Multiple Objective Particle Swarm Optimization Research Articles

Automatic generation of knee kinematic models from medical imaging

Background and ObjectiveThree-dimensional spatial mechanisms have been used to accurately predict passive knee kinematics, and have shown potential to be used in optimized multibody kinematic models. Such multi-body models are anatomically consistent and can accurately predict passive knee kinematics, but require extensive medical image processing and thus are not widely adopted. This study aimed to automate the generation of kinematic models of tibiofemoral (TFJ) and patellofemoral (PFJ) joints from segmented magnetic resonance imaging (MRI) and compare them against a corresponding manual pipeline. MethodsFrom segmented MRI of eight healthy participants (four females; aged 14.0 ± 2.6 years), geometric parameters (i.e., articular surfaces, ligament attachments) were determined both automatically and manually, and then assembled into TFJ and PFJ kinematic models to predict passive kinematics. The TFJ model was a six-link mechanism with deformable ligamentous constraints, whereas PFJ was a modified hinge. The ligament length changes through TFJ flexion were prescribed to literature strain profile. The geometric parameters were optimized to ensure physiological kinematic predictions through a Multiple Objective Particle Swarm Optimization. ResultsGeometric parameters showed strong agreement between automatic and manual pipelines (median error of 2.8 mm for anatomical landmarks and 1.5 mm for ligament lengths). Predicted TFJ and PFJ kinematics from the two pipelines were not statistically different, except for tibial superior/inferior translation near terminal TFJ extension. The TFJ kinematics predicted from the automatic pipeline had mean errors of 3.6° and 12.4° for adduction/abduction and internal/external rotation, respectively, and <7 mm mean translational error compared to the manual pipeline. Predicted PFJ had <9° mean rotational errors and <6 mm mean translational errors. ConclusionsThe automatic pipeline developed and presented here can predict passive knee kinematics comparable to a manual pipeline, but removes laborious manual processing and provides a systematic approach to model creation.

Multiobjective optimization of bridge and viaduct design: Comparative study of metaheuristics and parameter calibration

This article focuses on multiobjective optimization in the design of bridges and viaducts. The problem is characterized as a multi-objective optimization, with the objective functions being the construction cost, the environmental impact (CO2 emissions) and the design service life. For optimization, three commonly used metaheuristics in structural optimization problems were tested: Multiple Objective Particle Swarm Optimization (MOPSO), Nondominated Sorting Genetic Algorithm II (NSGA-II) and Strength Pareto Evolutionary Algorithm 2 (SPEA2). The results showed that MOPSO outperformed the other methods, achieving the highest hypervolume and Pure Diversity values. Once the best performing metaheuristic was defined, the calibration of the MOPSO parameters was then developed to improve the quality of the solutions found, reduce the execution time and increase the robustness of the algorithm. Using the Taguchi method with an orthogonal matrix consisting of 54 experiments, five parameters were evaluated at three different levels, totaling 270 analyses. The results indicated that parameter calibration led to an increase in the average hypervolume compared to the results before calibration. Moreover, the coverage of two sets revealed the superior performance of the calibrated set, demonstrating better trade-offs among the objective functions.

The multi-objective optimization and mix parameter evaluation of one-part alkali-activated grouting material

To obtain a green and cost-effective one-part alkali-activated grouting material (OAGM) with good comprehensive performance for subgrade reinforcement and determine its proper mix parameters. In this study, using response surface methodology (RSM), multiple objective particle swarm optimization (MOPSO) algorithm and the technique for order preference by similarity to an ideal solution (TOPSIS) algorithm coupled with entropy weight method, two multi-objective optimization schemes for OAGM were performed, one only considering performance and another considering performance, embodied CO2 emission (ECO2e) and cost. Then, the correlation-based feature selection (CFS) algorithm was used to evaluate the importance of various molar ratios as mix parameters on the performance of OAGM. Finally, the effects of key mix parameters on the microstructure and reaction products of OAGM were studied. RSM results show that W/S (water to solid) ratio, borax (BR) content and UCG content chiefly govern the flowability, initial setting time and mechanical strength of OAGM respectively, and the interactions between some factors also significantly affect these properties. MOPSO and entropy-TOPSIS algorithm can be used to optimize OAGM objectively. Two optimal OAGM pastes both have better comprehensive performance and much lower ECO2e than ordinary Portland cement (OPC) paste. And the optimal OAGM considering performance, ECO2e and cost even has 7.68% lower cost than OPC paste. But another optimal OAGM has the best comprehensive performance. CFS results show that the molar ratios of Si/Al, Al/Ca, Na2O/H2O, B2O3/CaO and B2O3/Al2O3 are the key mix parameters of OAGM. Al/Ca rather than Si/Al is the most important mix parameter to the 28-day compressive strength. And higher Si/Al and Al/Ca deteriorates the microstructure and hinders the formation of C-A-S-H gel, while higher Na2O/H2O has the opposite effect. This study provides guidance for objective optimization and the determination of proper mix parameters of OAGM, and promotes the market-oriented application of OAGM.

