Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches

In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.

Reliable Space Pursuing for Reliability-based Design Optimization with Black-box Performance Functions

Reliability-based design optimization （RBDO） is intrinsically a double-loop procedure since it involves an overall optimization and an iterative reliability assessment at each search point. Due to the double-loop procedure, the computational expense of RBDO is normally very high. Current RBDO research focuses on problems with explicitly expressed performance functions and readily available gradients. This paper addresses a more challenging type of RBDO problem in which the performance functions are computation intensive. These computation intensive functions are often considered as a ＂black-box＂ and their gradients are not available or not reliable. On the basis of the reliable design space （RDS） concept proposed earlier by the authors, this paper proposes a Reliable Space Pursuing （RSP） approach, in which RDS is first identified and then gradually refined while optimization is performed. It fundamentally avoids the nested optimization and probabilistic assessment loop. Three well known RBDO problems from the literature are used for testing and demonstrating the effectiveness of the proposed RSP method.

Rescue vehicle allocation problem based on optimal reliable path under uncertainty

Consideration of the travel time variation for rescue vehicles is significant in the field of emergency management research.Because of uncertain factors,such as the weather or OD(origin-destination)variations caused by traffic accidents,travel time is a random variable.In emergency situations,it is particularly necessary to determine the optimal reliable route of rescue vehicles from the perspective of uncertainty.This paper first proposes an optimal reliable path finding(ORPF)model for rescue vehicles,which considers the uncertainties of travel time,and link correlations.On this basis,it investigates how to optimize rescue vehicle allocation to minimize rescue time,taking into account travel time reliability under uncertain conditions.Because of the non-additive property of the objective function,this paper adopts a heuristic algorithm based on the K-shortest path algorithm,and inequality techniques to tackle the proposed modified integer programming model.Finally,the numerical experiments are presented to verify the accuracy and effectiveness of the proposed model and algorithm.The results show that ignoring travel time reliability may lead to an over-or under-estimation of the effective travel time of rescue vehicles on a particular path,and thereby an incorrect allocation scheme.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

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.

Monarch Butterfly Optimization for Reliable Scheduling in Cloud

Enterprises have extensively taken on cloud computing environment since it provides on-demand virtualized cloud application resources.The scheduling of the cloud tasks is a well-recognized NP-hard problem.The Task scheduling problem is convoluted while convincing different objectives,which are dispute in nature.In this paper,Multi-Objective Improved Monarch Butterfly Optimization(MOIMBO)algorithm is applied to solve multi-objective task scheduling problems in the cloud in preparation for Pareto optimal solutions.Three different dispute objectives,such as makespan,reliability,and resource utilization,are deliberated for task scheduling problems.The Epsilonfuzzy dominance sort method is utilized in the multi-objective domain to elect the foremost solutions from the Pareto optimal solution set.MOIMBO,together with the Self Adaptive and Greedy Strategies,have been incorporated to enrich the performance of the proposed algorithm.The capability and effectiveness of the proposed algorithm are measured with NSGA-II and MOPSO algorithms.The simulation results prompt that the proposed MOIMBO algorithm extensively diminishes the makespan,maximize the reliability,and guarantees the appropriate resource utilization when associating it with identified existing algorithms.

AWK-TIS:An Improved AK-IS Based on Whale Optimization Algorithm and Truncated Importance Sampling for Reliability Analysis

In this work,an improved active kriging method based on the AK-IS and truncated importance sampling(TIS)method is proposed to efficiently evaluate structural reliability.The novel method called AWK-TIS is inspired by AK-IS and RBF-GA previously published in the literature.The innovation of the AWK-TIS is that TIS is adopted to lessen the sample pool size significantly,and the whale optimization algorithm(WOA)is employed to acquire the optimal Krigingmodel and themost probable point(MPP).To verify the performance of theAWK-TISmethod for structural reliability,four numerical cases which are utilized as benchmarks in literature and one real engineering problem about a jet van manipulate mechanism are tested.The results indicate the accuracy and efficiency of the proposed method.

