways; span-to-depth ratios within IRC guidance.

Economic Constraints: Construction cost ceilings per project DPR approval; land acquisition budget limits under LARR Act 2013; maintenance cost projections within Municipal Corporation financial capacity; benefit-cost ratio threshold BCR ≥ 1.5 per Ministry of Finance appraisal guidelines; contingency provisions 5%–10% of civil works.

Environmental Constraints: Noise pollution limits per MoEFCC Environmental Standards (75 dB(A) daytime commercial zones); CPCB ambient air quality standards; ecosystem preservation buffer 500 m from reserved forests; embodied carbon targets under National Action Plan on Climate Change; visual impact assessment per National Urban Policy.

Regulatory and Social Constraints: Municipal zoning regulations and development control rules; right-of-way limitations per existing road reserve; community displacement per R&R Framework; heritage site buffer zones per ASI regulations; construction timeline mandates in project agreements; utility relocation coordination.

3.3 Independent and dependent parameter identification

Based on constraint analysis, design practice review, and hierarchical correlation analysis of the project dataset, we identified seven independent variables and five dependent performance metrics. Table 1 summarizes the independent variables with their ranges observed in the study dataset.

TABLE 1. Independent design variables and observed ranges.

The Environmental Impact Assessment (EIA) score was constructed as a composite index based on MoEFCC regulatory thresholds. Indicators included ambient noise increment, air quality (PM₂.₅, NOx), ecological buffer encroachment, and embodied carbon. Each indicator was normalized to a 0–1 scale and weighted according to regulatory importance (noise 0.25, air quality 0.25, ecology 0.25, carbon 0.25). The final score was calculated as the weighted sum, yielding a reproducible metric aligned with national EIA guidelines. Table 2 summarizes the dependent performance metrics. Each indicator Ii was normalized using Ni = (Ii – Imin) / (Imax – Imin). The final EIA score was computed as Score = 100 × Σ wiNi, with equal weights wi = 0.25 for noise, air quality, ecology, and carbon. Equal weighting reflects regulatory parity, though future work may explore differential weighting schemes.

TABLE 2. Dependent performance metrics.

3.4 Data collection and processing

Primary data were collected from 47 completed flyover projects across 12 Indian cities (Delhi, Mumbai, Bengaluru, Hyderabad, Chennai, Pune, Ahmedabad, Kolkata, Nagpur, Surat, Jaipur, and Lucknow), representing diverse geographical, geotechnical, and urban morphological contexts. Project selection followed stratified criteria to ensure representativeness: completion between 2013 and 2023 ensuring cost and regulatory currency; availability of comprehensive design documentation including DPR, structural drawings, and as-built records from client organizations; verified environmental impact assessment data from MoEFCC EAC proceedings; representation of all major structural configurations (simply supported PSC girder, continuous box girder, steel composite deck, precast segmental); and geographic distribution across IRC seismic Zones II through V.

Data were sourced from NHAI project completion reports, Municipal Corporation DPR databases, National Environmental Engineering Research Institute (NEERI) EIA reports, and direct consultation with project design consultants. Sensitive cost information was accessed under executed Non-Disclosure Agreements with project authorities, with individual project identities anonymized in reported results.

Data quality and consistency were ensured through a multi-stage processing protocol. Outlier detection employed modified Z-scores with threshold |Z^b| > 3.5, identifying three projects with anomalous cost data attributable to documented force majeure events; these were retained with indicator variables rather than excluded. Cost data were standardized to FY2023-24 prices using the CPWD construction cost index. Cross-referencing between client records, consultant documentation, and EIA reports resolved inconsistencies in 9 of 47 project records. Missing data (6.2% across all variables) were imputed using multivariate imputation by chained equations (MICE) rather than listwise deletion, preserving the full dataset for model training.

3.4.1 Sample size adequacy

A Monte Carlo–based statistical power analysis confirmed that the dataset of 47 projects provides sufficient coverage of the seven-dimensional input space. While sparse, the sample spans diverse urban contexts (Delhi, Mumbai, Bengaluru, etc.), enhancing representativeness and ensuring adequate model generalization.

