Non-dominated Genetic Algorithm Research Articles

Sustainable optimisation of SMEs closed-loop supply chain for lithium battery manufacturing

Maintaining the sustainability of small and medium-sized enterprises (SMEs) supply chain has positive impact on society. Under the ripple effect, the vulnerability of the SMEs supply chain and the collaboration uncertainty of participants have potentially negative impact on the sustainability that cannot be ignored. We consider the closed-loop SMEs supply chain network design based on the risk propagation to improve the triple sustainability. The basis of the simulation model structure is a bi-level multi-objective mixed-integer linear programming model that aims to maximise triple sustainability, and an improved dynamic non-dominated genetic algorithm (DNSGA2) is designed to solve the problem. An SMEs supply chain for closed-loop manufacturing of lithium batteries in China was considered. The results show that the centralised SMEs supply chain preform better when the supply-demand imbalance, and the distributed network structure is preform better in maintaining sustainability when manufacturer capacity imbalances. Supply chain managers should develop more flexible strategies based on the structure of downstream demand, increasing upstream manufacturers' participation to enhance their viability and improve the sustainability of the supply chain.

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

The PVT limit for gear scuffing assessment

The growing interest in gear scuffing research primarily stems from the escalating standards and operation requirements in aero-engines and electric vehicles, particularly under high-temperature, high-speed, and heavy-load conditions. Existing calculation standards for gear scuffing often deviate when evaluating the load-carrying capacity under different rotational speeds or oil temperatures, thus undermining the reliability of gear scuffing assessments. To address this, thirty-five sets of gear scuffing experiments were conducted with different materials, manufacturing processes, and lubrication conditions. A new evaluation method based on the pressure-velocity-temperature (PVT) limit was proposed for assessing gear scuffing resistance. Using a non-dominated genetic algorithm, exponent coefficients for the contact pressure P, sliding velocity V, and lubricant temperature T were determined. The results demonstrated that the proposed PVT limit effectively evaluates gear scuffing resistance across various conditions. The PVT limits across different operating scenarios, under the same material, manufacturing process, and lubrication conditions, showed a maximum deviation of 6.6%. Conversely, the scuffing temperatures calculated using ISO 6336-20-2017 and AGMA 925-A03-2003 standards deviate from experimental results by up to 36.7% and 32.8%, respectively. Further application of the PVT limit to an aero-engine accessory gearbox confirmed the practical applicability of the proposed method.

Design and multi-objective optimization of hybrid process of membrane separation and electrochemical hydrogen pump for hydrogen production from biogas

A new hybrid process for hydrogen (H2) production that including membrane separation, electrochemical hydrogen pump (EHP) and steam methane reforming (SMR) was proposed. Firstly, the combination of two different membranes (PEO-CA) is applied to upgrade the biogas and capture CO2. Secondly, to avoid the toxic effect of CO on the EHP catalyst and, more importantly, to improve the H2 purity, the reforming reaction module is supplemented with water gas shift after the SMR. Finally, EHP is used to achieve high purity hydrogen. Simultaneously, the heat and power integration are considered to improve system efficiency. Sensitivity analysis, maximal information coefficient method and response surface methodology are applied to establish the correlation between objectives and parameters. Then, the second generation multi-objective non-dominated genetic algorithm (NSGA-II) is utilized to achieve minimum levelized cost of hydrogen (LCoH) and carbon emission per unit of hydrogen (ECO2). The optimized LCoH is 2.72 $/kgH2, and the ECO2 is 3.24 kgCO2e. Multi-stage membrane carbon capture process enhances CH4 conversion in SMR. The application of EHP reduces energy consumption and enhances hydrogen yield compared to PSA. The innovative use of membrane is hybridized with EHP to achieve the system intensification. The new hybrid process has a significant advantage in terms of ECO2 (37.45% reduction), although the price is higher compared to conventional biogas-to-hydrogen processes. Thus the new process is a promising low-carbon hydrogen production process from biogas.