Artificial Intelligence Based Reliable Load Balancing Framework in Software-Defined Networks

Software-defined networking(SDN)plays a critical role in transforming networking from traditional to intelligent networking.The increasing demand for services from cloud users has increased the load on the network.An efficient system must handle various loads and increasing needs representing the relationships and dependence of businesses on automated measurement systems and guarantee the quality of service(QoS).Themultiple paths from source to destination give a scope to select an optimal path by maintaining an equilibrium of load using some best algorithms.Moreover,the requests need to be transferred to reliable network elements.To address SDN’s current and future challenges,there is a need to know how artificial intelligence(AI)optimization techniques can efficiently balance the load.This study aims to explore two artificial intelligence optimization techniques,namely Ant Colony Optimization(ACO)and Particle Swarm Optimization(PSO),used for load balancing in SDN.Further,we identified that a modification to the existing optimization technique could improve the performance by using a reliable link and node to form the path to reach the target node and improve load balancing.Finally,we propose a conceptual framework for SDN futurology by evaluating node and link reliability,which can balance the load efficiently and improve QoS in SDN.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

计及IGBT结温约束的光伏高渗透配电网无功电压优化控制策略

光伏电源参与配电网无功电压调节是提升光伏高渗透配电网运行经济性和可靠性的有效手段,但光伏电源提供无功支撑会使得光伏电源IGBT最大结温升高、结温波动加剧,进而影响光伏电源和配电网的安全稳定运行。为此,该文提出一种计及IGBT结温约束的光伏高渗透配电网无功电压优化控制策略。首先,利用CatBoost算法计算IGBT结温,提高了IGBT结温计算效率,避免了传统结温算法对IGBT热模型参数的依赖;然后,建立考虑IGBT结温约束的有源配电网多目标无功优化模型,利用二分法求解IGBT结温约束下的光伏电源最大输出功率,实现了IGBT结温约束向二阶锥约束的转换;最后,利用IEEE33节点典型配电系统验证了所提策略在光伏高渗透配电网无功电压优化、光伏电源运行可靠性提升方面的有效性,并提出了综合考虑配电网网损、光伏电源可靠性的光伏电源IGBT结温限值整定原则。

Wind Turbine Optimal Preventive Maintenance Scheduling Using Fibonacci Search and Genetic Algorithm

Maintenance scheduling is essential and crucial for wind turbines (WTs) to avoid breakdowns andreduce maintenance costs. Many maintenance models have been developed for WTs’ maintenance planning, suchas corrective, preventive, and predictive maintenance. Due to communities’ dependence on WTs for electricityneeds, preventive maintenance is the most widely used method for maintenance scheduling. The downside tousing this approach is that preventive maintenance (PM) is often done in fixed intervals, which is inefficient. In thispaper, a more detailed maintenance plan for a 2 MW WT has been developed. The paper’s focus is to minimize aWT’s maintenance cost based on a WT’s reliability model. This study uses a two-layer optimization framework:Fibonacci and genetic algorithm. The first layer in the optimization method (Fibonacci) finds the optimal numberof PM required for the system. In the second layer, the optimal times for preventative maintenance and optimalcomponents to maintain have been determined to minimize maintenance costs. The Monte Carlo simulationestimates WT component failure times using their lifetime distributions from the reliability model. The estimatedfailure times are then used to determine the overall corrective and PM costs during the system’s lifetime. Finally,an optimal PM schedule is proposed for a 2 MW WT using the presented method. The method used in this papercan be expanded to a wind farm or similar engineering systems.

考虑光伏电源可靠性的新能源配电网数据驱动无功电压优化控制

充分挖掘分布式光伏电源的无功支撑能力,有助于解决光伏高比例接入带来的配电网电压波动、电压越限以及新能源消纳等问题,但光伏电源无功输出会造成其功率器件结温越限或剧烈波动,严重威胁到光伏电源的可靠运行。为此,提出考虑光伏电源可靠性的新能源配电网数据驱动无功电压优化控制策略。首先,提出一种基于数据驱动的光伏电源可靠性评估方法,该方法采用XGBoost机器学习模型计算IGBT结温,提高了IGBT结温计算效率,避免了评估精度对IGBT参数的依赖;进而建立考虑光伏电源可靠性的配电网无功电压优化模型,将IGBT结温均值和结温波动引入模型优化目标;然后,将该模型进行马尔可夫决策过程转化,并基于深度确定性策略梯度强化学习算法完成智能体训练;最后,通过IEEE33节点系统验证所提策略在无功电压快速优化和光伏电源可靠性提升方面的优势。