3.5 Multivariate radial basis function model development

3.5.1 Mathematical formulation

The governing relationships are expressed in Equations 1–3, which define the MRBF approximation using Gaussian and multiquadric kernels.

The MRBF model approximates the functional relationship between the p-dimensional input parameter vector χ ∈ ℝ^p and scalar output metric y through a weighted superposition of N radial basis functions centered at the training data points:where wᵢ are scalar weights determined during model training, ||χ - χᵢ|| denotes the Euclidean distance between prediction point χ and training center χᵢ, ϕ(·) is the chosen radial kernel function, and p(χ) is a low-degree polynomial tail (linear, p(χ) = β₀ + β^Tχ) that ensures uniqueness of the interpolant and improves extrapolation behavior.

y x = ∑ i = 1 N W i · Φ x − x i + p x (1)

Two kernel functions were evaluated in this study. The Gaussian kernel:where σ is the shape parameter controlling the width of each basis function; and the multiquadric kernel:where c is the shape parameter. Training requires solution of the linear system Φω = y, where Φᵢ□ = ϕ(||χᵢ - χ□||) is the kernel matrix, with regularization term λ^TT added to the diagonal to prevent overfitting: (Φ + λ^TT)ω = y. The optimal regularization parameter λ was determined through generalized cross-validation.

Φ G r = exp − r 2 / σ 2 (2)

Φ M r = r 2 + c 2 (3)

Input variables were standardized to zero mean and unit variance prior to model training to prevent scale-dependent bias in the distance metric. Separate MRBF models were trained for each of the five dependent performance metrics, enabling simultaneous multi-objective prediction from a single set of input conditions.

In this study, the number of centers N was set equal to the number of training points (n = 47), resulting in a 47 × 47 kernel matrix. This choice ensures exact interpolation, consistent with prior MRBF applications in structural engineering (Zhou et al., 2023). Regularization was applied to prevent overfitting, with optimal λ values selected via generalized cross-validation for each dependent metric. Table 3 summarizes the optimal λ values alongside kernel parameters. The polynomial tail p(x) = β0 + βTx introduced eight additional parameters, which were incorporated into the cross-validation process and jointly regularized with kernel weights to maintain stability and generalization.

TABLE 3. Optimal regularization parameters (λ) for MRBF models across performance metrics.

The number of centers N was set equal to the number of training points (n = 47), resulting in a 47 × 47 kernel matrix. This choice ensures exact interpolation, consistent with prior MRBF applications in structural engineering (Zhou et al., 2023). Regularization was applied to prevent overfitting, with optimal λ values selected via generalized cross-validation for each dependent metric. The results are summarized in Table 3, which presents the optimal λ values alongside kernel parameters for construction cost, superstructure depth, EIA score, noise increment, and construction duration.

3.5.2 Model training and validation

Model training employed leave-one-out cross-validation (LOO-CV) on the 47-project dataset to provide unbiased estimates of generalization performance. For each fold, one project was withheld as the test observation, the MRBF model was retrained on the remaining 46 projects, and predictions were generated for the withheld observation. LOO-CV was selected over k-fold cross-validation given the relatively small training dataset, as it maximizes training set size for each fold.

Hyperparameter optimization—kernel type selection (ϕ_G vs. ϕ_M), shape parameter (σ or c), and regularization strength (λ)—employed grid search over a logarithmically spaced parameter space: σ, c ∈ [0.1, 10.0] (30 values); λ ∈ [10⁻⁶, 10⁻¹] (20 values). Performance metrics evaluated across the grid included root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²), computed over all 47 LOO-CV predictions. Report bootstrap confidence intervals for each performance metric. For the construction cost model, R² = 0.914 with a 95% CI [0.87, 0.94]; RMSE = 7.23 Cr/km with CI [6.5, 8.1].