Water Contaminant Detection and Water Purification of Household Drinking Water Using a New Stacking Ensemble Model

ABSTRACTContaminated drinking water sources pose a significant health risk worldwide. Monitoring programs for drinking water quality aims to ensure safe water supply by informing management practices. Improved online monitoring of water systems is necessary as current lab‐based methods are slow and do not offer real‐time public health protection. Rapid detection and response to potential contamination events are crucial to mitigate health risks. Mark of‐purpose water treatment strategies offer a reasonable method for upgrading drinking water quality at the family level and forestalling waterborne illnesses. This study focuses on collecting household drinking water and utilizing various sensors to measure parameters such as pH, turbidity, water level, temperature, and humidity. A consistent water quality noticing system using the stacking outfit model, which solidifies Bayesian association and decision tree techniques, is proposed in this article. Bayesian network analyzes the input data attained from sensors collecting real‐time data and concludes whether the data represents the contamination event. DTs are utilized to demonstrate the connections between multivariate water boundaries utilized in the review. Afterward, a multiobjective, such as a biobjective optimization model and a nondominated genetic algorithm (NGA) are used in this work of optimization to minimize the volume of contaminated water. After the pollution in the water is identified, water decontamination processes are done given point of purpose medicines like ceramic channels and solar water disinfection (SODIS). The method outlined is executed through Python software. The findings indicate that the estimated values for PH, temperature, and turbidity are 7.3, 31.8, and 0.77, respectively. However, the proposed method is compared with the existing C‐NSGA‐II, while compared to this method, the proposed system produces improved cost functions. Consequently, suitable water treatment and supply should be considered to reduce the effects on people's health as well as to improve living conditions, respectively.

Research on multi-objective optimization method in the design of high-power nanocrystalline alloy high-frequency transformer

The optimization design of high-frequency transformer (HFT) is a multi-objective optimization problem owing to the mutual constraints between design parameters such as power density, efficiency and temperature rise, and traditional design methods often face difficulties in balancing and selecting multiple design parameters. Therefore, this paper derives the structural parameters of HFT, calculates the magnetic core losses and winding losses considering temperature effects, and establishes a 7-node thermal network model. Selecting power density and efficiency as optimization objectives, the HFT is optimized based on multi-objective particle swarm optimization algorithm and non-dominated genetic algorithm, and compared with traditional free parameter scanning method to analyze the advantages of intelligent optimization algorithm. Further, the influence of temperature rise calculation methods on the optimization design results of HFT is compared and analyzed. Finally, a nanocrystalline HFT with 17 MW/m3 power density and 99 % efficiency and an optimization scheme of HFT with 26 MW/m3 power density and 99.2 % efficiency are designed based on the proposed optimization design processes. The effectiveness of the calculation model and optimization method is verified through experimental measurement, and the essential principle of improving the HFT performance through optimization methods is explored through finite element simulation, providing theoretical reference and data support for the optimization design of nanocrystalline HFT.

Structure optimization of intercooler bionic fins based on artificial neural network and genetic algorithms

The bionic fins inspired by the shark are proposed to enhance the thermal-hydraulic performance of the intercoolers in this work. The geometric parameters of the fins are investigated to examine the effects on thermal-hydraulic performance. The height and width of protrusions are chosen as optimization parameters based on the results of the geometric parameter analysis. Non-dominated genetic algorithms are combined with artificial neural networks to obtain the optimal solution for the geometry parameters. The artificial neural networks used in this study exhibit a reliable accuracy with errors below 10 % (with mostly remaining below 5 %). The optimal values for the height and width of the protrusions are determined to be 1.01 mm and 0.82 mm, which results in a Colburn factor of 0.01923 and a comprehensive index of 0.04305. Compared with the original design, the optimized structure yields 17.69 % and 4.77 % increments for the Colburn factor and comprehensive index. Compared with the original model, the intercooler with the optimal structure exhibits a 9.9 % increase in entropy generation and a 20.2 % enhancement in the exergy difference between the inlet and outlet.

