Multi-objective Optimization Method Research Articles

A dynamic multiple proximal bundle algorithm for locally Lipschitz multiobjective optimization problems

We propose a method for nonsmooth nonconvex multiobjective optimization problems that is based on a bundle-type approach. The proposed method employs an extension of the redistributed proximal bundle algorithm and uses an augmented improvement function to handle different objectives. In which, at each iteration, a common piecewise linear model is used to approximate the augmented improvement function. Contrary to many existing multiobjective optimization methods, this algorithm works directly with objective functions, without using any kind of a priori chosen parameters or employing any scalarization. Under appropriate assumptions, we discuss convergence to points which satisfy a necessary condition for Pareto optimality. We provide numerical results for a set of nonsmooth convex and nonconvex multiobjective optimization problems in the form of tables, figures and performance profiles. The numerical results confirm the superiority of the proposed algorithm in the considered test problems compared to other multiobjective solvers, in the computational effort necessary to compute weakly Pareto stationary points.

A steady-state weight adaptation method for decomposition-based evolutionary multi-objective optimisation

In decomposition-based multi-objective evolutionary algorithms (MOEAs), the inconsistency between a problem’s Pareto front shape and the distribution of the weights can lead to a poor, unevenly distributed solution set. A straightforward way to overcome this undesirable issue is to adapt the weights during the evolutionary process. However, existing methods, which typically adapt many weights at a time, may hinder the convergence of the population since changing weights essentially means changing sub-problems to be optimised. In this paper, we aim to tackle this issue by designing a steady-state weight adaptation (SSWA) method. SSWA employs a stable approach to maintain/update an archive (which stores high-quality solutions during the search). Based on the archive, at each generation, SSWA selects one solution from it to generate only one new weight while simultaneously removing an existing weight. We compare SSWA with eight state-of-the-art weight adaptative decomposition-based MOEAs and show its general outperformance on problems with various Pareto front shapes.

Multi-objective topology optimization design of silicon carbide metal oxide semiconductor field effect transistors power module liquid-cooled heatsink for electric vehicles

Silicon carbide (SiC) metal oxide semiconductor field effect transistors (MOSFETs) is gradually replacing silicon-based insulated gate bipolar transistor (IGBT) as the switching devices in electric vehicle power inverters due to its higher operating temperatures, switching speeds, and frequencyies. However, the high switching frequency of SiC MOSFETs can increase the losses of the power inverter, resulting in an increase in the temperature, which will limit the performance of power inverters. The improvement of power module performance is mainly controlled by optimizing its control methods during operation and improving its cooling system. Currently, the liquid-cooled heatsink used in power modules have disadvantages such as large flow resistance and poor heat dissipation performance. In order to enhance the performance of the heatsink, this study first established a three-dimensional finite element model of SiC MOSFETs power module based on a pin fin heatsink. The accuracy of the model was verified by numerical and experimental methods. Secondly, based on numerical analysis, a multi-objective topology optimization method for the power module liquid-cooled heatsink is proposed. This method takes heat exchange and fluid dissipation energy as the objective function and uses weight factors to adjust the influence of each on the objective functions. Additionally, the temperature distribution of the heatsink is considered to optimize its performance. Finally, the numerical results show that the topology-optimized heatsink exhibits better performance at high coolant volumetric flow rates. When the coolant volumetric flow rate is 14 L/min, the pressure drops of topology-optimized heatsink is reduced by 63.94 % and the junction temperature of the power module is reduced by 0.24 % compared with the pin fin heatsink. This topologically optimized heatsink could be helpful to improve the performance of existing power module heatsinks.