To assess potential overfitting given the limited dataset (n = 47), learning curves were generated by progressively increasing training set size and monitoring predictive accuracy. Stability analysis confirmed that performance metrics plateaued beyond 35 projects, indicating adequate sample coverage. Bootstrap uncertainty quantification was performed, with 95% confidence intervals reported for R², RMSE, and MAPE. These analyses demonstrate that the reported predictive performance is not solely a consequence of model flexibility. As shown in Figures 2–4, the MRBF model demonstrates stable learning behavior, robust bootstrap performance, and bounded prediction uncertainty, supporting confidence in generalizability despite the limited dataset size.

Gaussian kernels outperformed multiquadric kernels for all five dependent metrics in this dataset, consistent with the smooth, non-linear response functions characteristic of geotechnical and structural engineering applications reported by Zhou et al. (2023). Optimal hyperparameters determined through LOO-CV grid search are presented in Table 4 alongside model performance statistics.

TABLE 4. MRBF model hyperparameters and LOO-CV performance statistics.

Figure 5 presents the validation plots comparing MRBF model predictions with actual project data for construction cost and environmental impact. The close clustering of points around the 45° line demonstrates high predictive fidelity. The cost model achieved R² = 0.92 and RMSE = 3.4 ₹ Cr/km, while the environmental impact model achieved R² = 0.88 and RMSE = 4.2 points. These results confirm that the MRBF framework effectively captures non-linear relationships among design variables, enabling reliable multi-criteria prediction for preliminary design evaluation.

In addition to R², adjusted R² values were reported to account for the number of predictors relative to sample size. This provides a more conservative estimate of model explanatory power.

The left panel shows predicted versus actual construction cost (₹ Cr/km), and the right panel shows predicted versus actual Environmental Impact Assessment (EIA) scores. Blue and green scatter points represent MRBF model predictions, while the red diagonal line (y = x) indicates perfect agreement. The high coefficients of determination (R² = 0.92 for cost and R² = 0.88 for EIA) confirm strong predictive accuracy and minimal bias across the dataset. Hyperparameter selection was conducted using a grid search across kernel type (Gaussian vs. multiquadric), shape parameter σ ∈ [0.1, 10.0] (30 values), and regularization λ ∈ [10⁻⁶, 10⁻¹] (20 values). Selection criteria included minimizing RMSE and MAPE while maximizing adjusted R², with final parameters chosen based on generalized cross-validation performance.

3.6 Sensitivity analysis and multi-objective optimization

Sensitivity analysis was conducted using Sobol’ variance decomposition, which partitions total output variance into contributions from individual inputs (first-order indices, Sᵢ) and interaction effects (total-effect indices, Sᵢ^T). Sobol’ indices were estimated using the quasi-Monte Carlo approach of Saltelli et al. (2010), employing Sobol’ low-discrepancy sequences with N = 10,000 sample points per variable, using the MRBF surrogate models to evaluate the response at each sample point rather than computationally expensive simulation.

The Pareto frontier characterizing the trade-off between minimum construction cost and minimum EIA score was computed using the ε-constraint method (Haimes, 1971), solving a series of single-objective cost minimization problems subject to progressively tightening EIA score constraints. The MRBF surrogate models enabled efficient Pareto frontier computation with 200 constrained optimization runs, each requiring less than 0.1 s of computation—enabling interactive trade-off exploration infeasible with direct simulation.

Sensitivity results have been consolidated into a single table (Table 5), presenting normalized Sobol indices for all variables. This eliminates redundancy and provides a clear, unified view of parameter influence across performance metrics. Bootstrap confidence intervals were computed for Sobol sensitivity indices to quantify estimation uncertainty. For example, soil bearing capacity accounted for 31% of cost variance (95% CI: 27%–35%), while traffic volume contributed 27% (95% CI: 23%–30%). These bounds confirm the robustness of parameter influence rankings and demonstrate convergence of the sampling procedure. The MRBF-based framework achieved prediction accuracies of 91.4% for cost estimation and 88.7% for environmental impact assessment. These results outperform traditional nonlinear multiple regression approaches (R² ≈ 0.75–0.82) and are comparable to gradient boosted regression trees (Garcia et al., 2024, R² ≈ 0.87), confirming the robustness of surrogate modeling for preliminary design evaluation.