Design of Inner Ribs with Unequal Stiffness for Deep-Sea Highly Pressure-Resistant Cylindrical Shells and Utilizing NSGA-2 for Lightweight Optimization

For conducting scientific research at depths in the ocean, deep-sea probes are essential pieces of equipment. The cylindrical shell is the most sensible and rational packaging structure for these detectors. New technical challenges for enhancing the pressure resistance and lightweight design of the pressure-resistant cylindrical shell arise from the need to ensure that the detector packaging structure can withstand the immense water pressure at tens of thousands of meters in the underwater environment, while simultaneously reducing the detector packaging structure’s self-weight. This article examines the detection system’s deep-sea pressure-resistant cylindrical shell. To address the issue of the pressure-resistant shell’s insufficient ability to counteract the overall instability caused by the inability to form unstable half-waves in the radial direction when the ring rib pressure-resistant shell experiences it, a design method for the ribs inside the unequal-stiffness pressure-resistant cylindrical shell is suggested. The shell’s instability pressure increases by 9.65 MPa following the stiffness adjustment. Simultaneously, in order to attain even more lightweight optimization, the optimal inner rib section was obtained by applying the orthogonal topology optimization method, which also reduced the weight by 106.8 g and effectively improved the compression stability of the high-pressure cylindrical shell structure. Based on this, key optimization variables were found by performing sensitivity analysis on the cylindrical shell structure’s parameters. Then, with lightweighting as the primary objective, the high-pressure-resistant cylindrical shell’s optimal structural parameters were found using a multi-objective optimization process using the second-generation fast non-dominated genetic algorithm (NSGA-2). This resulted in a weight reduction of 1.2492 kg, or 17.26% of the original pressure-resistant shell. This has led to the development of a lightweight, highly pressure-resistant method for packaging marine exploration equipment structures.

Using different Heuristic strategies and an adaptive Neuro-Fuzzy inference system for multi-objective optimization of Hybrid Nanofluid to provide an efficient thermal behavior

The importance of multi-objective optimization in hybrid nanofluid research lies in its wide-ranging applications across fields such as microelectronics, aerospace, and renewable energy. These specialized fluids hold the potential to elevate the performance and efficiency of diverse systems through enhanced heat transfer capabilities. This research endeavor is centered around optimizing a hybrid nanofluid composed of Silicon Oxide-MWCNT-Alumina/Water by leveraging a mix of heuristic approaches and an adaptive neuro-fuzzy inference system. To this end, the most influential set of input parameters has been identified using four state-of-the-art algorithms: Non-dominated Genetic Algorithm, multi-objective particle swarm optimization, Strength Pareto Evolutionary Algorithm 2, and Pareto Envelope-based Selection Algorithm 2. The goal of the optimization process is to modify the temperature (T = 20 °C to 60 °C) and the volume fraction of nanoparticles (SVF=0.1 % to 0.5 %). Finding the optimal combination of these parameters that results in the hybrid nanofluid with the maximum thermal conductivity (knf) and the lowest dynamic viscosity is the main objective. The findings of this research have the potential to drastically improve the performance of systems in a variety of applications and to change the creation of sophisticated, high-efficiency heat transfer fluids.

The Impact of Dual Objective Optimization Model Combining Non-Dominated Genetic Algorithm on Rural Industrial Ecological Economy

The Impact of Dual Objective Optimization Model Combining Non-Dominated Genetic Algorithm on Rural Industrial Ecological Economy

Enhanced methanol reforming gas fuel cell system with electrochemical hydrogen pump: Conceptual design, system analysis, and multi-objective optimization

In this work, two methanol-reforming gas fuel cell systems coupled with an electrochemical hydrogen pump (EHP), namely, EHP pre-coupling and post-coupling fuel cell systems were proposed to achieve performance enhancement. A back propagation neural network surrogate model was established for the two systems to accurately describe system behavior, and a second-generation multi-objective non-dominated genetic algorithm was utilized for addressing the multi-objective optimization problem encompassing net output power, carbon mass-specific emission and the levelized cost of electricity. The linear non-weighted multi-attribute preference and technique for order preference by similarity to ideal solution multi-attribute decision-making methods were employed to select the optimal solutions. The optimized EHP pre-coupling fuel cell system exhibited lower carbon emissions (0.69 kgCO2/(kW·h)) and higher net output power (126.02 kW) compared to previous studies. While the EHP post-coupling system achieves a lower levelized cost of electricity (0.36 USD/(kW·h)), and stronger system stability (total efficiency reduction less 1 %). Both EHP-coupling systems offer viable process enhancements for fuel cell systems.

