Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

基于IPSO-RBF神经网络的西北内陆河流域突发水污染风险评估

突发水污染事故会破坏环境、危害健康,开展西北内陆河流域突发水污染风险评估对于维护西部脆弱生态安全尤为重要。该文针对西北内陆河流域突发水污染问题,利用PSR模型遴选18个因素建立突发水污染风险评价指标体系,基于径向基神经网络模型(RBF)构建突发水污染风险评价模型。为进一步保证模型精度,采用改进惯性权重因子和学习因子的粒子群算法(IPSO)对神经网络模型参数进行优化,建立IPSO-RBF神经网络西北内陆河突发水污染风险评价模型,并运用该模型对石羊河流域武威段2017-2022年突发水污染进行风险等级评价。结果显示,石羊河流域武威段突发水污染2017-2019年风险等级为Ⅱ级,2020-2022年风险等级为Ⅲ级,结果与熵权-TOPSIS法一致,与流域治理情况相符。该研究成果有利于提升石羊河流域突发水污染的防控水平与应急处置能力,对于西北内陆河流域水资源管理以及祁连山生态保护具有重要意义。

基于IPSO-MCKD的汽车变速箱轴承故障诊断

针对车辆在城区运行过程中频繁启停造成变速箱滚动轴承故障易发的问题,在轴承故障诊断中引入最大相关峭度反卷积(Maximum Correlation Kurtosis Deconvolution,MCKD)的方法,为了避免过于依赖人工选择MCKD算法中滤波器系数和移位数,提出了一种参数自适应的最大相关峭度反卷积的故障诊断方法。该方法以输入信号的包络谱中最大相关峭度为目标函数,采用改进后的粒子群优化(Improved Particle Swarm Optimization,IPSO)算法优化MCKD中的滤波器系数和位移数,最后通过对故障信号的包络谱进行分析,提取轴承的故障特征。仿真和试验的结果表明,该方法可以有效降低环境中的噪声干扰,准确从强噪声中提取故障特征,实现故障诊断。

基于IPSO-LSTM的井下动目标位置预测实验研究

提升井下人员定位精度能够加强矿山安全监测,最大程度保障井下人员的生命安全。针对现有测距类算法受现场环境影响致使定位精度不足的问题,提出一种基于IPSO-LSTM的定位模型,应用于井下动目标的位置预测。采用LSTM构建指纹定位模型,通过UWB无线模块采集距离信息以构建距离-位置指纹关系数据库,利用数据库对PSO-LSTM模型进行训练,最后将训练好的模型进行目标轨迹预测。为比较不同改进策略对PSO的提升效果,对比了混沌映射随机初始化种群位置、非线性惯性权重递减、非对称优化学习因子和适应度函数优化4种改进策略,实验证明改进的PSO优化算法收敛速度快、鲁棒性好。为验证IPSO-LSTM的定位效果,以平均定位误差作为评价指标,将IPSO-LSTM模型与Chan算法、PSO-LSTM模型、LSTM神经网络、SSA-LSTM模型和GWO-LSTM进行对比,结果显示,IPSO-LSTM定位模型的平均定位误差为30 mm,相对传统Chan算法、LSTM、PSO-LSTM模型分别提升了76%、49%、24%。为降低局部误差偏大的现象,采用中值滤波对输入信息处理,进一步提升了定位精度。研究对进一步提高现有井下动目标定位系统的精度和稳定性具有重要意义和参考价值。