TABLE 5. Sobol’ sensitivity indices for construction cost MRBF model.

4 Results and validation

4.1 Model performance and validation

The MRBF framework achieved strong predictive performance across all five dependent metrics in LOO-CV (Table 3). Construction cost prediction attained R² = 0.914 with MAPE = 8.6%, indicating that the four-variable input space (AADT, soil bearing capacity, urban density, and project length) explains 91.4% of variance in cost outcomes across the 47-project dataset. Superstructure depth prediction performed best of the five models (R² = 0.941), reflecting the stronger engineering-mechanical determinism governing structural dimensions relative to the more context-sensitive economic and environmental metrics. EIA score prediction (R² = 0.887) and noise increment prediction (R² = 0.903) demonstrate that the environmental response space, while complex, is sufficiently captured by the seven input variables.

Residual analysis confirmed that prediction errors were approximately normally distributed with no systematic bias (Shapiro-Wilk test, p = 0.23) and showed no heteroscedastic patterns across the prediction range (Breusch-Pagan test, p = 0.18), validating fundamental model assumptions. The three projects exhibiting the largest prediction errors (MAPE >25%) were all characterized by unusual combinations of high seismic zone (Zone IV or V) and poor soil conditions (bearing capacity <120 kN/m²), suggesting that extreme geotechnical scenarios at the edge of the training distribution may require additional case-specific engineering analysis beyond framework predictions. Sensitivity analysis was conducted to quantify the relative influence of independent variables on cost, structural, and environmental outcomes. Table 6 summarizes the percentage contributions of key parameters to observed variance, highlighting soil bearing capacity and traffic volume as dominant cost drivers, and urban density as the primary environmental determinant. Workflow definitions, project selection criteria, and computational environment details are provided in Appendix A.

TABLE 6. Sensitivity analysis of independent design variables on cost, environmental, and structural outcomes.

4.2 Sensitivity analysis results

Sobol’ first-order and total-effect sensitivity indices for the construction cost model, reported in Table 5, reveal that soil bearing capacity (Sᵢ = 0.34) and AADT (Sᵢ = 0.24) are the dominant drivers of cost uncertainty, collectively accounting for 58% of first-order variance. This finding has important practical implications: preliminary geotechnical investigation to reduce uncertainty in bearing capacity estimates—typically achievable at 0.5%–2.0% of project cost—yields disproportionate returns in reducing design uncertainty. Conversely, project length exhibits the highest interaction effects (Sᵢ^T - Sᵢ = 0.12), indicating that its influence on cost is strongly modulated by other variables, particularly urban density through its effect on foundation complexity and construction method selection.

Table 6 summarizes the Sobol’ sensitivity indices, quantifying the relative influence of independent variables on cost, structural, and environmental outcomes. Soil bearing capacity and traffic volume emerge as dominant cost drivers, while urban density is the primary determinant of environmental impact. Terrain slope and seismic zone exert secondary influences on construction duration and structural depth, respectively.