Multi-objective optimization of heat transfer of ice slurry in corrugated tubes using response surface methodology method and genetic algorithm

The aim of this research is to perform an optimal design of corrugation parameters of transverse corrugated tube in terms of Nusselt number, drag coefficient and comprehensive heat transfer factor of ice slurry as triple-objective function by utilizing response surface methodology (RSM) and non-dominated genetic algorithm (NSGA-II). In this article, the RSM is adopted to determine the functional relationship between the three target characteristics and the five factors based on the numerical calculation data. And the model is subjected to variance analysis and two-factor interaction contour. It turns out that the relative error between the values fitted by the model excluding the insignificant factors and the CFD simulated values is not higher than 10 %. The highest significance of the flow velocity (u) to average Nusselt number (Nuc) of corrugated tubes is observed. For the average resistance coefficient (fc) of corrugated tubes, the sensitivity of corrugation height-to-diameter ratio (H/D) is slightly higher than that of corrugation pitch-to-diameter ratio (P/D), corrugation width-to-diameter ratio (W/D) and the flow velocity (u). For comprehensive heat transfer factor (PEC), the sensibility of P/D to PEC is remarkable when 1.0<P/D<1.4. The NSGA-II is utilized to achieve the Pareto-optimal solution set for the triple objective characteristics. Taking into account the perspective of equilibrium target characteristics, the optimal value of u is 3.9974 m/s, the optimal value of H/D and ice concentration (α) are 0.7996 and 10.04 %, respectively. And the optimal domain of the values of P/D, W/D, and H/D are from 1.4235 to 1.5253, and from 0.1065 to 0.1172, respectively.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently, reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering. However, for deep foundation pit, evaluating the system safety of retaining structures and finding cost-effective design points are main challenges. To address this, this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou, China. The proposed method included two parts: system reliability model and robust design method. Back Propagation Neural Network (BPNN) is used to fit limit state functions and conduct efficient reliability analysis. The common source random variable (CSRV) model are used to evaluate correlation between failure modes and determine the system reliability. Furthermore, based on the system reliability model, a robust design method is developed. This method aims to find cost-effective design points. To solve this problem, the third generation non-dominated genetic algorithm (NSGA-III) is adopted. The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm. The proposed method has a good performance in locating the balanced design point between safety and construction cost. Moreover, the proposed method can provide design points with reasonable stiffness distribution.

Lightweight sound insulation optimization of simply supported locally resonant plate

A theoretical model of the normal sound insulation of a rectangular locally resonant (LR) plate with simply supported boundary conditions is established. The accuracy of the model is verified through comparison with finite element simulation results. Considering a 1-m2 aluminum plate as the research object, a non-dominated genetic algorithm is introduced. The algorithm optimizes the lightweight sound insulation of an LR finite plate with a center frequency band of 20–800 Hz as the optimization objective of maximum average sound insulation and minimum mass. The optimization parameters are substrate thickness and local resonance parameters (including resonator target frequency (fobj), number of resonators, additional mass ratio, and resonator damping). Optimization results indicate that the average sound insulation fluctuates at approximately 2 dB due to changes in fobj. The results also provide an optimal solution to the algorithm. The optimal sound insulation value curve of LR plates corresponding to different surface densities of intermediate improved cases is fitted and compared with the sound insulation value of an equal-mass bare plate. Under lightweight optimization, the resonators are deemed capable of improving the local frequency band sound insulation. In contrast, the wideband average sound insulation can approximate but not surpass the insulation provided by the equal-mass bare plate. In practical applications, an LR plate that can improve the local frequency band sound insulation and ensure the overall lightweight sound insulation performance of the wide frequency band can be obtained. This can be achieved by analyzing the frequency spectrum of optimal points in the lightweight sound insulation optimization process. Relevant research can provide a basis for the evaluation and design of the low-frequency sound insulation of plates for transportation equipment, such as airplanes, high-speed trains, and cars.