Process development and multi-criteria optimization of a biomass gasification unit combined with a novel CCHP model using helium gas turbine, kalina cycles, and dual-loop organic flash cycle

The non-renewable nature of conventional power plants and the challenges associated with fuel costs and environmental impact highlight the need for innovative solutions. This research proposes a biomass-based combined system designed to produce multiple products, including electric power, coolant, and heat, addressing the drawbacks associated with conventional power generation. The proposed system integrates a biomass gasification unit with a helium gas turbine and a Kalina power unit. Additionally, a domestic water heater is incorporated into the Kalina cycle for heat generation, and the heat loss from the helium gas turbine is utilized in a modified Kalina cycle with a refrigeration unit. To further enhance efficiency, a dual-loop organic flash cycle is employed to recycle waste heat from the modified Kalina cycle. The analysis of this framework encompasses technical aspects, including energy, exergy, and economic considerations. The system is optimized using the multiple-objective particle swarm optimization method. Two scenarios are explored based on the desired product capacities: heat-electric power and coolant-electric power. In the first scenario, the system demonstrates an optimal electric power generation capacity of 6239.56 kW, along with favorable exergetic and economic outcomes. The optimal exergetic efficiency, net present value, and payback period are determined as 35.57 %, 15.07 M$, and 3.97 years, respectively. This research presents a comprehensive approach to biomass-based power generation, considering both technical and economic aspects, and provides valuable insights for sustainable energy solutions.

Prediction of concrete abrasion depth and computational design optimization of concrete mixtures

The failure of concrete for hydraulic structures due to the excessive abrasion depth has caused great economic losses. Despite the tremendous work that has been done, the durability design of hydraulic concrete structures concerning abrasion damage is still a difficult task, especially with a long service life aiming at economic benefit and environmental sustainability. In this paper, machine learning methodologies including random forests (RFs) and artificial neural networks (ANNs), are used to establish prediction models based on concrete mixture proportions, curing age, and hydraulic conditions. Furthermore, RF models are coupled with multiple objective particle swarm optimization (MOPSO) algorithms to perform computational design optimization of concrete mixtures. The optimal solutions are generated based on 5000 randomly generated mixture proportions, among which three optimal designs of concrete mixtures are selected to guide field applications on account of concrete durability requirements and economic benefits.

Parameter estimation of the hydraulic turbine regulator system using multi-objective lion algorithm

Accurate modeling of electric power generating unit and its hydraulic turbine regulation systems provides support for the speed controller synthesis and stability analysis. It is however a difficult task due to the presence of many non-linear factors in this system. an approach to estimate the parameters of hydraulic turbine regulatory system models is to derive the physical representation of each component and, through simulation, to compare to compare their models, outputs with real data obtained from a hydroelectric plant located in Brazil. The objective of this paper is to find the best values that will represent the system under study as a whole. This problem can be seen as an optimization problem. To find its feasible and optimal solution, this work proposes a new metaheuristics multi-objective based on the Lion Algorithm (LA), called the Multi-Objective Lion Algorithm (MOLA), and its application in the estimation of parameters of the system under study. In addition, the new metaheuristic proposed is validated by using a set of benchmark cases. The results have demonstrated that MOLA outperforms or at least performs similarly to Multi-objective Grey Wolf Optimizer (MOGWO), Multiple Objective Particle Swarm Optimization (MOPSO), Multi-objective Salp Swarm Algorithm (MSSA), Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Non-dominated Sorting Genetic Algorithm III (NSGA-III) in the optimization of multi-objective benchmark functions. These results, suggest that the proposed MOLA algorithm works efficiently.

