بهینه‌سازی چندهدفه هزینه و تاب‌آوری شبکه توزیع آب با MOGWO و EPANET

Abstract
Urban water distribution network (WDN) design is a critical component of water resources engineering, required to withstand challenges posed by population growth, rising demand, climate variability, and financial constraints. The design process is inherently multi-objective, nonlinear, discrete, and highly complex, as it involves simultaneous selection of pipe diameters from commercial options, satisfaction of hydraulic constraints, maintaining adequate pressure under critical conditions, and minimizing both capital and operational costs. Recent studies have highlighted the effectiveness of advanced evolutionary algorithms in tackling such complexities. This study proposes an innovative multi-objective framework based on the Multi-Objective Grey Wolf Optimizer (MOGWO) to minimize total network cost and maximize hydraulic resilience concurrently. Hydraulic analysis was performed using a detailed network model developed in EPANET 2.0, dynamically coupled with MATLAB for optimization. The framework was evaluated on the D-zone of the Mashhad WDN, comprising 265 pipes, a total length exceeding 38 km, one primary supply source, an area of 1,087 hectares, and a serviced population of 47,013. Results indicate that the proposed approach can reduce design cost by 18–25% while improving the hydraulic resilience index by 15–30%. Furthermore, compared with benchmark algorithms such as NSGA-II and MOPSO, MOGWO produced a more uniform Pareto front with superior diversity and faster convergence. Analysis of convergence behavior, pressure distribution, selected pipe sizes, and system performance under critical operating conditions confirms that the proposed model offers a reliable and cost-effective strategy for urban WDN design. 
 
Extended Abstract
Background and Objective
Water distribution networks represent a critical component of urban infrastructure, ensuring the delivery of safe water at adequate pressure. Rapid urbanization and aging pipelines have increasingly led to failures, pressure deficits, leakage, and reduced network reliability, highlighting the need for efficient design and rehabilitation strategies. The design problem is inherently multi-objective, requiring a balance between minimizing construction costs and maintaining sufficient hydraulic performance. Traditional design approaches are largely heuristic and unable to guarantee near-optimal solutions, whereas evolutionary algorithms have shown superior performance in complex optimization tasks. However, many of these algorithms suffer from drawbacks such as premature convergence, instability, or sensitivity to parameter tuning. The Multi-Objective Grey Wolf Optimizer (MOGWO), inspired by cooperative hunting behavior, has emerged as a robust alternative due to its effective balance between global exploration and local exploitation. This study proposes a novel MOGWO-based framework that minimizes network cost while maximizing resilience, and evaluates its effectiveness on the real-world D-zone distribution network in Mashhad.
 
Methodology
A concise three-stage framework was developed to address the complexity of water distribution network (WDN) design. The problem was first formalized by analyzing hydraulic behavior, operational constraints, design goals, and available pipe sizes. A tailored solution strategy was then constructed, in which the Multi-Objective Grey Wolf Optimizer (MOGWO) was adapted for discrete pipe-diameter selection. Implementation was carried out via a dynamic MATLAB–EPANET platform, enabling rapid iterative simulations and evaluation through convergence metrics and Pareto fronts.
WDN design must ensure reliable delivery of required flows and pressures under both normal and extreme conditions while remaining cost-effective. To avoid the fragility associated with cost-driven layouts, modern optimization also incorporates resilience, redundancy, and surplus energy. The design problem is formulated as selecting diameters from a discrete commercial set under two competing objectives—minimizing pipe cost and maximizing hydraulic resilience—subject to continuity, energy conservation using the Hazen–Williams equation, pressure limits, velocity bounds, and discrete diameter constraints.
EPANET 2.0 served as the hydraulic solver, with each MOGWO candidate fully simulated to obtain pressures, flows, and velocities for objective evaluation. The solver’s efficiency allowed extensive search without model simplification. Benchmarking confirmed the limitations of NSGA-II and MOPSO in discrete design spaces, motivating the choice of MOGWO. The algorithm’s hierarchical hunting mechanism balances exploration and exploitation, while solution diversity is maintained through non-dominated sorting, crowding distance, and an external archive. Discrete diameters were assigned using adaptive rounding with controlled stochastic perturbation.
The framework was validated on Mashhad’s Zone D, a medium-scale system with 265 pipes (38.16 km) and 217 demand nodes serving approximately 47,000 residents across varied topography. All geometric and hydraulic parameters were modeled in EPANET, providing a realistic testbed for evaluating cost–resilience trade-offs.
 
Findings
Four approaches—the consultant’s baseline design, MOGWO, NSGA-II, and MOPSO—were compared using Pareto fronts for two objectives: minimizing cost and maximizing resilience index (RI). The baseline design appeared as a single point with high cost (~13.9 billion IRR) and low RI (~0.292), reflecting weak hydraulic robustness.
MOGWO achieved the most favorable trade-off, reducing average cost by ~19% and increasing RI by ~27% relative to the baseline. Its Pareto front was smoother and more compact, supported by the α–β–δ leadership mechanism. NSGA-II produced moderately inferior results with wider dispersion due to crossover–mutation effects, while MOPSO generated a broad but unstable front, affected by particle-velocity oscillations.
Convergence analysis confirmed MOGWO’s superiority, reaching the optimal region within ~60 iterations, compared with ~110 for NSGA-II and persistent fluctuations for MOPSO. Statistical tests validated MOGWO’s significant advantage (p ≈ 0.03). Design inspection showed cost reductions through smaller diameters in low-demand branches and reinforcement of critical loops, balancing economy and resilience.
Overall, MOGWO delivered the best performance, combining cost efficiency, resilience improvement, rapid convergence, and robust Pareto solutions. NSGA-II offered slower but consistent results, MOPSO lacked stability, and the baseline design was weakest in both objectives.
 
Conclusion
Designing urban water distribution networks requires balancing cost efficiency with hydraulic resilience. This study introduces a framework based on the MOGWO and evaluates its performance on a real network in Mashhad (Zone D). Results show that MOGWO reduces total cost by 18–25% compared to the Consultant’s plan, while simultaneously improving resilience by 15–30%. These gains stem from intelligent pipe diameter allocation-downsizing low-demand branches and reinforcing critical loops-ensuring both economic efficiency and hydraulic reliability. Compared with NSGA-II and MOPSO, MOGWO demonstrated faster convergence, greater stability, and superior Pareto front quality. NSGA-II produced diverse but slower solutions, while MOPSO suffered from particle oscillations and irregular fronts. The α–β–δ leadership mechanism in MOGWO proved decisive for search robustness. Overall, MOGWO emerged as the most effective method, offering a practical and reliable tool for real-world water network design. Its integration with EPANET provides a fast, accurate computational framework, and the use of commercial diameters and real data confirms operational feasibility. These findings highlight MOGWO’s potential as a foundation for decision-support systems in urban water planning, with future work recommended on multi-period optimization, uncertainty analysis, and operational cost integration.