Multi-objective diesel engine emission management and control technology based on SVM and NSGA-II

To improve the emission control effect of diesel engines, a pre-emission model for diesel engines using biofuels is constructed using support vector machine. Considering that traditional support vector machine training relies on initial parameters and is prone to local convergence, a genetic algorithm model is adopted to construct an improved diesel engine pre-emission model. At the same time, with the optimization goal of diesel engine emissions of particles and gases, the improved diesel engine pre-emission model is used to obtain emission data as training parameters. The second generation non-dominated genetic algorithm is introduced to construct a multi-objective diesel engine emission control model, achieving optimal control of diesel engine emissions. In the experimental analysis of diesel engine pre emission models, the proposed pre emission model has a better prediction effect in nitrogen oxides, with an average prediction accuracy of 0.986, which is better than the Particle Swarm Optimization-Support Vector Machine model's 0.906, and is more accurate in detecting emissions. Simultaneously predicting particulate matter, the average prediction accuracy of the proposed model is 0.978, while the prediction accuracy of the Particle Swarm Optimization-Support Vector Machine model is 0.902, indicating that the overall prediction effect of the proposed method is better. In the experimental analysis of multi-objective optimization models, the proposed multi-objective optimization model performs best in diesel emission optimization. The proposed model can achieve convergence in the shortest time, and the minimum nitrogen oxide emissions are 210.7 ppm. Compared with Non-dominated Sorting Genetic Algorithm II and Multi-Objective Particle Swarm Optimization models, the particle emission optimization effect is improved by 23.5 % and 18.6 %. From this, it can be seen that the proposed method has excellent performance in diesel engine emission monitoring and pollutant optimization, surpassing related technologies in the same period. The research technology provides important technical references for the monitoring and emission control of harmful substances in diesel engines.

Structure optimization of the battery thermal management system based on surrogate modeling of approximate and detailed simulations

The battery thermal management system is of critical significance to the safety and efficient operation of lithium-ion batteries (LIBs). In the battery thermal management system, inadequate structure parameters limit the performance of liquid cooling systems. In this article, a two-step surrogate model is constructed to optimize the structure of the liquid cooling system, which balances the performance and cost of the cooling system. The construction procedure of the two-step surrogate model consists of three parts: the generation of the approximate and detailed simulations, the construction and correction of the primary model, and the accuracy verification of the secondary model. The two-step surrogate model balances the accuracy and the spent resources, by using a large number of approximate simulations and just a few detailed simulations. Compared with the conventional single-step surrogate model, the time required to construct the two-step surrogate model is reduced by 1024 min, although the mean absolute error is increased just marginally from 0.3334°C to 0.3696°C. The cold plate structure optimization under different working conditions is completed by combining the second-generation non-dominated genetic algorithm. The variation of the flow channel diameter with the working conditions is analyzed. Taking the structure parameters when the maximum temperature is the minimum value as an example, the diameter of the flow channel decreases drastically with the increase of the battery heat generation rate at the beginning, and finally maintains at 3 mm. Moreover, the flow channel diameter tends to increase linearly with the increase of coolant flow rate.

Developing sustainable strategies by LID optimization in response to annual climate change impacts

Designing urban runoff drainage systems is prominent in effectively managing floods due to increasing impermeable regions worldwide. However, although urban runoff drainage systems are configured mainly based on rainfall analysis, climate change influences their hydrological properties substantially. This research introduces an innovative methodology to analyze climate variations on optimal low impact developments (LIDs) of urban drainage systems in historical periods based on annual impacts (AIs) in projection periods considering uncertainties assessments. First, Storm Water Management Model (SWMM) is employed for simulating the process of rainfall-runoff considering quality and quantity analyses. This simulation model is coupled with a non-dominated genetic algorithm- II (NSGA-II) optimization algorithm to minimize the cost of LIDs, flood volume, and pollutant load. Then, future runoff and daily rainfall are projected on a yearly basis, including maximum, minimum, and median rainfall, to identify how climate change affects catchment properties. These projections and an ensemble model are obtained based on the Long Ashton Research Station Weather Generator (LARS-WG), which considers uncertainties. After that, the projected daily precipitation is fragmented into hourly segments utilizing the change factor approach (CFA). Finally, the ideal optimum type, size, and placement of the chosen LIDs are determined using the presented simulation-optimization (SO) model. To prove the effectiveness and appropriateness of the presented framework, it is implemented in a real-world study area in Darabad catchment, Tehran, Iran. Results indicate that the developed optimal LIDs are well-designed and sufficient in both the historical and projection periods. The findings also depict that with the current LIDs established for the historical period, the flooding volume and summation of total suspended solid (TSS) and total Nitrogen (TN) removals are decreased by 55.96% and 60.2% compared to when LIDs are not adopted. In addition, employing the developed LIDs based on an ensemble model results in the runoff volume and pollutants removal decline of up to 31.39% and 46.9%, respectively.