A Novel Multi-Objective Based Feature Selection Method for Response Prediction

Accurate response prediction is essential towards personalized treatment in radiation therapy. Excessive imaging features, extracted from medical images, pose a great challenge in radiomic analyses. Feature selection is an essential step to remove redundant and irrelevant features for model construction. We proposed a novel multi-objective based radiomic feature selection method (MRMOPSO), where the number of features, sensitivity, and specificity are jointly considered as optimization objectives for feature selection. The MRMOPSO innovated by three aspects: 1) Fisher score initialize the feature population to speed up the convergence; 2) Min-redundancy particle generation operations to reduce the redundancy between radiomic features, a truncation strategy was also introduced; 3) Particle selection operation guided by elitism strategies to improve local search ability of the algorithm. We evaluated the effectiveness of the proposed MRMOPSO method using a cohort of oropharyngeal cancer patients from The Cancer Imaging Archive (TCIA). 357 patients were used for model training and additional 64 patients were used for independent evaluation. The proposed methods were compared with (a) classical feature selection methods, i.e., Lasso, minimal-redundancy-maximal-relevance criterion (mRMR), F-score, and mutual information (MI), (b) single-objective feature selection methods, i.e., genetic algorithm (GA), particle swarm optimization algorithm (PSO) and (c) multi-objective feature selection methods, i.e., multiple objective particle swarm optimization (MOPSO), nondominated sorting genetic algorithm II (NSGA II). The other feature selection methods yielded AUCs, sensitivity, specificity of (0.48-0.71), (0.49-0.86), (0.33-0.67), respectively. The MRMOPSO achieved significantly highly AUC of 0.84 with smaller number of selected features on the independent dataset (Table 1). Additionally, the MRMOPSO remarkably improved the sensitivity (0.81), specificity (0.81) and achieved an excellent balance between sensitively and specificity. We demonstrated a novel multi-objective based radiomic feature selection method. The proposed algorithm effectively reduced feature dimension, and achieved superior AUC with simultaneous improved sensitivity and specificity, for radiomic response prediction.

Overlapping Coalition Formation Game via Multi-Objective Optimization for Crowdsensing Task Allocation

With the rapid development of sensor technology and mobile services, the service model of mobile crowd sensing (MCS) has emerged. In this model, user groups perceive data through carried mobile terminal devices, thereby completing large-scale and distributed tasks. Task allocation is an important link in MCS, but the interests of task publishers, users, and platforms often conflict. Therefore, to improve the performance of MCS task allocation, this study proposes a repeated overlapping coalition formation game MCS task allocation scheme based on multiple-objective particle swarm optimization (ROCG-MOPSO). The overlapping coalition formation (OCF) game model is used to describe the resource allocation relationship between users and tasks, and design two game strategies, allowing users to form overlapping coalitions for different sensing tasks. Multi-objective optimization, on the other hand, is a strategy that considers multiple interests simultaneously in optimization problems. Therefore, we use the multi-objective particle swarm optimization algorithm to adjust the parameters of the OCF to better balance the interests of task publishers, users, and platforms and thus obtain a more optimal task allocation scheme. To verify the effectiveness of ROCG-MOPSO, we conduct experiments on a dataset and compare the results with the schemes in the related literature. The experimental results show that our ROCG-MOPSO performs superiorly on key performance indicators such as average user revenue, platform revenue, task completion rate, and user average surplus resources.

Thermal performance and structural optimization of a hybrid thermal management system based on MHPA/PCM/liquid cooling for lithium-ion battery

It is crucial to propose an efficient hybrid Battery Thermal Management System (BTMS) and a multi-objective optimization method with high-accuracy and low computational load due to many factors greatly influence the performance and energy density (ED) of hybrid BTMS. In this paper, a novel hybrid BTMS combined with phase change material (PCM), micro heat pipe array, and liquid cooling is proposed, whose cooling performance is verified experimentally. Then, the effects of the main structural parameters of BTMS on cooling performance and ED were numerically analyzed with the Box-Behnken design (BBD). Finally, a multi-objective optimization with Multiple Objective Particle Swarm Optimization based on Response Surface Methodology (RSM) is introduced to optimize ED and cooling performance. The experimental result shows that the temperature difference of the hybrid module is maintained within a safe range reducing from 6.9 °C to 3.9 °C, and the maximum temperature is reduced by 13.78% from 46.0 °C to 39.8 °C during 2C discharging progress compared with the module only PCM cooling. The optimization outcomes predict that the optimized BTMS’s ED can rise 11.23% to 157.8 Wh/kg with only a slight variation in cooling performance in comparison to the original module.