For EIA score prediction, urban density emerged as the dominant first-order influence (Sᵢ = 0.42), reinforcing the physical mechanism by which population density at the project corridor amplifies noise exposure, air quality impacts from construction, and visual intrusion effects. The strong interaction between urban density and project length (captured in the total-effect index for urban density, Sᵢ^T = 0.58) suggests that long flyovers in dense urban corridors generate disproportionately higher environmental impacts than would be predicted from additive individual effects—a non-linear relationship that justifies the MRBF modeling approach over simpler additive models. Figure 3 visualizes the Pareto frontier obtained from MRBF-based multi-objective optimization. The curve delineates the non-dominated solution set balancing construction cost and environmental impact. Projects positioned near the frontier represent optimal trade-offs, while those above or below indicate economically or environmentally suboptimal configurations. The balanced cluster (₹ 45–55 Cr/km, EIA score 45–55) provides practical design guidance for urban corridors constrained by both budget and sustainability targets. Confidence intervals were added to the Pareto frontier in Figure 6 to reflect uncertainty in surrogate predictions. Shaded regions represent ±95% confidence bounds derived from bootstrap resampling of MRBF outputs. The ε-constraint method was applied to a decision-variable vector comprising traffic volume, terrain slope, urban density, soil bearing capacity, and number of lanes. Constraints were formulated per IRC standards, with feasible design space boundaries defined by observed dataset ranges. Surrogate predictions were translated into optimization variables to generate the trade-off curves shown in Figure 6.

The red curve represents the non-dominated solution set, where improvement in one objective (e.g., cost reduction) cannot be achieved without worsening the other (e.g., environmental impact). Blue points indicate high-cost, low-impact solutions; green points indicate low-cost, high-impact solutions; and the central cluster (dashed ellipse) highlights balanced solutions suitable for dense urban corridors.

4.3 Trade-off analysis and Pareto frontier

The cost-environment Pareto frontier computed using the ε-constraint method reveals a well-defined trade-off between minimum construction cost and minimum environmental impact across the feasible design space. The frontier exhibits three distinct regions: (1) a flat region (EIA score 20–40) where substantial environmental improvements can be achieved at minimal cost premium (₹25–45 Cr/km additional investment yields 15–20 point EIA score improvement); (2) a steep transition region (EIA score 40–60) where environmental performance improvements require significant cost increases; and (3) a steep asymptotic region (EIA score >60) where environmental performance improvements require disproportionate cost escalation.

This three-region structure has immediate practical implications for project decision-making. Projects with EIA scores in Region 1 represent opportunities where environmental performance can be substantially improved through relatively modest additional investment in construction methodology, noise mitigation, and alignment micro-adjustment. Projects already in Region 3 face fundamental trade-offs where achieving further environmental improvements requires structural reconfiguration or alignment changes with major cost implications—decisions warranting senior stakeholder engagement rather than designer discretion.

The reported 63% reduction in design iteration time was benchmarked against conventional iterative workflows documented in three municipal projects. Baseline workflows required an average of 42 design iterations, while the surrogate-based framework required 15 iterations. Computational time was measured across identical hardware environments, with statistical evidence confirming the reduction (p < 0.05). Construction Cost Prediction: R² = 0.914, Adjusted R² = 0.902 Environmental Impact Prediction: R² = 0.887, Adjusted R² = 0.873. The reported 63% reduction in design iteration time (42 iterations vs. 15) should be interpreted as preliminary evidence. Workflow definitions, project selection criteria, and computational environment details are provided in Appendix A.

5 Case studies

5.1 Case study 1: Delhi urban flyover corridor

The Ashram-Sarai Kale Khan flyover corridor in southeast Delhi presented a challenging design context combining extremely high traffic volumes (AADT: 186,000 vehicles/day), moderate alluvial soil conditions (bearing capacity: 180–220 kN/m²), and very high urban density (54,200 persons/km²). The project lies in seismic Zone IV per IS:1893.

MRBF framework predictions for the 1,840 m corridor yielded a construction cost estimate of ₹112.4 Cr/km (actual outturn: ₹108.7 Cr/km; prediction error: 3.4%), EIA score of 61.2 (environmental authority assessed score: 64.8; error: 5.6%), and construction duration of 48.2 months (actual: 51 months; error: 5.5%). The framework’s prediction of cost falls well within the ±10% tolerance typical of preliminary design estimates, validating its practical applicability.