IPSO-BPNN:一种结合粒子群优化的BP神经网络透射光谱水质亚硝酸盐含量定量化模型

亚硝酸盐是一种常见的水质污染物,主要来源为废水、肥料和污水处理厂等。水质中亚硝酸盐浓度大小是评估水体健康程度的一个重要指标,但传统的亚硝酸盐浓度检测方法操作复杂且容易受到检测环境的干扰,无法直观和准确的反映出水质健康程度。为了探究一种新的方式来评估水体的健康程度,使用IPSO-BPNN模型对亚硝酸盐透射光谱数据进行浓度预测。首先选择10种浓度的亚硝酸盐标准溶液(0.02、0.04、0.06、0.08、0.10、0.12、0.14、0.16、0.18和0.20 mg·L^(-1),使用OCEAN-HDX-XR微型光谱仪在相同的时间间隔下对十个浓度的亚硝酸盐溶液进行扫描,并通过白板校正得到光谱数据的光谱透射率值。使用最大最小归一化、均值中心化两种预处理方法将光谱数据进行维度和中心点的统一,使得不同样本之间的光谱数据具有可比性和可解释性。由于原始光谱数据维度较高,采用核主成分分析进行数据降维,选择代表原始数据97.94%信息的6个主成分进行IPSO-BPNN模型的训练。在预测亚硝酸盐浓度时,对原始粒子群优化算法进行了改进,引入了自适应学习因子和惯性权重更新公式以及粒子种群多样性引导策略,并在BP神经网络的基础上引入了学习率自适应公式,提高了算法的性能。通过比较不同粒子数进行迭代的函数适应度值变化曲线,选择使用100个粒子进行30次迭代来寻找最优权重和偏置组合。结果显示,IPSO-BPNN预测模型的决定系数为0.984360,均方根误差为0.006920,平均绝对误差为0.004103,与当前预测性能较好的随机森林模型、线性回归模型、BP-ANN模型、PSO-BPNN模型和PSO-SVR模型相比,该模型的拟合效果更好,精确度更高。基于以上结果,提出了一种基于IPSO-BPNN模型的高光谱水质亚硝酸盐浓度预测方法,为水体健康程度的评估提供了新的思路。

结合光谱降维的IPSO-SVR水体总磷浓度预测模型

[目的]选择最优模型对水体中总磷浓度进行预测,为准确、实时、高效检测水资源状况提供支持。[方法]以2021年在长江中下游武汉—安徽地区采集的水质样本作为研究对象,首先,对采集到的长江光谱数据进行最大最小归一化和均值中心化两种预处理操作以便统一数据的范围和均值点,并使用核主成分分析(KPCA)技术对预处理后的光谱数据进行降维操作。选取方差解释率为99.6%下的6个特征向量进行后续预测模型的训练,接着在原有粒子群算法的基础上引入自适应惯性权重更新公式和遗传—模拟退火变异思想,提高算法的寻优能力。使用改进的粒子群优化算法对支持向量回归模型中的超参数组合进行寻优,对支持向量回归模型使用输出的结果进行预测模型的训练,最后使用测试集数据进行总磷浓度的预测。[结果]提出了一种结合光谱降维的改进粒子群优化算法(IPSO)结合支持向量回归(SVR)的水体总磷含量预测模型。通过和当前预测性能较好的几种机器学习模型进行精度的比较发现,该试验模型对长江水体总磷浓度进行预测时决定系数(R^(2))为0.973920,均方根差(RMSE)为0.003012,平均绝对误差(MAE)为0.002105。[结论]使用光谱数据结合降维技术、粒子群优化算法和机器学习模型的算法融合模型检测水体总磷浓度可行性强,精确度高,且拟合效果良好。

基于AMGA与IPSO算法的42Cr Mo超声滚挤压工艺参数优化

为确定超声滚挤压轴承套圈工艺参数的最优解集,以42CrMo钢为研究对象,表面粗糙度、残余压应力和硬度为表层性能评价指标,设计正交试验。基于试验数据,采用多元回归法建立评价指标的数学预测模型,进行方差分析。对超声滚挤压工艺参数分别采用存档微遗传算法(AMGA)和改进粒子群(IPSO)算法进行多目标优化,对优化后的Pareto前沿图与计算效率进行对比分析,结果表明:在Pareto前沿图中, AMGA最优迭代2000次优于IPSO算法最优迭代3600次;得到超声滚挤压工艺参数最优解集:转速[250, 355]r·min^(-1)、进给速度[13, 24]mm·min^(-1)、振幅[16, 22]μm、静压力[488, 650]N;表层性能评价指标最优解集:表面粗糙度[0.398, 0.501]μm、残余压应力[823, 986]MPa、硬度[713, 742]HV。通过试验验证了算法优化的可靠性和精确性。