A method of finding optimal number of clusters in a wireless network based on power efficiency using MOPSO

Sensors play an important role in monitoring, detecting, recording and recording the physical and environmental conditions of a particular place. These physical conditions mainly include temperature, sound, wind, etc. These nodes are connected to each other via a transmission channel and the nodes are battery-operated. So, energy efficient algorithms are needed to reduce energy consumption in the overall setup and increase the lifetime of sensor nodes. In this paper, we propose a method to solve the problem of routing in “Wireless Sensor Networks”, forming clusters such that there are minimal node transfers and the overall energy consumption of the system is reduced. We have implemented Multiple Objective Particle Swarm Optimization (MOPSO) algorithm to devise a technique that considers several parameters like temperature, minimal clustering, routing path distance and energy efficiency to obtain optimal clusters.

A near-optimum multi-objective optimization approach for structural design

Multi-objective design optimization problems offer a set of solution alternatives within a Pareto-front. In structural design, the design variables are typically the section properties. The outcomes of these design variables are usually used in selecting standard sections. However, the properties of the selected standard sections normally have different values from the determined design variables. Accordingly, the values of the objective functions for these solutions will change after selecting standard sections. This change may be different among these solutions. Thus far, only Pareto-optimal solutions have been standardized in the literature. The effects of the inclusion of non-Pareto solutions in the standardization process have never been examined. In this paper, the differences between including the near-optimal solutions and not including them in the final structural design optimization set are explored. The paper investigates the impact of selecting standard sections on both Pareto-front solutions and near-optimal solutions, and it studies the importance of keeping track of the near-optimal solutions. A modified version of a multiple-objective particle swarm optimization method, enhanced with a proposed computationally efficient section standardization algorithm, is used to solve multi-objective system-reliability design optimization problems. The concepts of the paper are applied to examples of bridge structures. The results demonstrate the efficiency of the proposed technique in capturing final design solutions that would have been otherwise missed due to standardization.

Inverse kinematics and multi-objective configuration optimization of the SSRMS manipulator

The Space Station Remote Manipulator System (SSRMS) type redundant manipulator with higher flexibility and foldability is widely used in the space environment. Inverse kinematics and multi-objective configuration optimization are analyzed in this paper. An arm angle parameterized inverse kinematics method using the approximate solution and error compensation scheme is proposed, which has the advantages of not requiring a selection of initial estimates of joint variables, being insensitive to Jacobian matrix singularities, having no pose error, and finding multiple solutions. In addition, Multiple Objective Particle Swarm Optimization (MOPSO) scheme is adopted to optimize the arm angle trajectory in null space, and the optimization index is set as joint torque and manipulability. Unlike traditional trajectory planning methods, we synthesize null space and configuration control to provide a novel perspective for trajectory planning. Finally, the experiments prove that the inverse kinematics algorithm is efficient and reliable, and the effectiveness of the configuration optimization method is verified by the numerical simulation of single objective and multi-objective optimization.

A multi-objective based radiomics feature selection method for response prediction following radiotherapy