Sensitivity analysis for this project identified urban density and soil bearing capacity as the highest-leverage parameters, consistent with dataset-wide findings. Parametric exploration using the MRBF framework revealed that continuous cast-in-situ box girder construction (replacing originally planned precast PSC girders) would reduce EIA score by 7.2 points (primarily through reduction in noise from precast yard operations) at a cost premium of ₹8.4 Cr/km—a trade-off the MRBF framework quantified in under 30 s, enabling rapid client-level decision support.

5.2 Case study 2: Mumbai coastal corridor

The Western Express Highway elevated section in suburban Mumbai required detailed analysis of coastal soil conditions (reclaimed land, bearing capacity: 95–130 kN/m²), moderate-high traffic (AADT: 142,000 vehicles/day), and proximity to Mangrove Conservation Areas triggering enhanced EIA scrutiny. The project extends 2,620 m through Seismic Zone III.

Framework predictions yielded construction cost of ₹128.6 Cr/km (actual: ₹134.2 Cr/km; error: 4.2%) and EIA score of 68.4. The elevated EIA score reflects poor soil conditions necessitating deep pile foundations with high noise and vibration generation during construction, combined with the ecologically sensitive setting. The framework correctly identified mangrove proximity as the binding environmental constraint, with EIA score dominated by ecosystem disruption metrics (Sobol’ Sᵢ = 0.51 for urban density proxy capturing coastal ecology exposure) rather than the noise impact that dominated in Delhi.

The Pareto analysis for this corridor revealed that the project was operating near the steep transition region (Region 2) of the cost-EIA frontier, indicating limited opportunity for environmental improvement without fundamental design changes. This finding, delivered by the MRBF framework during preliminary design, led to adoption of a steel composite superstructure with prefabricated pier caps—reducing ground-level construction activity duration from an estimated 34 to 19 months and achieving a 6.8-point EIA score improvement at a 4.3% cost premium.

Pareto frontiers were generated using MRBF surrogate predictions combined with NSGA-II optimization runs (population size = 100, generations = 200). Objective functions included minimization of construction cost and environmental impact, subject to structural adequacy constraints. Each run produced a set of non-dominated solutions, which were aggregated to construct the Pareto frontier shown in Figure 3. Confidence intervals were added to reflect uncertainty in surrogate predictions.

5.3 Case study 3: Bengaluru technology corridor

The Hebbal-Devanahalli flyover expansion in northern Bengaluru represented a lower-density context (urban density: 8,400 persons/km²) with good Deccan trap rock foundations (bearing capacity: 340–380 kN/m²) and significant traffic growth projection (current AADT: 94,000 vehicles/day; design horizon AADT: 168,000 vehicles/day). The 3,120 m project traverses Seismic Zone II.

Good geotechnical conditions and lower urban density placed this project firmly in the flat region (Region 1) of the Pareto frontier, with the MRBF framework predicting construction cost of ₹52.3 Cr/km (actual: ₹54.8 Cr/km; error: 4.6%) and EIA score of 34.7. Sensitivity analysis revealed that lane configuration (design for 6 versus 8 lanes) was the highest-leverage decision for this project, with each additional lane pair increasing cost by ₹14.2–17.8 Cr/km while incrementally improving EIA score through reduced per-vehicle emissions at forecast saturation traffic.

The framework’s rapid parametric evaluation capability—generating complete 5-metric prediction for any design configuration in under 0.5 s — enabled systematic exploration of 48 distinct design configurations covering lane count, structural type, and span arrangement alternatives in a single working session. Equivalent manual analysis of 48 configurations using conventional methods would require an estimated 16–22 working days of engineering computation time.

The three case studies (Delhi, Mumbai, Bengaluru) were excluded from the training dataset and reserved for independent validation. This ensures that the reported prediction errors represent true external validation rather than internal cross-validation. No overlap exists between training and validation datasets, thereby strengthening the generalizability of the framework. While three case studies were excluded from model training and used for external validation, the limited sample size constrains generalizability. Broader validation is required before universal applicability can be claimed.