Multi-Objective Optimization for Thrust Allocation of Dynamic Positioning Ship

Thrust allocation (TA) plays a critical role in the dynamic positioning system (DPS). The task of TA is to allocate the rotational speed and angle of each thruster to generate the generalized control forces. Most studies take TA as a single-objective optimization problem; however, TA is a multi-objective optimization problem (MOP), which needs to satisfy multiple conflicting allocation objectives simultaneously. This study proposes an improved multi-objective particle swarm optimization (IMOPSO) method to deal with the non-convex MOP of TA. The objective functions of reducing the allocation error, and minimizing the power consumption and the tear-and-wear of thrusters under physical constraints, are established and solved via MOPSO. To enhance the global seeking ability, the improved mutation strategy combined with the roulette wheel mechanism is adopted. It is shown through test data that IMOPSO converges better than multi-objective algorithms such as MOPSO and nondominated sorting genetic algorithm II (NSGA-II). Simulations are conducted for a DP ship with two propeller–rudder combinations. The simulation results with the single-objective PSO algorithm show that the proposed IMOPSO algorithm reduces thrust allocation errors in the three directions of surge, sway, and yaw by 48.48%, 39.64%, and 15.02%, respectively, and reduces power consumption by 44.53%, which demonstrates the feasibility and effectiveness of the proposed method.

Multi-objective optimization and thermodynamic assessment of a solar unit with a novel tube shape equipped with a helical tape

The performance of several heat transfer mechanisms, including solar energy sources, is being improved through optimization, which also effectively supports the most efficient feasible design. A numerical study has been done on a turbulator-enhanced flat plate solar collector (FPSC) while also introducing the utilization of a quad-lobed tube as a pioneering innovation in the system’s design. The incorporation of nanoparticles into the working fluid was implemented to enhance performance, with aluminum oxide particles selected for this purpose. Furthermore, assessing the second law and analyzing exergy generation was employed to discern irreversibility within the system. Optimization of both geometric and non-geometric elements has been accomplished through the integration of a multi-objective optimization (MOO) method with machine learning (ML). Random Forest (RF), LASSO Regression (LaR), and Support Vector Regression (SVR) are the machine learning models that were utilized in order to ascertain the correlations that exist between the system’s inputs and outputs. According to the findings, RF was found to be the most appropriate algorithm for capturing the impacts of parameter variations. This was demonstrated by the high coefficient of determination (R2) quantities that RF possessed, which were 0.95, 0.99, and 0.99 for friction factor (f), exergy loss (Xd), and second law effectiveness (ηII), respectively. However, the SVR and LaR algorithms showed significant deviations from the FPSC simulation results. The SVR algorithm achieved R2 values of 0.54 for f, 0.78 for Xd, and 0.84 for ηII, while the LaR algorithm achieved R2 values of 0.65 for f, 0.99 for Xd, and 0.98 for ηII. This research aims to find the optimal input parameters that minimize f and Xd while maximizing ηII. Therefore, to determine the Pareto optimal solutions the non-dominated sorting genetic algorithm (NSGA-II) has been utilized. The result was an illustration of the Pareto set, which stands for a collection of optimal solutions. Every solution in this collection achieved the desiredbalance, obtaining the best outcomes without compromising any objectives.

Разработка и применение многокритериального метода муравьиных колоний в задаче оптимизации инвестиционного портфеля

<p>A numerical method of multi-objective optimization is proposed for an approximate solution of the problem based on the generation of feasible solutions using the continuous ant colony method, non-dominated sorting and the epsilon-constraint technique. Solving a problem means finding the Pareto front. Solutions of typical model examples are given. The applied problem of optimizing an investment portfolio has been solved, in which the initial data are the tabulated average returns and covariance of stocks.</p>

Multi-Objective Optimization Methods for Train Load Planning in Seaport Container Terminals

In this paper we study the planning problem of loading trains in seaport container terminals, which consists in assigning containers to the wagon slots. The train load can be realized considering different objectives, in this work we focus on two very important objectives for terminal managers, that are the minimization of the number of reshuffles in the storage area and the minimization of the total distance covered by the handling equipment between the storage area and the wagons. To address this problem, some multi-objective methods are investigated in the paper, based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon$</tex-math> </inline-formula> -constraint approach and the lexicographic algorithm, allowing to find different sets of efficient solutions to be provided to train planners. The experimental tests, devised to compare the proposed multi-objective methods, show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon$</tex-math> </inline-formula> -constraint method integrated with a lexicographic approach is the most efficient choice since it allows to obtain a higher number of efficient solutions in shorter computational times. This method can be applied in decision support systems for train planners in order to allow them to decide the train load in an efficient way. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The automation and the process optimization in seaport container terminals is a relevant issue for terminal managers in order to face the strong competitiveness in the logistics and shipping sector and the new emerging problems due to the presence of mega vessels. Among the different operations to be optimally managed in a terminal, the loading of trains is becoming more and more significant, also due to the increase of freight traffic by rail, seen as a cheaper and more sustainable option compared with road transport. The optimal assignment of containers present in a storage area to the wagon slots is a crucial decision in order to reduce operational times and costs in a container terminal. In this paper, we address the train load planning problem considering two important objectives to be minimized, i.e. the number of reshuffles and the distance covered by the handling equipment. The multi-objective methods proposed in the paper are devised to find different efficient solutions in short computational times. The proposed algorithms are intended to be implemented within a decision support tool in which the solutions found are shown to the train planner who chooses the preferred option depending on personal evaluations and on the basis of information coming in real time.