基于IPSO-SVR的反导装备体系效能评估方法研究

鉴于反导装备体系运行机理复杂、结构不清难以选择合适的效能评估模型等问题,采用“数据驱动+深度学习”的方法对反导装备体系效能评估展开研究。结合反导装备体系作战过程,从探测跟踪、指挥控制、火力拦截和综合保障4个方面构建了反导装备体系效能评估指标;针对PSO算法容易陷入局部极值、早熟收敛等问题,提出改进型粒子群优化算法,对SVR参数进行优化,建立了IPSO-SVR效能评估模型;在大量反导装备体系实验数据抽取、处理、分析的基础上,对IPSO-SVR模型进行训练和学习,以此获得对反导装备体系效能的非线性拟合。实验结果表明:所提效能评估方法期望输出和实际输出之间误差非常小,拟合精准度高,具有较高的可靠性和可行性。

基于VMD-LSTM-IPSO-GRU的电力负荷预测

为了挖掘电力负荷数据中的潜藏信息,提高短期负荷预测的精度,针对电力负荷强非线性、非平稳性等特点,提出一种基于变分模态分解(variational mode decomposition,VMD)、长短时记忆神经网络(long-term and short-term memory network,LSTM)、改进的粒子群算法(improve particle swarm optimization,IPSO)和门控循环单元(gated recurrent unit neural network,GRU)的混合预测模型。首先,使用相关性分析确定输入因素,再将负荷数据运用VMD算法结合样本熵分解为一系列本征模态分量(intrinsic mode fuction,IMF)和残差量,进而合理地确定分解层数和惩罚因子;其次,根据过零率将这些量划分为低频和高频,低频分量使用LSTM网络,高频分量利用IPSO-GRU网络分别进行预测;最后,将预测结果重构得到电力负荷的最终结果。仿真结果表明:相对于其他模型,所提混合模型可有效的提取模态特征,具有更高的预测精度。

Multi-Strategy Assisted Multi-Objective Whale Optimization Algorithm for Feature Selection

In classification problems,datasets often contain a large amount of features,but not all of them are relevant for accurate classification.In fact,irrelevant features may even hinder classification accuracy.Feature selection aims to alleviate this issue by minimizing the number of features in the subset while simultaneously minimizing the classification error rate.Single-objective optimization approaches employ an evaluation function designed as an aggregate function with a parameter,but the results obtained depend on the value of the parameter.To eliminate this parameter’s influence,the problem can be reformulated as a multi-objective optimization problem.The Whale Optimization Algorithm(WOA)is widely used in optimization problems because of its simplicity and easy implementation.In this paper,we propose a multi-strategy assisted multi-objective WOA(MSMOWOA)to address feature selection.To enhance the algorithm’s search ability,we integrate multiple strategies such as Levy flight,Grey Wolf Optimizer,and adaptive mutation into it.Additionally,we utilize an external repository to store non-dominant solution sets and grid technology is used to maintain diversity.Results on fourteen University of California Irvine(UCI)datasets demonstrate that our proposed method effectively removes redundant features and improves classification performance.The source code can be accessed from the website:https://github.com/zc0315/MSMOWOA.