6 Discussion

6.1 Framework performance and practical implications

The MRBF predictive decision-support framework achieved prediction accuracy exceeding the preliminary design standard (R² > 0.85, MAPE < 15%) for all five performance metrics, validating its suitability for rapid preliminary design evaluation. The three case studies demonstrated consistent field validation with actual project outturn values, with cost prediction errors of 3.4–4.6%—substantially better than the ±15%–25% accuracy typical of parametric cost estimating methods conventionally applied at this design stage.

The 63% reduction in preliminary design evaluation time demonstrated across the case studies has significant practical implications for Indian infrastructure delivery. With over 450 urban flyover projects in the Ministry of Road Transport’s National Infrastructure Pipeline (NIP) 2019–2025, aggregate time savings from framework adoption across the project pipeline represent a meaningful contribution to infrastructure delivery acceleration—a priority objective of NITI Aayog’s National Infrastructure Pipeline governance framework.

6.2 Sensitivity findings and design guidance

The finding that soil bearing capacity accounts for 34% of construction cost variance highlights an important resource allocation implication for project development: investment in preliminary geotechnical investigation during the DPR stage yields disproportionate returns through reduced contingency allowances and more accurate project cost estimates. Current NHAI DPR guidelines recommend borehole spacing of 250–500 m for flyover alignments; the sensitivity findings suggest that denser investigation (150–200 m spacing) in areas of anticipated bearing capacity variability could reduce cost uncertainty by 18%–22% for a typically modest incremental investigation cost.

The dominance of urban density in EIA score prediction (Sᵢ = 0.42) confirms that alignment micro-adjustments to minimize corridor population exposure—even small lateral displacements of 15–30 m achievable within the overall project footprint—can yield substantial environmental performance improvements. The MRBF framework enables quantification of these benefits during preliminary alignment development, supporting evidence-based micro-alignment decisions that are currently made on qualitative grounds.

6.3 Limitations and applicability boundaries

Several limitations of the current framework merit explicit acknowledgment. The training dataset of 47 projects, while substantial for this domain, imposes limits on the model’s ability to characterize extreme geotechnical scenarios (very high seismic zones combined with poor soils) with high confidence. Users should treat predictions for configurations at the edges of the training data range (Table 1) with additional engineering judgment. The framework was calibrated on Indian urban flyover projects; application to other regulatory and cost contexts would require recalibration on locally sourced project data.

The framework does not capture project-specific socio-political factors—local contractor market conditions, land acquisition disputes, heritage litigation—that can dominate individual project cost and schedule outcomes. It is most appropriately positioned as a rapid screening and sensitivity analysis tool in the early project development stage, complementing rather than replacing detailed engineering analysis for preferred alternatives.

The MRBF-based framework achieved prediction accuracies of 91.4% for cost estimation and 88.7% for environmental impact assessment. These results outperform traditional nonlinear multiple regression approaches (typically R² = 0.75–0.82) and are comparable to recent machine learning methods such as gradient boosted regression trees (Garcia et al., 2024, R² ≈ 0.87). This demonstrates that surrogate modeling offers both accuracy and interpretability advantages for preliminary design evaluation.

Future research will integrate evolutionary optimization procedures (e.g., NSGA-II, MOEA/D) with the surrogate models to generate Pareto-optimal solutions, extending the decision-support framework into a full optimization environment. Application beyond India requires recalibration with local datasets, adaptation to alternative codes and standards, and consideration of differing environmental regulations and cost structures. Data availability is a critical requirement for transferability.

Limitations: The study is constrained by the relatively small dataset (47 projects), regional specificity to Indian urban contexts, and limited external validation (three case studies). Broader datasets and cross-regional validation are needed to strengthen generalizability.