Degradation performance rapid prediction and multi-objective operation optimization of gas turbine blades

The performance degradation of high-temperature blades will affect the safety and efficiency of operation. In response to issues such as ignoring strength characteristics, slow degradation performance prediction, insufficient applicability and accuracy of traditional proxy models, and long operation optimization cycle, a degradation performance prediction model of turbine blades based on the back propagation neural network is established in this research. Furthermore, the efficiency-stress multi-objective operation optimization method based on genetic algorithm is proposed. The results show that the R-square value of the degradation performance neural network prediction model is greater than 0.9 for predicting characteristic parameters. The prediction speed is improved by 104 orders of magnitude compared to the traditional computational fluid dynamics method. The influence mechanisms of turbine outlet flow rate, cooling gas inlet total temperature, and cooling gas flow rate on the degradation performance are revealed. Under fouling extreme conditions and corrosion/wear extreme conditions, the operating parameters of turbine blades are optimized. The maximum values of the efficiency improvement, power increase and maximum von Mises stress reduction are 0.74 %, 2.13 MW and 43 MPa, respectively. This study can provide an effective and novel method for real-time degradation performance prediction and rapid operating condition optimization of turbine blades.

Optimization Design of Core Ultra-Stable Structure for Space Gravitational Wave Detection Satellite Based on Response Surface Methodology

In order to meet the urgent demand for novel zero-expansion materials and ultra-stable structures in space gravitational wave detection, it is necessary to develop an ultra-stable structural spacecraft system. This paper focuses on the research of the optimization of the core ultra-stable structure design of spacecraft, proposing a cross-scale parameterized model of structural deformation response and a multi-objective optimization method. By satisfying the prerequisites of mass and fundamental frequency, this paper breaks through the limitations of current linear analysis methods, and the overall thermal deformation of nonlinear material composite structures is optimized by modifying structural parameters.

Simulation Analysis and Parameter Optimization of Seed–Flesh Separation Process of Seed Melon Crushing and Seed Extraction Separator Based on DEM

In order to enhance the comprehensive processing quality and production efficiency of seed melons, a seed melon crushing and seed-extraction separator has been developed and designed. Aiming at the issues of high impurity rate and scratch rate of melon seeds in the process of seed–flesh separation, the structure and parameters of the seed–flesh separation device were optimized in this study by simulation analysis and field testing. The simulation model of melon seed, melon flesh, and the seed–flesh separation device based on the discrete element method (DEM) was established, and the simulation parameters were calibrated. Subsequently, the melon seed impurity rate (G1) and the melon seed scratch rate (G2) were used as the evaluation indexes. The single-factor simulation test was carried out on the separation roller speed (A). The spacing between the scraper and the screen (B), the separation roller scraper inclination angle (C), and the influence rules of each factor on the separation effect of the seed–flesh were obtained. Finally, the three-factor and three-level orthogonal test was carried out. Using the method of ANOVA and multi-objective optimization, the optimal working parameters of the device were obtained as A-117.53 r/min, B-5 mm, and C-10°, at which time the optimal evaluation indexes were G1-5.59% and G2-2.85%. The prototype test was carried out with the optimization results. The values of G1 and G2 were measured at 5.71% and 2.91%, respectively, and the relative errors with the simulation values were 2.15% and 2.11%, respectively, which were basically the same between the simulation model and the prototype test. The results indicate that the designed separation roller speed, spacing between the scraper and screen, and separation roller scraper inclination angle can meet the requirements of seed–flesh separation in the seed melon crushing and seed-extraction separator. The results of the DEM study can provide a reference for the optimal design of the seed–flesh separation device.