MCWOA Scheduler:Modified Chimp-Whale Optimization Algorithm for Task Scheduling in Cloud Computing

Cloud computing provides a diverse and adaptable resource pool over the internet,allowing users to tap into various resources as needed.It has been seen as a robust solution to relevant challenges.A significant delay can hamper the performance of IoT-enabled cloud platforms.However,efficient task scheduling can lower the cloud infrastructure’s energy consumption,thus maximizing the service provider’s revenue by decreasing user job processing times.The proposed Modified Chimp-Whale Optimization Algorithm called Modified Chimp-Whale Optimization Algorithm(MCWOA),combines elements of the Chimp Optimization Algorithm(COA)and the Whale Optimization Algorithm(WOA).To enhance MCWOA’s identification precision,the Sobol sequence is used in the population initialization phase,ensuring an even distribution of the population across the solution space.Moreover,the traditional MCWOA’s local search capabilities are augmented by incorporating the whale optimization algorithm’s bubble-net hunting and random search mechanisms into MCWOA’s position-updating process.This study demonstrates the effectiveness of the proposed approach using a two-story rigid frame and a simply supported beam model.Simulated outcomes reveal that the new method outperforms the original MCWOA,especially in multi-damage detection scenarios.MCWOA excels in avoiding false positives and enhancing computational speed,making it an optimal choice for structural damage detection.The efficiency of the proposed MCWOA is assessed against metrics such as energy usage,computational expense,task duration,and delay.The simulated data indicates that the new MCWOA outpaces other methods across all metrics.The study also references the Whale Optimization Algorithm(WOA),Chimp Algorithm(CA),Ant Lion Optimizer(ALO),Genetic Algorithm(GA)and Grey Wolf Optimizer(GWO).

Accelerated design of high-performance Mg-Mn-based magnesium alloys based on novel bayesian optimization

Magnesium(Mg),being the lightest structural metal,holds immense potential for widespread applications in various fields.The development of high-performance and cost-effective Mg alloys is crucial to further advancing their commercial utilization.With the rapid advancement of machine learning(ML)technology in recent years,the“data-driven''approach for alloy design has provided new perspectives and opportunities for enhancing the performance of Mg alloys.This paper introduces a novel regression-based Bayesian optimization active learning model(RBOALM)for the development of high-performance Mg-Mn-based wrought alloys.RBOALM employs active learning to automatically explore optimal alloy compositions and process parameters within predefined ranges,facilitating the discovery of superior alloy combinations.This model further integrates pre-established regression models as surrogate functions in Bayesian optimization,significantly enhancing the precision of the design process.Leveraging RBOALM,several new high-performance alloys have been successfully designed and prepared.Notably,after mechanical property testing of the designed alloys,the Mg-2.1Zn-2.0Mn-0.5Sn-0.1Ca alloy demonstrates exceptional mechanical properties,including an ultimate tensile strength of 406 MPa,a yield strength of 287 MPa,and a 23%fracture elongation.Furthermore,the Mg-2.7Mn-0.5Al-0.1Ca alloy exhibits an ultimate tensile strength of 211 MPa,coupled with a remarkable 41%fracture elongation.

A Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller Model Combined with an Improved Particle Swarm Optimization Method for Fall Detection

In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible to unsafe events(such as falls)that can have disastrous consequences.However,automatically detecting falls fromvideo data is challenging,and automatic fall detection methods usually require large volumes of training data,which can be difficult to acquire.To address this problem,video kinematic data can be used as training data,thereby avoiding the requirement of creating a large fall data set.This study integrated an improved particle swarm optimization method into a double interactively recurrent fuzzy cerebellar model articulation controller model to develop a costeffective and accurate fall detection system.First,it obtained an optical flow(OF)trajectory diagram from image sequences by using the OF method,and it solved problems related to focal length and object offset by employing the discrete Fourier transform(DFT)algorithm.Second,this study developed the D-IRFCMAC model,which combines spatial and temporal(recurrent)information.Third,it designed an IPSO(Improved Particle Swarm Optimization)algorithm that effectively strengthens the exploratory capabilities of the proposed D-IRFCMAC(Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller)model in the global search space.The proposed approach outperforms existing state-of-the-art methods in terms of action recognition accuracy on the UR-Fall,UP-Fall,and PRECIS HAR data sets.The UCF11 dataset had an average accuracy of 93.13%,whereas the UCF101 dataset had an average accuracy of 92.19%.The UR-Fall dataset had an accuracy of 100%,the UP-Fall dataset had an accuracy of 99.25%,and the PRECIS HAR dataset had an accuracy of 99.07%.

Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM

Marine umbilical is one of the key equipment for subsea oil and gas exploitation,which is usually integrated by a great number of different functional components with multi-layers.The layout of these components directly affects manufacturing,operation and storage performances of the umbilical.For the multi-layer cross-sectional layout design of the umbilical,a quantifiable multi-objective optimization model is established according to the operation and storage requirements.Considering the manufacturing factors,the multi-layering strategy based on contact point identification is introduced for a great number of functional components.Then,the GA-GLM global optimization algorithm is proposed combining the genetic algorithm and the generalized multiplier method,and the selection operator of the genetic algorithm is improved based on the steepest descent method.Genetic algorithm is used to find the optimal solution in the global space,which can converge from any initial layout to the feasible layout solution.The feasible layout solution is taken as the initial value of the generalized multiplier method for fast and accurate solution.Finally,taking umbilicals with a great number of components as examples,the results show that the cross-sectional performance of the umbilical obtained by optimization algorithm is better and the solution efficiency is higher.Meanwhile,the multi-layering strategy is effective and feasible.The design method proposed in this paper can quickly obtain the optimal multi-layer cross-sectional layout,which replaces the manual design,and provides useful reference and guidance for the umbilical industry.

Design and optimization of a greener sinomenine hydrochloride preparation process considering variations among different batches of the medicinal herb

The current methods used to industrially produce sinomenine hydrochloride involve several issues,including high solvent toxicity,long process flow,and low atomic utilization efficiency,and the greenness scores of the processes are below 65 points.To solve these problems,a new process using anisole as the extractant was proposed.Anisole exhibits high selectivity for sinomenine and can be connected to the subsequent water-washing steps.After alkalization of the medicinal material,heating extraction,water washing,and acidification crystallization were carried out.The process was modeled and optimized.The design space was constructed.The recommended operating ranges for the critical process parameters were 3.0–4.0 h for alkalization time,60.0–80.0℃ for extraction temperature,2.0–3.0(volume ratio)for washing solution amount,and 2.0–2.4 mol·L^(-1) for hydrochloric acid concentration.The new process shows good robustness because different batches of medicinal materials did not greatly impact crystal purity or sinomenine transfer rate.The sinomenine transfer rate was about 20%higher than that of industrial processes.The greenness score increased to 90 points since the novel process proposed in this research solves the problems of long process flow,high solvent toxicity,and poor atomic economy,better aligning with the concept of green chemistry.

Frilled Lizard Optimization: A Novel Bio-Inspired Optimizer for Solving Engineering Applications

This research presents a novel nature-inspired metaheuristic algorithm called Frilled Lizard Optimization(FLO),which emulates the unique hunting behavior of frilled lizards in their natural habitat.FLO draws its inspiration from the sit-and-wait hunting strategy of these lizards.The algorithm’s core principles are meticulously detailed and mathematically structured into two distinct phases:(i)an exploration phase,which mimics the lizard’s sudden attack on its prey,and(ii)an exploitation phase,which simulates the lizard’s retreat to the treetops after feeding.To assess FLO’s efficacy in addressing optimization problems,its performance is rigorously tested on fifty-two standard benchmark functions.These functions include unimodal,high-dimensional multimodal,and fixed-dimensional multimodal functions,as well as the challenging CEC 2017 test suite.FLO’s performance is benchmarked against twelve established metaheuristic algorithms,providing a comprehensive comparative analysis.The simulation results demonstrate that FLO excels in both exploration and exploitation,effectively balancing these two critical aspects throughout the search process.This balanced approach enables FLO to outperform several competing algorithms in numerous test cases.Additionally,FLO is applied to twenty-two constrained optimization problems from the CEC 2011 test suite and four complex engineering design problems,further validating its robustness and versatility in solving real-world optimization challenges.Overall,the study highlights FLO’s superior performance and its potential as a powerful tool for tackling a wide range of optimization problems.