Objective. Radiomics contains a large amount of mineable information extracted from medical images, which has important significance in treatment response prediction for personalized treatment. Radiomics analyses generally involve high dimensions and redundant features, feature selection is essential for construction of prediction models. Approach. We proposed a novel multi-objective based radiomics feature selection method (MRMOPSO), where the number of features, sensitivity, and specificity are jointly considered as optimization objectives in feature selection. The MRMOPSO innovated in the following three aspects: (1) Fisher score to initialize the population to speed up the convergence; (2) Min-redundancy particle generation operations to reduce the redundancy between radiomics features, a truncation strategy was introduced to further reduce the number of features effectively; (3) Particle selection operations guided by elitism strategies to improve local search ability of the algorithm. We evaluated the effectiveness of the MRMOPSO by using a multi-institution oropharyngeal cancer dataset from The Cancer Imaging Archive. 357 patients were used for model training and cross validation, an additional 64 patients were used for evaluation. Main results. The area under the curve (AUC) of our method achieved AUCs of 0.82 and 0.84 for cross validation and independent dataset, respectively. Compared with classical feature selection methods, the AUC of MRMOPSO is significantly higher than the Lasso (AUC = 0.74, p-value = 0.02), minimal-redundancy-maximal-relevance criterion (mRMR) (AUC = 0.73, p-value = 0.05), F-score (AUC = 0.48, p-value < 0.01), and mutual information (AUC = 0.69, p-value < 0.01) methods. Compared to single-objective methods, the AUC of MRMOPSO is 12% higher than those of the genetic algorithm (GA) (AUC = 0.68, p-value = 0.02) and particle swarm optimization algorithm (AUC = 0.72, p-value = 0.05) methods. Compared to other multi-objective feature selection methods, the AUC of MRMOPSO is 14% higher than those of multiple objective particle swarm optimization (MOPSO) (AUC = 0.68, p-value = 0.02) and nondominated sorting genetic algorithm II (NSGA2) (AUC = 0.70, p-value = 0.03). Significance. We proposed a multi-objective based radiomics feature selection method. Compared to conventional feature reduction algorithms, the proposed algorithm effectively reduced feature dimension, and achieved superior performance, with improved sensitivity and specificity, for response prediction in radiotherapy.

A novel multi-objective optimization of mass dampers for controlling the vortex-induced vibration in bridges

This paper investigates an optimization framework of the four mass dampers for controlling the vortex-induced vibration (VIV) in long-span bridges, including the tuned mass damper (TMD), the series double tuned mass dampers (DTMD) and the inerter-equipped tuned mass damper (ITMD). The equations of motion of the bridge-damper system subjected to the vortex-induced force are established. The vortex-induced amplitude of the girder is analytically given. Furthermore, the optimal design is implemented by taking the vortex-induced amplitude as the constraint condition. Introducing two optimization objectives, the stroke index and the robustness index, a novel bi-objective optimization framework with constraints is proposed and then solved by multiple objective particle swarm optimization (MOPSO). A comparative analysis of the four mass dampers with varying total mass ratios is performed. The results show that the vortex-induced amplitude of the girder is greatly reduced to satisfy the requirement after installing the four optimized mass dampers. Both performances of the two optimization objectives are improved with the increase of the total mass ratio. The inertial device parallel to the spring and dashpot provides no advantage in controlling the VIV in bridges. The DTMD has dramatic robustness to changes in the bridge natural frequency and cannot strongly amplify its stroke, especially under the condition of a small mass ratio. The framework provides an excellent balance between control effect and stability in the VIV of bridges for the optimal design of the mass dampers.

A cluster positioning architecture and relative positioning algorithm based on pigeon flock bionics

Unmanned clusters can realize collaborative work, flexible configuration, and efficient operation, which has become an important development trend of unmanned platforms. Cluster positioning is important for ensuring the normal operation of unmanned clusters. The existing solutions have some problems such as requiring external system assistance, high system complexity, poor architecture scalability, and accumulation of positioning errors over time. Without the aid of the information outside the cluster, we plan to construct the relative position relationship with north alignment to adopt formation control and achieve robust cluster relative positioning. Based on the idea of bionics, this paper proposes a cluster robust hierarchical positioning architecture by analyzing the autonomous behavior of pigeon flocks. We divide the clusters into follower clusters, core clusters, and leader nodes, which can realize flexible networking and cluster expansion. Aiming at the core cluster that is the most critical to relative positioning in the architecture, we propose a cluster relative positioning algorithm based on spatiotemporal correlation information. With the design idea of low cost and large-scale application, the algorithm uses intra-cluster ranging and the inertial navigation motion vector to construct the positioning equation and solves it through the Multidimensional Scaling (MDS) and Multiple Objective Particle Swarm Optimization (MOPSO) algorithms. The cluster formation is abstracted as a mixed direction-distance graph and the graph rigidity theory is used to analyze localizability conditions of the algorithm. We designed the cluster positioning simulation software and conducted localizability tests and positioning accuracy tests in different scenarios. Compared with the relative positioning algorithm based on Extended Kalman Filter (EKF), the algorithm proposed in this paper has more relaxed positioning conditions and can adapt to a variety of scenarios. It also has higher relative positioning accuracy, and the error does not accumulate over time.