汽车结构可靠性分析与优化设计研究进展

为研究汽车结构的可靠性,对机械结构分析和设计中的不确定性进行总结,从结构参数不确定性、材料性能参数不确定性和载荷不确定性3方面分析了汽车结构设计变量及其参数的不确定性;对概率可靠性分析和非概率可靠性分析方法的研究进展进行了梳理和综述;列举了可靠性分析方法在汽车结构中的应用;对可靠性的数学模型与算法进行梳理,重点研究了可靠性优化设计在汽车轻量化及耐撞性等方面的应用,并指出了汽车结构可靠性分析与优化设计中的发展趋势。

基于并行拓扑优化的假体股骨柄设计

与股骨接触的假体柄是人工髋关节的主要部件,在全髋置换手术中起着重要作用。采用变密度固体各向同性材料惩罚(Solid Isotropic Material with Penalization,SIMP)拓扑优化方法和多尺度的并行拓扑优化方法,分别得到A型和B型两种股骨柄结构,并将股骨柄结构柔度变化幅度作为对比指标,比较了两种股骨柄对载荷方向变化的敏感度。利用有限元方法对A型股骨柄和B型股骨柄进行多工况下所对应股骨的应力分析。研究结果表明,在3种工况下,A型股骨柄和B型股骨柄对股骨的平均应力分别为14.80、22.55、16.94 MPa和10.89、20.92、16.50 MPa。对B型股骨柄进行压力加载试验,试验结果表明,在内侧测点,试验的应变值与仿真值的平均误差为-1682με,平均相对误差为20.3%;在外侧测点,试验的应变值与仿真值的平均误差为1281με,平均相对误差为19.5%。该方法为股骨假体柄结构的可靠性设计提供了有效参考。

基于响应面法的血管支架拉伸、扭转性能优化及考虑加工精度影响的强度可靠性分析

为分析设计变量对血管支架拉伸性能、扭转性能的精准影响,进行血管支架拉伸性能、扭转性能优化,考虑加工精度的影响,进行血管支架的强度可靠性分析。方法:取血管支架支撑筋宽度、支撑筋长度、连接筋宽度和支架厚度为设计变量,应用斯皮尔曼等级相关系数法分析设计变量对血管支架拉伸刚度、扭转刚度等响应变量的精准影响;采用响应面方法进行以拉伸刚度、扭转刚度为目标进行血管支架的优化设计;对优化后的血管支架,考虑加工精度所致设计变量的随机性,利用六西格玛工具分析应力的概率分布。结果:对于血管支架拉伸刚度,支撑筋宽度和连接筋宽度灵敏度系数大,且均为正值;对于血管支架扭转刚度,支撑筋宽度灵敏度系数较大,且为负值;优化后的血管支架相比原始血管支架,拉伸刚度降低了11.5%;扭转刚度减小了50.6%;考虑加工精度所致设计变量的随机性进行可靠性分析,在可靠度为99.8%时,虽然血管支架的拉伸刚度和扭转刚度最大值高于优化值,但血管支架的最大应力满足强度条件。结论:支撑筋宽度对血管支架的拉伸性能影响最大,连接筋宽度次之,支撑筋长度和支架厚度影响较小;支撑筋宽度对血管支架的扭转性能影响最大,连接筋宽度、支撑筋长度和支架厚度影响较小;随机因素加工精度对血管支架优化目标有一定的影响,但优化结果仍是可靠的。本文提供了一种血管支架优化的思路:首先是进行基于目标的优化,然后考虑随机因素的影响进行基于概率的强度可靠性分析。

基于IAOA-SVM模型结构时变可靠性研究

目的为有效解决使用传统代理模型进行结构时变可靠性研究中存在流程复杂、计算效率低等问题。方法提出以改进算术优化算法(Improved Arithmetic Optimization Algorithm,IAOA)优化支持向量机模型(Support Vector Machine,SVM)进行时变可靠性研究的方法,结合IAOA-SVM模型和极值理论,以某塔式起重机回转支承为研究对象,对其进行动态确定性分析获取样本数据,建立IAOA-SVM可靠性模型,采用蒙特卡洛法求解得到其可靠度结果,并与EKM和ERSM算法对比分析其仿真精度和效率。结果当回转支承径向变形许用值为0.278×10^(-3)m时,采用蒙特卡洛法求解得到其可靠度为99.68%,IAOA-SVM模型相比EKM和ERSM方法仿真效率有所提升,建模精度分别提高了10.42%和9.23%。结论IAOA-SVM方法在建模和仿真精度与效率方面具有较明显的优势,IAOA-SVM方法为求解机构时变可靠度难题提供了一种新的解决思路。