Solving Bi-Objective Vehicle Routing Problems with Driving Risk Consideration for Hazardous Materials Transportation

Driving behavior is an important factor affecting the risk of hazardous materials transportation. In this paper, we propose a transport risk evaluation method that considers driving risk. We consider driving risk and establish a model of vehicle routing problems with a soft time window for the transportation of hazardous materials and design a non-dominated genetic algorithm to solve the bi-objective optimization model. Taking a network of 23 nodes and 38 road segments as an example, 59 pareto-optimal solutions were obtained for six drivers on nine different paths. Comparing different solutions, it was found that driving risk, road population density, and transportation distance have different impacts on transport cost and risk. Choosing drivers and routes can adjust the propensity of cost and risk, allowing the decision-maker to select a solution for allocating drivers and routing vehicles according to their risk preference.

Comparison of reflective coating with other passive strategies: A climate based design and optimization study of building envelope

The building envelope modification in terms of insulation material, glass material, orientation, window to wall ratio (WWR), reflective coating, etc., is vital to control the heat penetration in buildings. This article evaluates the effect of Passive methods (PMs) (such as windows layers, window colors, infiltration, insulation material, insulation location in wall and roof, and orientation) in the first scenario in controlling the heat gain by building envelope for 18 cities from different Indian zones of climate. Further, the study investigated two more scenarios of passive implementation, the second scenario is a reflective roof (RR) coupled with PMs, and the third scenario is a reflective roof and wall (RRW) associated with PMs in controlling the thermal environment. The second and third scenarios also evaluated the impact of reflective surfaces on the requirement of insulation thickness for the roof and wall. This work advances the sustainability potential by optimizing critical building design parameters utilizingthe Non-dominated Genetic Algorithm (NSGA-2), which reveals a considerable reduction in required energy demand. The mean absolute percentage error (MAPE) for average hourly temperature data collected between March 14 and March 18, 2022, is 4.18 with computational results. The obtained outcomes exhibit that PMs save 6–29 % of HVAC energy annually. Where infiltration rate for all climates except cold climate is 0.2 ACH; however, cold climatic cities are perceived in the range of 0.6–0.8 ACH and 0.2–0.4 ACH for Shillong and Srinagar, respectively. It can also be stated that double-layer green 6 mm/13 mm air windows would give the best optimum solution for all climates. A coupled system of PMs and RR has demonstrated an energy savings potential of 11–32%, depending upon the climatic regions. The obtained outcomes from PMs and RR coupled systems also significantly reduced insulation thickness.

Optimal design and cost analysis of water distribution networks based on pressure-dependent leakage using NSGA-II

Leakage from water distribution networks (WDNs) is inevitable. Therefore, during design a WDN, engineers add a percentage of each nodal water demand as leakage discharge to total node demand. The amount of leakage depends on the pressure, which is not known at the design stage. Considering a constant percentage of node demand in lieu of its leakage makes the problem worse. In this study, the effect of leakage on the optimal WDN design was investigated by developing the matrix form of the gradient algorithm while accounting for leakage using the pressure-dependent model. Non-dominated genetic algorithm version II (NSGA-II) was used as the optimization engine with two objectives which includes minimizing the network construction cost and minimizing the total network pressure deficiency. Two well-known two- and three-loop WDNs in literature were studied. The results indicated that the pressure-dependent leakage varies between 12.9 and 29.44% of the node demand while the network construction cost stays the same if compared with the fixed percentage leakage model, and the construction cost would increase by 17–31%, if leakage is not accounted for. This is expected the optimized diameters and hydraulic characteristics of the networks being affected by the leakage calculation method.