A multi-objective configuration optimization method of passive hybrid energy storage system for pulse loads operating under very low temperatures

The lithium-ion battery energy storage system currently widely used faces a problem of rapid degradation of electrical performance at very low temperatures (such as −40 °C), making it difficult to meet the power supply requirements of high-power pulse loads in low-temperature environments. To address this issue, this paper proposes a multi-objective configuration optimization method for passive lithium-ion battery-supercapacitor hybrid energy storage systems (HESS) based on an electro-thermal-aging coupling model, in order to achieve non-preheating power supply for pulse loads under low temperatures. Firstly, an electro-thermal-aging coupling model for the passive HESS is established to accurately describe the dynamic characteristics during discharge. Subsequently, aiming at the low-temperature application requirements of high-power pulse loads, a multi-objective configuration optimization model is established based on the coupling model with the objectives of minimizing the mass and the minimum operating ambient temperature of the HESS; a solving method of the optimization model is designed based on the non-dominated sorting genetic algorithm with elite strategy. Finally, a case study is conducted on configuration optimization for a certain type of pulse load. The optimization results show that when the minimum operating temperature is consistent and below 0 °C, the passive HESS compared with the lithium-ion battery energy storage system can reduce the system mass by more than 23% and the acquisition cost by more than 18% while maintaining basically consistent single-pulse costs. When the minimum operating temperature is lower, the advantages of the HESS are even more significant.

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms.

Joint UAV Deployment and Task Offloading in Large-Cale UAV-Assisted MEC: A Multiobjective Evolutionary Algorithm

With the development of digital economy technologies, mobile edge computing (MEC) has emerged as a promising computing paradigm that provides mobile devices with closer edge computing resources. Because of high mobility, unmanned aerial vehicles (UAVs) have been extensively utilized to augment MEC to improve scalability and adaptability. However, with more UAVs or mobile devices, the search space grows exponentially, leading to the curse of dimensionality. This paper focus on the combined challenges of the deployment of UAVs and the task of offloading mobile devices in a large-scale UAV-assisted MEC. Specifically, the joint UAV deployment and task offloading problem is first modeled as a large-scale multiobjective optimization problem with the purpose of minimizing energy consumption while improving user satisfaction. Then, a large-scale UAV deployment and task offloading multiobjective optimization method based on the evolutionary algorithm, called LDOMO, is designed to address the above formulated problem. In LDOMO, a CSO-based evolutionary strategy and a MLP-based evolutionary strategy are proposed to explore solution spaces with different features for accelerating convergence and maintaining the diversity of the population, and two local search optimizers are designed to improve the quality of the solution. Finally, simulation results show that our proposed LDOMO outperforms several representative multiobjective evolutionary algorithms.

Multi-Objective Optimization towards Heat Dissipation Performance of the New Tesla Valve Channels with Partitions in a Liquid-Cooled Plate

The utilization of liquid-cooled plates has been increasingly prevalent within the thermal management of batteries for new energy vehicles. Using Tesla valves as internal flow channels of liquid-cooled plates can improve heat dissipation characteristics. However, conventional Tesla valve flow channels frequently experience challenges such as inconsistencies in heat dissipations and unacceptably high levels of pressure loss. In light of this, this paper proposes a new type of Tesla valve with partitions, which is used as internal channel for liquid-cooled plate. Its purpose is to solve the shortcomings of existing flow channels. Under the working conditions of Reynolds number equal to 1000, the neural network prediction-NSGA-II multi-objective optimization method is used to optimize the channel structural parameters. The objective is to identify the optimal structural configuration that exhibits the greatest Nusselt number while simultaneously exhibiting the lowest Fanning friction factor. The variables to consider are the half of partition thickness H, partition length L, and the fillet radius R. The study result revealed that the optimal parameter combination consisted of H = 0.25 mm, R = 1.253 mm, L = 0.768 mm, which demonstrated the best performance. The Fanning friction factor of the optimized flow channel is substantially reduced compared to the reference channel, reducing by approximately 16.4%. However, the Nusselt number is not noticeably increased, increasing by only 0.9%. This indicates that the optimized structure can notably reduce the fluid’s friction resistance and pressure loss and slightly enhance the heat dissipation characteristics.