Spatial Configuration Design for Multistatic Airborne SAR Based on Multiple Objective Particle Swarm Optimization

Spatial Configuration Design for Multistatic Airborne SAR Based on Multiple Objective Particle Swarm Optimization

Utilizing artificial intelligence to solving time – cost – quality trade-off problem

This study presents the Slime Mold Algorithm (SMA) to solve the time—cost—quality trade-off problem in a construction project. The proposed SMA is a flexible and efficient algorithm in exploration and exploitation to reach the best optimal solution to process the input model’s data. This paper aims to discuss and solve the optimization problem and compare the evaluation with other algorithms such as Opposition-based Multiple Objective Differential Evolution, Non-dominated sorting genetic algorithm, Multiple objective particle swarm optimization, Multiple objective differential evolution and Chaotic initialized multiple objective differential evolution (CAMODE) to verify the efficiency and potential of the proposed algorithm. According to the analysis results, the SMA model generated a diversification measure for case studies, producing superior outcomes to those of previous algorithms.

Multiple objective optimization based on particle swarm algorithm for MMC-MTDC system

Multi-terminal high voltage DC (MTDC) network is an effective technology to integrate large-scale offshore wind energy sources into conventional AC grids and improve the stability and flexibility of the power system. In this paper, firstly, an analytical model of a general applicable MTDC system integrated with several isolated AC grids is established. Then, an improved AC-DC power flow algorithm is used to eliminate the additional DC slack bus or droop bus iteration (SBI/DBI) step of the conventional AC-DC sequential power flow. A multi-objective optimal power flow (MOPF) algorithm is proposed to minimize two optimization targets, i.e., overall active power loss and generation costs of the system. To increase the degree of freedom, adaptive droop control is used in the proposed optimization algorithm in which the voltage references and droop coefficients of the modular multilevel converters (MMCs) are control variables. A multiple objective particle swarm optimization (MOPSO) method is applied to solve the MOPF problem and achieve the Pareto front. A technique for order of preference by similarity to ideal solution (TOPSIS) is incorporated in the decision analysis section and helps the decision maker to identify the best compromise solution.

Determining the Pareto front of distributed generator and static VAR compensator units placement in distribution networks

&lt;span&gt;The integration of distributed generators (DGs), which are based on renewable energy sources, energy storage systems, and static VAR compensators (SVCs), requires considering more challenging operational cases due to the variability of DG production contributed by different characteristics for different time sequences. The size, quantity, technology, and location of DG units have major effects on the system to benefit from the integration. All these aspects create a multi-objective scope; therefore, it is considered a multi-objective mixed-integer optimization problem. This paper presents an improved multi-objective salp swarm optimization algorithm (MOSSA) to obtain multiple Pareto efficient solutions for the optimal number, location, and capacity of DGs and the controlling strategy of SVC a radial distribution system. MOSSA is a bio-inspired optimizer based on swarm intelligence techniques and it is used in finding the optimal solution for a global optimization problem. Two sets of objective functions have been formulated minimizing DGs and SVC cost, voltage violation, energy losses, and system emission cost. The usefulness of the proposed MOSSA has been tested with the 33-bus and 141-bus radial distribution systems and the qualitative comparisons against two well-known algorithms, multiple objective evolutionary algorithms based on decomposition (MOEA/D), and multiple objective particle swarm optimization (MOPSO) algorithm.&lt;/span&gt;

Sensitivity-based adaptive procedure (SAP) for optimal rehabilitation of sewer systems

ABSTRACT Urban flood resilience requires high-performance sewer systems, and multi-objective optimization methods are widely used to improve sewer system efficiency. A non-polynomial complete (NP complete) optimization problem may exist in urban sewer rehabilitation, which may cause low efficiency in optimizing large network systems. In this research, a sensitivity-based adaptive procedure (SAP) is proposed, which can be integrated with optimization algorithms. SAP was integrated with Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multiple Objective Particle Swarm Optimization (MOPSO) methods. We further used the Hydraulics and Risk Combined Model (HRCM), which is a risk-informed multi-objective optimization model designed for drainage system rehabilitation to validate the performance of SAP procedure. Results showed that SAP can improve the optimizing performance, and SAP-NSGA-II exhibited superior performance in solving the combined problems of pipe breakage and overflooding.