基于柔顺性的血管支架优化设计及强度可靠性分析

目的建立血管支架的参数化模型,进行血管支架柔顺性能的优化设计。基于优化结果考虑加工精度引起的设计尺寸的不确定性,进行血管支架强度的概率计算以验证优化结果的可靠性。方法探寻结构特征,建立血管支架参数化模型。取弯曲刚度作为优化目标,血管支架支撑筋宽度、支撑筋长度、连接筋宽度和支架厚度为设计变量,采用响应面法进行血管支架优化设计,选取应力局部灵敏度较低的候选设计点作为最优设计点。基于优化血管支架,取受加工精度影响的设计尺寸作为随机变量,利用六西格玛工具进行血管支架强度的概率计算。结果建立了参数化的血管支架模型,优化后的血管支架弯曲刚度相比原始血管支架减小32.91%,累积分布概率为99.85%时,血管支架最大应力满足强度条件。结论连接筋宽度对血管支架的柔顺性影响最大,支架厚度次之,支撑筋长度和宽度影响较小;加工精度影响下优化血管支架强度可靠。血管支架在工程实际中会受到一些不确定性因素的影响,在进行确定性优化设计之后,要考虑不确定性因素引起的设计变量的不确定性进行强度可靠性分析验证。

考虑多失效模式的桩锚结构鲁棒性设计及经济性优化

目的 研究岩土力学参数的不确定性对桩锚支护体系的整体影响,探究经济性和鲁棒性共同作用的优化设计。方法 选取黄土地区工程案例,考虑支护桩隆起破坏、支护桩倾覆破坏、整体稳定性破坏三类破坏形式,使用蒙特卡洛及点估计法嵌套的方式求出不同设计组合下的失效概率及标准差;同时考虑优化设计的经济性,筛选出桩锚支护结构体系的鲁棒性优化设计方案。结果 随着桩长增加,主控模式由隆起破坏向整体稳定性改变,不同的几何参数对结构鲁棒性影响不同,优化后可以获得同时满足经济性、鲁棒性及可靠度要求的最佳设计方案。结论 在桩锚结构设计中考虑经济性优化及多失效模式的鲁棒性设计是必要的。

汽车前舱冷却流场可靠性优化模型设计与仿真

针对汽车前舱冷却系统设计的复杂性和设计变量的不确定性,将Chebyshev不确定分析方法引入前舱冷却流场优化设计流程,建立适用于汽车前舱冷却流场的区间可靠性优化设计模型。以某轿车前舱冷却系统为例,引入Chebyshev函数用于结构优化设计。选取冷凝器和散热器的平均流速和气流流量为目标阈值,使用k-ε湍流模型进行有限元分析,结合Chebyshev可靠性分析迭代,对前舱冷却模块进行结构优化,提升前舱冷却流场性能。试验结果表明,通过增大前保吸能泡沫截面和优化风扇扇叶与支架间的间隙可在一定程度上改进前舱冷却流场性能。

生存进化阶段性搜索微粒群算法及其可靠性冗余分配优化应用

为高效解决含有异质冗余的多态系统(MSS)可靠性优化问题,并弥补微粒群优化(PSO)算法易早熟收敛的不足,从作用力方式和种群拓扑结构两方面对算法进行改进。改进PSO算法中单一的作用力方式,设置前后两个搜索阶段,对应两个搜索阶段分别构造平衡引斥力方式和双层引力(个体和全局最优解引力、中间适应度微粒引力)方式,提出阶段性搜索微粒群(SPSO)算法;利用生物个体“择友而交”和优胜劣汰的生存体系构建生存进化(SE)拓扑结构,以结构演化和算法进化并行方式将该拓扑结构融入SPSO算法,提出生存进化阶段性搜索微粒群(SPSO-SE)算法,进一步提升算法的优化性能;利用Benchmark函数对所提算法与PSO的改进算法进行测试对比,结果表明,所提SPSO-SE算法具有更好的寻优能力。采用SPSO-SE算法对串-并联和桥式结构的多态系统的可靠性冗余分配问题进行优化,得到的系统结构费用更低、可靠度更高。