Virtual Sound Image Reconstruction Method for Multi-objective Optimization of Folk Music Based on Evolutionary Algorithm

At present, the exchanges in various fields such as culture, economy, and politics are becoming more and more close in the world. From the perspective of the relationship between national music and cultural development, the development of national music has also received more and more attention, and it has become an inevitable trend in the development of today's era. The purpose of this paper was to perform virtual reconstruction of the sound image of folk music through multiple objective optimizations, and to model the virtual sound image of folk music as a multi-objective optimization problem. According to the research on sound image positioning, the relevant noise factors were removed, so as to achieve the playback of ethnic music that enhanced the surround effect and visual enjoyment. The evolutionary algorithm in this paper was mainly based on the multi-objective optimized sound image localization technology. For the music virtual sound image, an improved FCM algorithm and an evolutionary multi-objective optimization algorithm combining local and non-local information of the sound image were proposed, respectively. Through the analysis of the traditional sound image algorithm method, the accuracy of the sound image localization on the horizontal plane could be effectively improved. After the conversion, the audience could feel the better stereo image and surround feeling of the folk music. Through experimental analysis, it can be seen that the system can not only perform virtual conversion of audio-visual signals of different frequencies, but also provide data for different audio playback systems. The feature point registration error is low, and the reconstruction effect is good, especially the random delay processing in the range of 0∼20m, and the performance is better than the traditional method. Finally, virtual left and right surround sound image signals were obtained, which effectively improved the three-dimensional surround feeling of folk music.

Multi-objective optimization method for medium and long-term power supply and demand balance considering the spatiotemporal correlation of source and load

The medium and long-term supply-demand imbalance of the power system in the context of the new power system is becoming more and more prominent due to the fluctuation and intermittency brought about by the high proportion of new energy sources connected to the grid. In this regard, a multi-objective power supply-demand balance optimization method considering the spatiotemporal correlation of source and load is proposed in this work. First, the autocorrelation and inter-correlation characteristics of source and load are analyzed. On this basis, a multi-dimensional scenario set construction method considering the spatiotemporal correlation of source and load is proposed. Then, the planning capacity of each regional power source and the system operation under each scenario are taken as the optimization variables. Renewable energy electricity curtailment, equivalent annual total cost, and inter-region transmission electricity are taken as the optimization objectives. Various constraints such as power source planning and operation, power balance, inter-region power transmission, and renewable energy power curtailment rate are considered comprehensively. The optimization method for the medium and long-term power supply and demand balance is proposed. Finally, the method is applied to Hunan Province, China to guide power planning. The results show that compared with traditional multi-dimensional correlation scene construction methods, the average probability density functions error of wind turbine output, photovoltaic output, and load constructed in this work decrease by 44.08 %, 73.64 %, and 57.54 %, respectively. It takes into account the regional, temporal, temporal autocorrelation, and inter-correlation of the source and load, and has similar characteristics to historical data. Compared with traditional planning that only considers economy, the optimization plan for power supply and demand balance in this work reduces electricity curtailment and inter-region transmission by 97.04 % and 72.71 %, respectively, balancing renewable energy consumption, economy, and regional independent balancing indicators.