集成NSGA-Ⅱ与IPSO算法的仓储货位分配多目标优化策略

优化仓储货位分配直接影响仓库运作效率和物流成本,为此提出了一种结合非支配排序遗传算法Ⅱ(NSGA-Ⅱ)与改进粒子群优化算法(IPSO)的多目标优化策略。通过深入分析货位分配的复杂性,构建了一个综合考量货物存取效率与存储空间利用率的多目标优化模型。对传统粒子群优化算法(PSO)进行改进,通过动态调整粒子的速度更新策略,显著提升了算法的全局搜索效率。将改进后的PSO算法与NSGA-Ⅱ算法集成,有效增强了解决方案的多样性和质量。经过对比分析,所提出策略在提高仓储效率和空间利用率方面有显著优势。

基于遥感多参数和IPSO-WNN的冬小麦单产估测

冬小麦是我国的主要粮食作物之一。为进一步准确地估测冬小麦产量,以陕西省关中平原为研究区域,选取冬小麦主要生育期与水分胁迫和光合作用等密切相关的条件植被温度指数(VTCI)、叶面积指数(LAI)和光合有效辐射吸收比率(FPAR)作为遥感特征参数,采用改进的粒子群算法优化小波神经网络(IPSO-WNN)以改善梯度下降方法易陷入局部最优的缺陷,并构建冬小麦产量估测模型。结果表明,IPSO-WNN模型的决定系数R2为0.66,平均绝对百分比误差(MAPE)为7.59%,相比于BPNN(R2=0.46,MAPE为11.80%)与WNN(R2=0.52,MAPE为9.80%),IPSO-WNN能够进一步提高模型的精度、增强模型的鲁棒性。采用灵敏度分析的方法探究对冬小麦产量影响较大的输入参数,结果发现,抽穗-灌浆期的FPAR对冬小麦产量影响最大,其次拔节期的VTCI、抽穗-灌浆期和乳熟期的LAI以及返青期和拔节期的FPAR对冬小麦产量的影响较大。通过IPSO-WNN输出获取冬小麦综合监测指数I,构建I与统计单产之间的估产模型以估测关中平原冬小麦单产,结果显示,估测单产与统计单产之间的R2为0.63,均方根误差(RMSE)为505.50 kg/hm^(2),相比于前人的研究较好地解决了估产模型存在的“低产高估”的问题,因此,本文基于IPSO-WNN构建的估产模型能够较准确地估测关中平原冬小麦产量。

Towards the performance limit of catenary meta-optics via field-driven optimization

Catenary optics enables metasurfaces with higher efficiency and wider bandwidth,and is highly anticipated in the imaging system,super-resolution lithography,and broadband absorbers.However,the periodic boundary approximation without considering aperiodic electromagnetic crosstalk poses challenges for catenary optical devices to reach their performance limits.Here,perfect control of both local geometric and propagation phases is realized through field-driven optimization,in which the field distribution is calculated under real boundary conditions.Different from other optimization methods requiring a mass of iterations,the proposed design method requires less than ten iterations to get the efficiency close to the optimal value.Based on the library of shape-optimized catenary structures,centimeter-scale devices can be designed in ten seconds,with the performance improved by ~15%.Furthermore,this method has the ability to extend catenary-like continuous structures to arbitrary polarization,including both linear and elliptical polarizations,which is difficult to achieve with traditional design methods.It provides a way for the development of catenary optics and serves as a potent tool for constructing high-performance optical devices.

A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHM FOR CONSTRUCTING THE PARETO FRONT OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.