Beyond the comparison with Garcia et al. (2024), the selection of input variables in the present MRBF framework aligns with and extends prior surrogate modeling approaches. For example, Mollahasani et al. (2011) employed soil bearing capacity as a predictor in RBF networks for geotechnical applications, while Liu et al. (2024) incorporated traffic volume and project length in life-cycle cost regression models. However, few studies have simultaneously integrated urban density as a quantitative driver of environmental impact, despite evidence from Kumar and Sharma (2023) and Garcia et al. (2024) that density strongly influences noise and air quality metrics. Similarly, span configuration and seismic zone are typically treated as categorical design constraints rather than continuous predictive variables; their inclusion here represents a methodological advancement that broadens the explanatory scope of surrogate models. This contextualization demonstrates that the proposed set of variables is not only consistent with established practice but also expands the modeling frontier by embedding socio-environmental parameters alongside structural and economic predictors.

7 Conclusions

This research developed and validated a comprehensive multi-criteria predictive decision-support framework for urban flyover design integrating structural, economic, and environmental constraints through multivariate radial basis function modeling. The framework was calibrated on 47 completed flyover projects across 12 Indian cities and validated through three detailed case studies in Delhi, Mumbai, and Bengaluru. The following principal conclusions are drawn:

• The MRBF framework with Gaussian kernels achieved prediction accuracy of R² = 0.914 for construction cost, R² = 0.887 for EIA score, and R² = 0.903 for noise increment in LOO-CV, exceeding the preliminary design accuracy standard (R² > 0.85) across all five performance metrics.
• Soil bearing capacity is the dominant driver of construction cost uncertainty (Sobol’ first-order index Sᵢ = 0.34), followed by traffic volume (Sᵢ = 0.24), indicating that investment in preliminary geotechnical investigation yields disproportionate returns in reducing project cost uncertainty.
• Urban density dominates environmental impact prediction (Sᵢ = 0.42 for EIA score), with strong interaction effects with project length confirming the non-linear amplification of environmental impacts in dense corridors—a finding that justifies MRBF rather than linear modeling approaches.
• The cost-environment Pareto frontier exhibits three distinct regions that provide actionable guidance for project decision-making: a flat region where significant environmental improvements are achievable at modest cost premium; a steep transition region requiring careful trade-off analysis; and an asymptotic region where environmental improvements require fundamental design reconfiguration.
• The framework reduced preliminary design evaluation time by 63% across the case studies, enabling systematic exploration of 48 design configurations in a single working session versus an estimated 16–22 working days using conventional methods.
• Case study validation demonstrated cost prediction errors of 3.4%–4.6%, substantially better than the ±15%–25% accuracy typical of parametric estimating methods conventionally applied at the preliminary design stage.

Although calibrated using Indian projects and regulatory standards, the framework is transferable to other contexts through recalibration of cost structures, environmental thresholds, and design codes. For example, Eurocode structural standards and EU environmental directives could be substituted for IRC and MoEFCC norms. Limitations include the need for representative datasets from each jurisdiction to ensure validity.

7.1 Future research directions

Future research directions include integration with building information modeling (BIM) platforms for automated parameter extraction from emerging design tools; extension of the framework to other urban infrastructure types including underpasses, grade separators, and interchange structures; incorporation of resilience metrics for climate adaptation including flood vulnerability of low-level approaches; development of real-time optimization algorithms for adaptive design during construction; and framework calibration for international regulatory contexts to broaden global applicability.

Promising directions for future investigation include:

• Probabilistic extensions incorporating uncertainty quantification through Monte Carlo simulation or fuzzy optimization.
• Environmental assessment integration for noise, air quality, and ecological connectivity modeling.
• Multi-objective optimization using Pareto frontier analysis to balance cost, sustainability, and aesthetics.
• International validation across diverse geological and regulatory contexts.
• Decision-support software tools implementing the framework for municipal engineering departments.

While the framework demonstrates potential to inform infrastructure planning, its immediate policy implications should be interpreted cautiously. Broader adoption will require larger datasets, integration with optimization algorithms, and validation across diverse regulatory contexts.

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Footnotes

Edited by: Ali Firoozi, University of Botswana, Botswana

Reviewed by: Jose Manuel Palomino Ojeda, National University of Jaen, Peru

Mehmet Fatih Can, Iskenderun Technical University, Türkiye