Experimental Investigation on Wire Electric Erosion Behaviour of Silicon Dioxide Particulate Reinforced Composite

The intend of current study was focused on the prediction of material removal rate (MRR) and surface roughness (SR) for the AA7050-SiO2 composite during wire electric erosion or discharge machining (WEDM) process using a brass (Br) wire electrode. Here, stir casting process was employed to develop the AA7050 matrix composite with inclusion of 10wt.% SiO2 particle reinforcement. The multi-objective optimization method of Technique for order preference by similarity to ideal solution (TOPSIS) approach has been applied to find out the optimal setting of input machining parameters such as peak current (Ip), pulse-on time (Ton) and pulse-off time (Toff). Furthermore, the significant effects of parameters were identified by analysis of variance (ANOVA). Taguchi L9 (33) orthogonal design has been formulated to perform the experimental work. TOP SIS results stated that the optimal setting of Ip at 30 amps, Ton of 130 μs and Toff of 55 μs provide the better MRR with lesser SR. The ANOVA results noticed that Ip has the prime noteworthy parameter over the adopted responses having a contribution of 45.67%, followed by Ton (32.34%) and Toff (12.26%), respectively. The confirmation test was carried out by the optimal parameters setting to verify the predicted results. Finally, the scanning electron microscopy (SEM) test was carried out for the machined surface of the composite specimen and it was reveals that the formation of craters and recast layer thickness in the machined surfaces.

Research on a Multi-Objective Optimization Method for Transient Flow Oscillation in Multi-Stage Pressurized Pump Stations

The long-distance multi-stage pressurized pump station water delivery system involves numerous valve closure parameters, complicating the rapid identification of an optimal valve closure scheme that satisfies multiple transient flow oscillation protection requirements. A hydraulic transient model was established based on transient flow calculation theory to address this challenge. Decision biases were identified using the Analytic Hierarchy Process and the Entropy Weight Method. A multi-objective optimization model, incorporating Support Vector Regression (SVR) and the Beluga Whale Optimization (BWO) algorithm, iteratively searches for optimal schemes under different biases. The results indicate that Support Vector Regression exhibits optimal performance, while Beluga Whale Optimization demonstrates excellent performance. The optimal schemes obtained from the multi-objective optimization model meet the transient flow protection requirements of the water delivery system. The study demonstrates that this model effectively solves the multi-objective optimization problem for water hammer protection in multi-stage pressurized pump station water delivery systems.

Prediction of frost resistance and multiobjective optimisation of low-carbon concrete on the basis of machine learning

The use of Portland cement is a major source of carbon dioxide emissions, causing considerable environmental pollution worldwide. Therefore, reducing carbon emissions in concrete is of paramount importance. This study presents a multiobjective optimisation method for low-carbon concrete mix design, combining the use of optimal machine learning models for prediction, with the aim of minimising the cost and carbon emissions of concrete. Several optimisation models, including SVR, CatBoost, RF, XGBoost, DBO-RF and VMD-DBO-RF, were employed to predict the frost resistance of low-carbon concrete. The research findings demonstrate that the VMD-DBO-RF optimisation algorithm achieves high prediction accuracy in terms of RDEM and MLR. For RDEM prediction, R2 = 0.9346, MSE = 0.0508, MAE = 0.1686, and RMSE = 0.2253. For MLR prediction, R2 = 0.9557, MSE = 0.0245, MAE = 0.1042, and RMSE = 0.1565. Furthermore, the model’s interpretability was improved by combining SHAP and PDP analyses.

A demand-based three-stage seismic resilience assessment and multi-objective optimization method of community water distribution networks

This paper proposes a three-stage resilience concept that takes into account reliability, vulnerability and recovery resilience of water distribution networks (WDNs) from three phases, namely, pre-disaster preparation (PDP) phase, disaster response (DR) phase and the post-disaster recovery (PDR) phase. Based on the three-stage resilience concept, the initial performance, robustness and multi-objective optimization recovery method are proposed. In PDP phase, based on the reliability concept and the user demand, the initial performance of WDNs is defined, and the method is proposed based on Monte Carlo simulation method combined with seismic fragility of pipelines. In DR phase, a comprehensive quantitative index is proposed to quantify the robustness of WDNs by integrating the structural attributes, topological attributes and operational characteristics of WDNs. Finally, on the basis of the previous two stages, the disaster recovery process of failed pipelines of WDNs is further analyzed, and a multi-objective recovery optimization model of failed pipelines with consideration of users’ demands under the resources constraints is proposed to achieve the resilience enhancement. Through a case, the three-stage resilience assessment optimization enhancement of WDNs is implemented using the improved NSGA-II. The proposed method can be used as a basis for disaster prevention planning and seismic measures.